## Past Events

https://math.columbian.gwu.edu/colloquia

**Spring 2017**

**Title:** How a deterministic life gets influenced by a bunch of stochastic shocks

**Speaker:** Speaker: Annie Millet (University Paris 1 Panthéon-Sorbonne)__http://samm.univ-paris1.fr/-An nie-Millet-__

**Date and Time:** Friday, May 5, 1:00–2:00pm

**Place:** Rome 204

**Abstract:** We will present some results on parabolic (heat-type) and hyperbolic (wave-type) nonlinear partial differential equations subject to a random perturbation. Such «noise» models the sum of infinitesimal shocks in the environment. Besides well-posedness, some properties of the solution will be discussed, such as discretization schemes, concentration of the distribution when the intensity of the noise approaches 0, and long time behavior.

**Short bio:** Annie Millet is currently a professor at the University Paris 1 Panthéon-Sorbonne. She graduated from Paris 6 under the supervision of Antoine Brunel and has held positions in the University of Poitiers, the Ohio State University, the University of Angers and in the University of Paris 10-Nanterre. Her research topics are mainly in infinite dimensional stochastic calculus. Besides being on research frontiers, she has also been elected Research Vice-President and head of the Scientific Council of the University at Paris 1 Panthéon-Sorbonne from 2012 to 2016.

**Title:** Delta-matroids and Vassiliev invariants, Opening talk of Knots in Washington XLIV

__http://at.yorku.ca/cgi-bin/ abstract/cbof-01__

**Speaker:** Sergei Lando, Higher School of Economics, Skolkovo Institute of Science and Technology, Russia

**Date and Time:** Friday, April 28, 1:00–2:00pm

**Place:** Rome 351

**Abstract: **Vassiliev (finite type) invariants of knots can be described in terms of weight systems. These are functions on chord diagrams satisfying so-called 4-term relations. There is also a natural way to define 4-term relations for abstract graphs, and graph invariants satisfying these relations produce weight systems: to each chord diagram its intersection graph is associated.

The notion of weight system can be extended from chord diagrams, which are orientable embedded graphs with a single vertex, to embedded graphs with arbitrary number of vertices that can well be nonorientable. These embedded graphs are a tool to describe finite order invariants of links: the vertices of a graph are in one-to-one correspondence with the link components.

We are going to describe two approaches to constructing analogues of intersection graphs for embedded graphs with arbitrary number of vertices. One approach, due to V. Kleptsyn and E. Smirnov, assigns to an embedded graph a Lagrangian subspace in the relative first homology of a 2-dimensional surface associated to this graph. Another approach, due to S. Lando and V. Zhukov, replaces the embedded graph with the corresponding delta-matroid, as suggested by A. Bouchet in 1980's. In both cases, 4-term relations are written out, and Hopf algebras are constructed.

Vyacheslav Zhukov proved recently that the two approaches coincide.

__Special Colloquium/Logic Seminar__

**Title:** *The age of cohesive powers*

**Speaker:** Rumen Dimitrov, Western Illinois University

__http://www.wiu.edu/users/ rdd104/home.htm__

**Date and Time**: Friday, April 28, 10:30–11:30a.m.

**Place:** Rome Hall (801 22^{nd} Street), Room 204

**Abstract:** Fraïssé defined the age of a structure *A* to be the class of all structures isomorphic to the finitely generated substructures of *A*. He then used this term to refer to one structure as being younger than another. In this talk, I will consider the age of the rationals *Q* as a dense linear ordering without endpoints and as a field, and will discuss connections with the earlier notion of the cohesive powers of *Q*. I will also establish different model-theoretic properties of cohesive powers.

**Title:** Dynamics of complex singularities and wavebreaking in 2D hydrodynamics with free surface

**Speaker:** Pavel Lushnikov, University of New Mexico and Landau Institute for Theoretical Physics__http://math.unm.edu/~plushnik/____http://www.itp.ac.ru/en/person s/lushnikov-pavel-mikhailovich/__

**Date and Time:** Friday, April 21, 1:00–2:00pm

**Place:** Rome 204

**Abstract: **We consider 2D hydrodynamics of ideal fluid with free surface. A time-dependent conformal transformation is used which maps a free fluid surface into the real line with fluid domain mapped into the lower complex half-plane. The fluid dynamics is fully characterized by the complex singularities in the upper complex half-plane of the conformal map and the complex velocity. The initially flat surface with the pole in the complex velocity turns over arbitrary small time into the branch cut connecting two square root branch points. Without gravity one of these branch points approaches the fluid surface with the approximate exponential law corresponding to the formation of the fluid jet. The addition of gravity results in wavebreaking in the form of plunging of the jet into the water surface. The use of the additional conformal transformation to resolve the dynamics near branch points allows to analyze wavebreaking in details. The formation of multiple Crapper capillarysolutions is observed during overturning of the wave contributing to the turbulence of surface wave. Another possible way for thewavebreaking is the slow increase of Stokes wave amplitude through nonlinear interactions until the limiting Stokes wave forms with subsequent wavebreaking. For non-limiting Stokes wave the only singularity in the physical sheet of Riemann surface is the square-root branch point located. The corresponding branch cut defines the second sheet of the Riemann surface if one crosses the branch cut. The infinite number of pairs of square root singularities is found corresponding to infinite number of non-physical sheets of Riemann surface. Each pair belongs to its own non-physical sheet of Riemann surface. Increase of the steepness of the Stokes wave means that all these singularities simultaneously approach the real line from different sheets of Riemann surface and merge together forming 2/3 power law singularity of the limitingStokes wave. It is conjectured that non-limiting Stokes wave at the leading order consists of the infinite product of nested square root singularities which form the infinite number of sheets of Riemann surface. The conjecture is also supported by high precision simulations, where a quad (32 digits) and a variable precision (up to 200 digits) were used to reliably recover the structure of square root branch cuts in multiple sheets of Riemann surface

**Joint Colloquium/Applie Math/Analysis talk**

**Title: **Singularity Formation in Nonlinear Derivative Schrödinger Equations

**Speaker: ** Gideon Simpson, Drexel University

**Date and Time: April 19****, 2017**, Wednesday,2:30 pm-3:30pm

**Place:** Rome 771

**Abstract: **Direct numerical simulation of an $L^2$ supercritical variant of the derivative nonlinear Schrödinger equation suggests that there is a finite time singularity. Subsequent exploration with the dynamic rescaling method provided more detail about the blowup and a recent refined asymptotic analysis of the blowup solution gives predictions of the blowup rates. Due to the mixed hyperbolic-dispersive nature of the equation, these methods have limited the proximity to the blowup time. Using a locally adaptive meshing method, we are able to overcome these difficulties.

**Title:** Rotational symmetries of knots

**Speaker:** Swatee Naik, University of Nevada and NSF__http://wolfweb.unr.edu/ homepage/naik/__

**Date and Time:** Friday, April 14, 1:00–2:00pm

**Place:** Rome 204

**Abstract:**Knots are circles embedded in the three dimensional sphere. Periodic knots, such as the overhand or trefoil knot, are invariant under a rotation, and this symmetry can be easily illustrated in a knot diagram drawn in the plane. It so happens that the orbit space is also a three-sphere, in which the image of a periodic knot is called a quotient knot. Many properties of periodic knots are a direct consequence of the branched covering set up that occurs between various three-manifolds that are naturally associated with the periodic knot and the quotient knot, respectively.

In this talk we will begin with definitions and examples, introduce the basics of the theory, and demonstrate how properties of periodic knots can be used to detect knots that are not periodic. Our tools will include knot polynomials, homology of branched covers, and Heegaard-Floer correction terms.

**Short Bio:**Dr. Swatee Naik is a Professor at the University of Nevada, Reno and currently a program director at the National Science Foundation. Her area of research is knot theory and low dimensional topology. The

__draft__of a book on Classical Knot Concordance is work in progress with Charles Livingston, and we welcome feedback. Swatee has served in administrative roles including vice chair and chair of the department and chair of the university faculty senate. At NSF, her main duties are in Topology and Geometric Analysis. She is involved in many other programs, such as Research Experience for Undergraduates, Graduate Research Fellowships, Postdoctoral Fellowships, Enriched Doctoral Training and NSF Research Traineeships.

**Title:**The shortest path poset of Bruhat intervals

**Speaker:**Saul Blanco Rodriguez, Indiana University Bloomington__https://www.soic.indiana.edu/ all-people/profile.html?profile_id=165__

**Date and Time:** Friday, April 7, 1:00-2:00pm

**Place: Rome 204**

**Abstract:** A Coxeter group W is a group generated by reflections; examples are the symmetric group and the hyperoctahedral group. These groups have many interesting combinatorial properties. For instance, one can define a partial order, called the Bruhat order, on the elements of W . If [u,v] is an interval in the Bruhat order, its Bruhat graph, B(u,v) includes the Hasse diagram of the poset [u,v] with edges directed upwards, as well as other edges that I will describe in the talk. While the longest u-v paths in B(u,v) are well-understood (they form a face poset of a regular cell decomposition of a sphere), not much is known about the other u-v paths in B(u,v). In this talk, I will describe what is known of the shortest u-v paths and point out connections to other areas.

**Special Colloquium**

**Title:**Just so stories a la carte around Geometry, Dynamics, and PDEs.

**Speaker:** Dmitri Burago, Penn State University

**Date and Time:** Tuesday, April 4, 2:20-3:20pm

**Place: Rome 351**

**Abstract:** The lecture consists of several mini-talks with just definitions, motivations, some ideas of proofs, and open problems. I will discuss some (hardly all) of the following topics, based on the input from the audience:

**Short Bio: **Dmitri Burago is a Distinguished Professor of Mathematics at Penn State University. His research interests include dynamical systems, algorithmic complexity, Finsler geometry, combinatorial group theory, and partial differential equations. In 1997, Burago was the recipient of an Alfred P. Sloan Research fellowship and, in 1995, he received Penn State's Faculty Scholar Medal for Outstanding Achievements. He has been a member of the St. Petersburg Mathematical Society since 1992. Before joining the Eberly College of Science faculty at Penn State in 1994, Burago was a faculty member at the University of Pennsylvania, a researcher at the St. Petersburg Institute for Informatics and Automation, and an assistant professor in the Department of Mathematics and Mechanics at St. Petersburg State University in Russia. He received doctoral and master's degrees from St. Petersburg State University in 1992 and 1986, respectively.

__Distinguished Speculative First of April Talk__

(with Center for Quantum Computing, Information, Logic, and Topology)

**Title: **Skein modules and Quantum Computing in 3-manifolds

**Speaker:** Uwe Kaiser, Boise State University__http://diamond.boisestate.edu/ ~kaiser/__

**Date and Time:** Friday, March 31, 1:00-2:00pm

**Place: Rome 204**

**Abstract:** The mathematical model of anyons (quasi-particles used in the theory of topological quantum computation) are Unitary Modular Tensor Categories. These are also used to construct topological quantum field theories (TQFT) in dimension 2+1, and in particular define invariants of framed links in 3-manifolds. The invariants can be thought of as quantum amplitudes of anyon world lines in a 3-dimensional spacetime. They also satisfy skein relations, which can be used to define skein modules of framed links in 3-manifolds. Thus quantum amplitudes, which we think of as the measurement results of “quantum computing in a 3-manifold,” are functionals on skein modules. These modules are hard to compute in general, and it is not very well-known how they relate to the geometric topology of 3-manifolds. This, of course, is also true for the quantum invariants. Thus it is interesting to study the relation between these concepts. We describe some results known around these problems and speculate about relations to finite type invariants (Kontsevich integral) and categorifications (link homologies).

**Short Bio:** Dr. Uwe Kaiser received his PhD and habilitation from the University of Siegen in Germany. Additionally he also holds a K12-teaching certificate for Mathematics and Physics in Germany. Currently he is Associate Professor in the Mathematics Department at Boise State University, where he also serves as Associate Chair. His research interests are in Geometric and Algebraic Topology, more recently in Low Dimensional Topology and Quantum Topology. He is also working on several projects and grants related to STEM Education at Boise State University.

__Graduate Student Seminar followed by Friday’s Colloquium__

**Title:** Mapping space methods for skein modules

**Speaker:** Uwe Kaiser, Boise State University__http://diamond.boisestate.edu/~kaiser/ __

**Date and Time:** Thursday, March 30, 5:15-6:30pm

**Place:** Rome 352

**Special Colloquium**

**Title:**Making nonelementary classes more elementary

**Speaker:** William Boney, Harvard University

**Date and Time:** Friday, February 24, 1:30-2:30pm

**Place: MPA 305**

**Abstract: **Classification theory seeks to organize classes of structures (such as algebraically closed fields, random graphs, dense linear orders) along dividing lines that separate classes into well-behaved on one side and chaotic on the other. Since its beginning, classification theory has discovered a plethora of dividing lines for classes axiomatizable in first-order logic and has been applied to solve problems in algebraic geometry, topological dynamics, and more.

However, when looking at examining nonelementary classes (such as rank 1 valued fields or pseudoexponentiation), the lack of compactness is a serious impediment to developing this theory. In the past decade, Grossberg and VanDieren have isolated the notion of tameness. Tameness can be seen as a fragment of compactness that is strong enough to allow the construction of classification theory, but weak enough to be enjoyed by many natural examples. We will discuss the motivation for classification theory in nonelementary classes and some recent results using tameness, focusing on illuminating examples. No logic background will be assumed.

**Special Colloquium**

**Title:**Model theory and Painlevé equations

**Speaker:** James Freitag, University of Illinois at Chicago

**Date and Time:** Thursday, February 23, 1:30-2:30pm

**Place: Phillips 217**

**Abstract: **The Painlevé equations are six families of nonlinear order two differential equations with complex parameters. Around the start of the last century, the equations were isolated for foundational reasons in analysis, but the equations have since arisen naturally in various mathematical contexts. In this talk, we will discuss how to use model theory, a part of mathematical logic, to answer several open questions about Painlevé equations. We will also describe several other applications of model theory and differential algebraic equations to number theory.

**Special Colloquium**

**Title:**q-analogues of factorization problems in the symmetric group

**Speaker:** Joel Lewis, University of Minnesota

**Date and Time:** Friday, February 17, 2:15-3:15pm

**Place: Rome 351**

**Abstract: **Given a nice piece of combinatorics for the symmetric group S_n, there is often a corresponding nice piece of combinatorics for the general linear group GL_n(F_q) over a finite field F_q, called a q-analogue. In this talk, we'll describe an example of this phenomenon coming from the enumeration of factorizations. In S_n, the number of ways to write an n-cycle as a product of n - 1 transpositions is Cayley's number n^(n - 2). In GL_n(F_q), the corresponding problem is to write a Singer cycle as a product of n reflections. We show that the number of such factorizations is (q^n - 1)^(n - 1), and give some extensions. Mysteriously, the second answer is closely related to the first as q approaches 1. Our proofs do not provide an explanation for this relationship; instead, they proceed by exploiting the (complex) representation theory of GL_n(F_q).

**Special Colloquium**

**Title:** Connectivity and structure in matroids

**Speaker:** Stefan van Zwam, Louisiana State University

**Date and Time:** Wednesday, February 15, 11:00am-12:00pm

**Place:** Rome 459

**Abstract: **A general theme in matroid structure theory is that highly connected matroids exhibit more structure than matroids with low-order separations. We will discuss several examples of this phenomenon, as well as an application to the theory of error-correcting codes.

**Special Colloquium**

**Title:** Gaussian measures on infinite dimensional spaces and applications

**Speaker:** Nathan Totz, University of Massachusetts Amherst

**Date and Time:** Monday, February 13, 1:45-2:45pm

**Place:** Rome 459

**Abstract: **We review the classical extension of the Gaussian probability measure from finite dimensional spaces to infinite dimensional spaces. Such Gaussian measures (along with their weighted relatives) play an important role as invariants of flows defined on infinite dimensional spaces. As an application of this idea, we employ Gaussian measures to address the question of the long time existence of a flow corresponding to a family of modified surface quasigeostrophic equations, regarded as a flow on a space of Fourier coefficients. We present recent results (joint with Andrea Nahmod, Natasha Pavlovic, and Gigliola Staffilani) showing that such flows are global in time on a subset of a rough Sobolev space of full measure.

**Special Colloquium**

**Title:** Shapes of polynomial Julia sets

**Speaker:** Kathryn Lindsey, University of Chicago

**Date and Time:** Friday, February 10, 2:15-3:15pm

**Place:** Rome 351

**Abstract: **The filled Julia set of a complex polynomial P is the set of points whose orbit under iteration of the map P is bounded. W. Thurston asked “What are the possible shapes of polynomial Julia sets?” For example, is there a polynomial whose Julia set looks like a cat, or your silhouette, or spells out your name? It turns out the answer to all of these is “yes.” I will characterize the shapes of polynomial Julia sets and present an algorithm for constructing polynomials whose Julia sets have desired shapes.

**Title:** Some almost sharp scattering results for the cubic nonlinear wave equation

**Speaker:** Benjamin Dodson, John Hopkins University

**Date and Time:** Tuesday, January 31, 2017, 3:00-4:00pm

**Place:** Rome 771

**Abstract: **In this talk we will discuss some scattering results for the cubic nonlinear wave equation. We will prove these results for radial data nearly lying in the critical Sobolev space. We prove this using hyperbolic coordinates.

**Short Bio:** Prof. Ben Dodson is an assistant professor of mathematics at John Hopkins University who made a breakthrough in the scattering theory of global solutions in the nonlinear wave-like equations when he was at UC-Riverside for a year after graduating from the University of North Carolina-Chapel Hill in 2009. His did his postdoctoral studies at UC-Berkeley.

**Title:** Examples of Linear Algebra over Division Algebras

**Speaker:** Salahoddin Shokranian, University of Brasilia

**Date and Time:** Friday, January 27, 1:00-2:00pm

**Place:** Rome 204

**Abstract: **Matrices over some division algebras are considered. In the case of finite fields, applications are in coding theory, and in the case of non‐commutative division algebras, Hermitian matrices over quaternions provide examples toward geometry of such matrices and analysis.

**Short Bio: **Salahoddin Shokranian has studied mathematics, graduate level, at the University of California, Berkeley where he did his Ph.D. in automorphic forms. He moved to Brasilia since then, working at the University of Brasilia where he is to be retired. He has been visitor to several research institutes such as the Institute for Advanced Study, Tata Institute of Fundamental Research, Max-Planck Institute for Mathematics and worked at the Universities of Purdue, Toronto and Yale. He has lectured at many universities and research centers. He likes to write books; on linear algebra, number theory, modular forms, cryptography and history of modern number theory. Some of them have already been republished or reprinted

**Fall 2016**

**Jointly with the opening talk of Knots in Washington XLIII**

http://home.gwu.edu/~przytyck/knots/knotsinwashington43.htm

(Introduction by Ali Eskandarian, Dean & Professor of Physics)

**Title:** Knot colorings by quandles and their animations

**Speaker:** Masahico Saito, University of South Florida

**Date and Time:** Friday, December 9, 1:00-2:00pm

**Place:** Phillips B156

**Abstract: **A Fox coloring of a knot diagram is defined by assigning integers modulo n to arcs of the diagram with a certain condition at every crossing. The number of colorings is independent of the choice of a diagram, and is a knot-invariant. This idea leads to a concept of algebraic systems called quandles, that have self-distributive binary operations with few other conditions. Knot colorings are defined with quandles and yield knot invariants. This was further generalized to knot invariants called quandle cocycle invariants, incorporating ideas from quantum knot invariants and group cohomology. After a review of these concepts, we consider quandle cocycle invariants with matrix groups. A continuous family of knot colorings is represented by animations of polygons moving on the sphere. These animations will be presented.

**Short bio: **Masahico Saito received PhD from the University of Texas at Austin in 1990. After a few post-doc positions, he has been at University of South Florida in Tampa since1995. His research interests include knot theory, related algebraic structures, and applications to DNA recombination.

**Title: **Linking, causality and smooth structures on spacetimes

**Speaker:** Vladimir Chernov, Dartmouth College

**Date and Time: December 2**, 2016, Friday, 1:00 -2:00 pm

**Place:** Rome 206

**Abstract: **Globally hyperbolic spacetimes form probably the most important class of spacetimes. Low conjecture and the Legendrian Low conjecture formulated by Natario and Tod say that for many globally hyperbolic spacetimes X two events x,y in X are causally related if and only if the link of spheres S_x, S_y whose points are light rays passing through x and y is non-trivial in the contact manifold N of all light rays in X. This means that the causal relation between events can be reconstructed from the intersection of the light cones with a Cauchy surface of the spacetime.

We prove the Low and the Legendrian Low conjectures and show that similar statements are in fact true in almost all $4$-dimensional globally hyperbolic spacetimes. This also answers the question on Arnold's problem list communicated by Penrose.

We also show that on many 4-manifolds there is a unique smooth structure underlying a globally hyperbolic Lorentz metric, thus global hyperbolicity imposes censorship on the possible smooth structures on a spacetime. For instance, every contractible smooth 4-manifold admitting a globally hyperbolic Lorentz metric is diffeomorphic to the standard R^4. (based on joint work with Stefan Nemirovski).

**Short bio: **Vladimir Chernov is a researcher in contact geometry, Lorentz geometry and in low dimensional topology. His interests also include various aspects of general relativity. He is a professor at the Mathematics Department of Dartmouth College. Before that he had one year positions at University Zurich, MPIM Bonn, and ETH Zurich. He has graduated from University of California Riverside and Uppsala University Sweden. His advisor was Oleg Viro.

**Title: **A new method to distinguish Legendrian knots

**Speaker:** Ivan Dynnikov, Steklov Mathematical Institute, Moscow

**Date and Time: November 18**, 2016, Friday, 1:00 -2:00 pm

**Place:** Rome 206

**Abstract: **The talk is based on a joint ongoing work with Maxim Prasolov. Our main objects of interest are rectangular diagrams of knots, which are a promising tool in knot theory. They appear to be intimately related to Legendrian knots. Whereas the problem of comparing topological types of two knots is solvable both theoretically and---for a small number of crossings---practically, there is no regular method to decide whether two Legendrian knots having the same topological type and the same classical invariants are equivalent or not. A lot is known in particular cases, but there remain open questions already for knots with just six crossings.

Recently we extended the formalism of rectangular diagrams to representation of surfaces. This formalism turned out to work nicely for Giroux' convex surfaces. The latter are very useful for distinguishing contact structures and Legendrian knots. By using our formalism and properties of Giroux's convex surfaces we introduced a combinatorial method to distinguish Legendrian knots, which I will overview after introducing the basic notions of the subject like rectangular diagram or Legendrian knot.

**Short bio:**After obtaining his PhD from Moscow State University in 1996, Ivan Dynnikov has had teaching positions in MSU where he is a professor since 2007. Since 2009, he works as a researcher in Steklov Mathematical Institute. Dynnikov was awarded Moscow Mathematical Society Prize in 2000. He specializes in low dimensional topology, dynamical systems, and mathematical physics.

**Title: **Structural Computable Analysis

**Speaker:** Timothy McNicholl, Iowa State University

**Date and Time: November** 11, 2016, Friday, 1:00 -2:00 pm

**Place:** Rome 206

**Abstract: **** **Computability theory is the mathematical study of the limits and potentialities of discrete computing devices. Computable analysis is the theory of computing with continuous data such as real numbers. Computable structure theory examines which computability-theoretic properties are possessed by the structures in various classes such as partial orders, Abelian groups, and Boolean algebras. Until recently computable structure theory has focused on classes of countable algebraic structures and has neglected the uncountable structures that occur in analysis such as metric spaces and Banach spaces. However, a program has now emerged to use computable analysis to broaden the purview of computable structure theory so as to include analytic structures. The solutions of some of the resulting problems have involved a delicate blend of methods from functional analysis and classical computability theory. We will discuss progress so far on metric spaces and Banach spaces, in particular $\ell^p$ spaces, as well as open problems and new areas for investigation.

**Bio: **Tim McNicholl received his Ph.D. from The George Washington University in 1995. He pursues research projects that involve a mixture of computability theory, complex analysis, and functional analysis and enjoys working with mathematicians from fields other than logic. He has been an Associate Professor of Mathematics at Iowa State University since 2012 where he has directed the redesign of the precalculus curriculum. HIs work on precalculus curricula helped the Iowa State University Mathematics Department win an award for an Exemplary Program or Achievement in a Mathematics Department from the American Mathematical Society in 2015.

**Title: **Fixed point theorem and solutions for the Nonlinear Schrödinger equation.

**Speaker:** Luiz Gustavo Farah, GWU

**Date and Time: **October 7, 2016, Friday, 1:00 -2:00 pm

**Place:** Rome 206

**Abstract: **In 1933, the Austrian physicist Erwing Schrödinger was awarded the Nobel Prize in Physics. Among its notable scientific contributions he formulated one of the fundamental equations of quantum physics, now known as Schrödinger equation. In this talk, we will develop mathematical tools to prove the existence of solutions for this equation in a special case. Our exposition will be self contained and all of the mathematics needed (most of it well-known) will be introduced en route.

**Bio: **Luiz Gustavo Farah has been a professor of mathematics at the Federal University of Minas Gerais - UFMG (Brazil) since 2010 and is currently a visiting researcher scholar at the George Washington University. He graduated from IMPA (Brazil) with a PhD in Mathematics in 2008. During 2009 he was a postdoctoral researcher in the Department of Mathematics at the University of California, Santa Barbara. His research interests are in Harmonic Analysis and Partial Differential Equations and he has published several papers concerning the existence and asymptotic behavior of solutions to nonlinear dispersive models.

Spring 2016

Speaker: VLADIMIR VERSHININ (Universite de Montpellier, France)

Time: Tuesday, 4/26, 11am-12pm

Location: Media and Public Affairs B07

Title: BRAIDS AND HOMOTOPY GROUPS OF SPHERES

Abstract: We start with the geometrical (naive) definition of braids and then identify them with the fundamental group of configuration space of a manifold. The case of a surface is particular interesting. We recall some classical properties of braids and then pass to Brunnian braids. A braid is Brunnian if it becomes trivial after removing any one of its strands. We describe algebraically the group of Brunnian braids on a general surface, if the surface is not a sphere or projective plane. In these exceptional cases the group of Brunnian braids is described by an algebraic procedure together with the homotopy groups of a 2-sphere. If there will be time we shall speak about the graded Lie algebra of the descending central series related to Brunnian braid group. It is proved that this is a free Lie algebra and the set of free generators is described.

Bio: Vladimir Vershinin is a professor of mathematics at the Alexader Grothendieck Institute in Montpellier, France, and a researcher at the Sobolev Institute of Mathematics, Novosibirsk, Russia.

His interests in Mathematics include Algebraic Topology, and braid groups and their generalizations.

He had hold one year visiting position in Autonoma University of Barcelona, half year positions in the IHES, Paris, and the Poncelet Laboratory, Moscow.

Colloquium on Education in Mathematics

Speaker: Hyman Bass (University of Michigan)

Time: Friday, 4/15, 1-2pm

Location: Corcoran 101

Title: A vignette of mathematical practices in action

Abstract: Mathematical Practices are, essentially, the things you do when you do mathematics. While they are emphasized in the Common Core, many teachers find it difficult to fully understand what they mean, or what they “look like.” I will a present small piece of mathematics that arose from a question about fractions in third grade. I will use this as a context to illustrate mathematical practices in action. Here is the problem: Suppose that s students want to equally share c cakes.

What is the smallest number, p(c, s), of cake pieces, needed to achieve this fair distribution? We will derive a formula for p(c, s) and describe two different distribution schemes that achieve this, the “linear” and the “Euclidean” distributions. The Euclidean distribution corresponds to the “Euclidean square tiling” of a c x s rectangle R, and we shall see that this square tiling is “isoperimetric” in the sense that it has smallest “perimeter” among all square tilings of R. I will describe generalized version of this problem that is still open.

Bio: Hyman Bass is the Samuel Eilenberg Distinguished University Professor of Mathematics and Mathematics Education at the University of Michigan. He has served as President of the American Mathematical Society and the International Commission on Mathematical Instruction and as Chair of the National Academy of Sciences’ Mathematical Sciences Education Board, and of the AMS Committee on Education. He is a member of the U.S. National Academy of Sciences, the American Academy of Arts and Sciences, the Third World Academy of Sciences, and the National Academy of Education. In 2006 he received the U. S. National Medal of Science. His mathematical research spans various domains of algebra, notably algebraic K-theory and geometric group theory. His work in education (largely with Deborah Ball) focuses mainly on mathematical knowledge for teaching, and on the teaching and learning of mathematical practices, such as reasoning and proving, and discerning and developing mathematical structure, in K-16 classrooms.

Math Department Colloquium -- Distinguished Speculative First of April Talk

Speaker: Scott Carter (University of South Alabama)

Time: Friday, 4/1, 1-2pm

Location: Corcoran 101

Title: The Role of Knots and Higher Dimensional Knots in Our

Understanding of the Quantum World

Abstract: According to the organizers of this event, this talk is meant to be speculative. The title alone satisfies that criterion! Yet, there seem to be at least two conflicting views of matter within our collective consciousness: the discrete and the continuous. Atoms, electrons, quarks, {\it etc.} are discrete particles while the meaning of particle in the first place has to do with a continuum --- the collection of representations of a (product of) unitary groups.

Since the time of Taite and Thompson (Lord Kelvin), and perhaps

earlier, matter was thought to be composed of knotted vortices in the

aether. Such a model is notoriously wrong, yet some aspects persist.

Knotted vortices can be created in the lab via the quantum hall

effect. The space-time trace of a particle is a string, and indeed a

$4$-dimensional view of the universe suggests that we should examine

the interactions of critical events.

So in this talk we start from toy models of particles that are created or annihilated, and that radiate and examine their critical interactions. Those aspects that you would like to consider ``the same," I will consider as isomorphic. And I will then study the isomorphism among them. To continue the speculation, we'll successively project figures to planes and see if the interactions among critical events therein resemble the physical models of reality.

The talk will be informed by pictures.

Bio: Dr. Carter graduated from Yale with a PhD in 1982. After that, he taught at University of Texas, Lake Forrest College and Wayne State University. In 1989, he became a professor of University of South Alabama. Since then, he has been active in the Mobile Math Circle and on Youtube. He was the chair of the Department of Math and Statistics of University of South Alabama from 2003 to 2010. He is currently a managing editor of Journal of Knot Theory and its Ramifications.

Speaker: Taduri Srinivasa Siva Rama Krishnarao (Indian Statistical

Institute, Bangalore Centre, and University of Memphis)

Time: Friday, 3/25, 1-2pm.

Location: Corcoran 101

Title: Proximinality for sums of closed subspaces

Abstract: In this talk we deal with the question of approximating minimizing sequences by sequence of proximinal vectors, for sums of closed subspaces. Motivated by some results of M. Feder and Pei-Kee Lin, we show that for a finite dimensional sub-space F and a strongly proximinal subspace Y of a Banach space X , F + Y is a strongly proximinal subspace of X . We also show the universality of the difficulty involved for sums of subspaces by showing that for any

infinite dimensional Banach space X there exists an infinite dimensional space Z containing an isometric copy of X as a strongly proximinal subspace and a strongly proximinal subspace W of Z such that the sum X +W is a closed, proximinal subspace of Z that is not strongly proximinal in Z .

Bio: Professor Taduri is currently Fulbright-Nehru Academic and Professional Excellence Scholar at the Department of Mathematical scienced, University of Memphis. A senior professor from the Indian Statistical Institute, a Fellow of the Indian Academy of Sciences, he is the current Head of the Indian Statistical Institute, Bangalore centre.

Special Colloquium

Speaker: Qing Han (Notre Dame)

Time: Tuesday, 3/8, 3:45-4:35pm

Location: Rome 204

Title: Isometric Embedding of 2-Dim Riemannian Manifolds in Euclidean 3-Space

Abstract: It is a classical problem to study whether any 2-dimensional Riemannian manifolds admit isometric embedding in the 3-dimensional Euclidean space. There are two versions of this problem, the local

version and the global version. The local version was presented by Schlaefli in 1973 and is still open. In this talk, we review both versions of the problem and present some recent results.

Bio: Professor Han got his PhD from Courant Institute in 1993. After that, he was a Dickson Instructor at University of Chicago for a year. He became a faculty member of University of Notre Dame in 1994. He was also a visiting member of Courant Institute and Max-Planck Institute for Mathematics, Leipzig. He was recognized by a Sloan Foundation Research Fellowship in 1999.

Speaker: Nikita Alekseev (GWU)

Time: Friday, 3/4, 1-2pm

Location: Corcoran 106

Title: Combinatorial and Probabilistic approaches in Comparative Genomics.

Abstract: The ability to estimate the evolutionary distance between extant genomes plays a crucial role in modern phylogenomic studies. When we say "evolutionary distance between two genomes on the same set of genes" we mean a number of genome rearrangements which transformed one genome into another in the course of evolution. In this talk we discuss how to find the evolutionary distance within different mathematical models. We demonstrate combinatorial and probabilistic approaches to the problem.

Bio: Dr. Nikita Alexeev is a postdoctoral researcher in Computational Biology Institute at the George Washington University. He graduated from St. Petersburg State University (Russia) with a PhD in Mathematics and Statistics in 2012. During 2008-2011 he was a visiting researcher in Bielefeld University, Germany. During 2011-2014 he was a researcher at the Chebyshev Laboratory, SPbSU. His research interests are Combinatorics, Graph Theory, Probability Theory and Computational Biology.

Speaker: Roman Sznajder (Bowie State)

Time: Friday, 2/26, 1-2pm

Location: Corcoran 106

Title: ENIGMA: Harnessing mathematics in cryptology

Abstract: ENIGMA was a German ciphering machine developed soon after WWI for commercial use. Shortly after, it was acquired by the German army and used for encrypting and decrypting military messages and orders. We discuss the circumstances that led to the initial breaking of the Enigma code in 1932 by three young cryptologists: Rejewski, Różycki, and Zygalski from the Polish Cipher Office. This was the first time when mathematics was systematically used in cryptography. Specifically, there were applications of permutation groups used to reconstruct the wiring of military Enigma and then to recover the daily keys and keys for individual messages. In the summer of 1939, when the outbreak of WWII was imminent, the Polish Cipher Office provided Allies with two copies of the Enigma machine and daily keys. Aided by these materials, the British immediately began working on breaking Enigma messages. Their office in Bletchley Park had access to human, engineering, and technological resources on an industrial scale. The ability to read encrypted messages used by the German army—enabled by the breaking of the Enigma code—contributed to the shortening of WWII and, according to some estimates, spared several million lives. With the British WWII archives sealed and Poland behind the Iron Curtain, the British Secret Service suppressed the knowledge about the role of Polish intelligence in breaking the Enigma

code for about thirty years. The heroic effort of three Polish cryptologists was virtually unknown to the world until the 1973 publication of a book by the French general Gustave Bertrand. In this presentation, we will shed some light on mathematical methods, the events and people involved in the successful effort to break the Enigma code. Since the beginning of the US involvement in WWII (1942), there was a very close cooperation between the US and British intelligence. Two prominent American cryptologists, Drs. Solomon Kullback and Abraham Sinkov were involved in this project. Two high school friends, both obtained their doctorates from The Washington University (in 1934 and 1933, respectively). Dr. Sinkov was a full fledge cryptologist, while Dr. Kullback who, at a certain moment of his career, was on the faculty of The GWU, was a statistician by heart. Colonels Kullback and Sinkov are members of the Military Intelligence Hall of Fame.

Bio: Dr. Roman Sznajder is a professor of mathematics and Graduate Program Coordinator in Applied and Computational Mathematics at Bowie State University. He received his Ph.D. in applied mathematics in 1994 from University of Maryland, Baltimore County. His current research interests include nonlinear analysis, optimization and history of mathematics. He authored and co-authored 35 articles, presented his findings at various international conferences, and reviewed papers to

about 30 research journals.

Special Colloquium

Speaker: Alex Iosevich (University of Rochester)

Time: Thursday, 2/18, 3:45-4:35pm

Location: Rome 204

Title: Orthogonal bases and tiling: analysis, number theory and combinatorics

Abstract: In 1974 Bent Fuglede conjectured that if a set Omega is abounded domain in R^d, then the space L^2(Omega) has an orthogonalbasis of exponentials if and only if Omega tiles the space R^d bytranslation. Even though this conjecture was disproved by Terrance Tao in 2004 in dimensions 5 and higher, it is continuing to leadresearchers to fascinating connections and ideas that involve avariety of areas of modern mathematics. In this talk we will present asampling of these ideas and connections between them, as well as some recent developments in this fascinating field.

Bio: Alex Iosevich got his B.S. in Mathematics at the University of Chicago in 1989 and a Ph.D. in Mathematics at UCLA in 1993 under thedirection of Christopher Sogge. After a postdoctoral fellowship at McMaster University, he worked at Wright State University, Georgetown University and the University of Missouri. Iosevich is currently a Professor of Mathematics at the University of Rochester. He has

graduated 11 Ph.D. students and in 2015 he became a Fellow of the AMS. Iosevich works in harmonic analysis, geometric combinatorics and additive number theory, with emphasis on connections between those areas.

Special Colloquium

Speaker: Carolyn Chun (US Naval Academy)

Time: Tuesday, 2/16, 3:45-4:35pm

Location: Corcoran 101

Title: Inductive tools for graphs (and matroids)

Abstract: In this talk, we consider inductive tools for graphs (and matroids) that preserve a kind of robustness, called connectivity. In 1966, Tutte proved that every 3-connected graph (or matroid) other than a wheel (or whirl) has a single-edge deletion or contraction that is 3-connected. Seymour extended this result in 1980 to show that, in addition to preserving 3-connectivity, we can preserve a given substructure, namely a 3-connected minor. We present the long-running

project joint between the speaker, James Oxley, and Dillon Mayhew to obtain such results for graphs (and matroids) that are internally 4-connected.

Bio: Carolyn Chun completed her PhD at Louisiana State University in 2009, advised by James Oxley. She moved to New Zealand for three years to be a research postdoc at Victoria University of Wellington with Geoff Whittle. She spent the following three years in London, as a research postdoc at Brunel University London with Steven Noble. In

January 2016, Carolyn became an assistant professor in the math department at the US Naval Academy. She loves graphs, matroids, delta-matroids, and traveling.

Speaker: Jonathan Katz (UMD)

Time: Thursday, Feb 11, 3:45-4:35pm

Location: Rome 204

Title: On the Nature of Mathematical Proofs: A Cryptographic Perspective

Abstract: Beginning in the mid-'80s, complexity theorists began radically revising the notion of what (mathematical) proof might entail, introducing and extending the ideas of using both randomness and interaction as part of the proof-verification process. Cryptographers took this one step further with the idea of *zero-knowledge proofs*, which are supposed to reveal "no information" beyond the validity of the theorem being proven.

We give an introductory survey of these fundamental and now-classical concepts, and conclude with a brief discussion of current research exploring their applications and extensions to the settings of secure distributed computation and verifiable outsourcing.

Bio: Jonathan Katz is a professor of computer science at the University of Maryland, and director of the Maryland Cybersecurity Center. He received an undergraduate degree in mathematics from MIT, and a PhD in computer science from Columbia University. His research interests lie broadly in the fields of cryptography, privacy, and science of cybersecurity, and he is a co-author of the widely used textbook "Introduction to Modern Cryptography." Katz was a member of the DARPA Computer Science Study Group from 2009-2010, and received a Humboldt Research Award in 2015. He currently serves on the steering committee for the IEEE cybersecurity initiative, as well as the State of Maryland Cybersecurity Council.

Speaker: Jonathan Katz (UMD)

Time: Friday, Jan 22, 3:45-4:45pm(rescheduled to Thursday Feb 11, 2016)

Location: Corcoran 106

Title: On the Nature of Mathematical Proofs: A Cryptographic Perspective

Abstract: Beginning in the mid-'80s, complexity theorists began radically revising the notion of what (mathematical) proof might entail, introducing and extending the ideas of using both randomness and interaction as part of the proof-verification process. Cryptographers took this one step further with the idea of *zero-knowledge proofs*, which are supposed to reveal "no information" beyond the validity of the theorem being proven.

We give an introductory survey of these fundamental and now-classical concepts, and conclude with a brief discussion of current research exploring their applications and extensions to the settings of secure distributed computation and verifiable outsourcing.

Bio: Jonathan Katz is a professor of computer science at the University of Maryland, and director of the Maryland Cybersecurity Center. He received an undergraduate degree in mathematics from MIT, and a PhD in computer science from Columbia University. His research interests lie broadly in the fields of cryptography, privacy, and science of cybersecurity, and he is a co-author of the widely used textbook "Introduction to Modern Cryptography." Katz was a member of the DARPA Computer Science Study Group from 2009-2010, and received a Humboldt Research Award in 2015. He currently serves on the steering committee for the IEEE cybersecurity initiative, as well as the State of Maryland Cybersecurity Council.

Fall 2015

Date and Time: December 11, 2015; 1:00-2:00

Place: Corcoran 101

**Abstract:**The website DMV.org contains hints on how to parallel park such as: don't get too close or you might scratch the other car; if your rear tire hits the curb, you've gone too far. It is mentioned that even the most gifted and seasoned parallel parkers do this - often. The mathematician sees opportunity here to describe theory of practical value.

**Speaker: **Patrick M. Gilmer**, **Louisiana State University

Title: *Signature Jumps and Alexander Polynomials for Links***Date and Time: **December 4, 2015; 1:00–2:00 pm**Place:** Government 104

**Abstract**: http://at.yorku.ca/cgi-bin/

**Bio **at :** https://www.math.lsu.edu/~ gilmer/**

**Speaker: **Paul Wedrich, University of Cambridge, UK

Title: *Knot homologies and their deformations***Date and Time: **November 13, 2015; 1:00–2:00 pm**Place:** Government 101

**Abstract**: Knot homology theories are powerful generalizations of classical (and quantum) knot polynomials. Besides providing stronger invariants, these theories are often functorial under knot cobordisms and contain additional geometric information. I will start by introducing Khovanov homology, a paradigmatic example of a knot homology theory, and explain how it fits into the family of colored sl(N) knot homology theories. The goal of this talk is to explain how deformation techniques help to answer two important questions about this family: What relations exist between its members? What geometric information about knots and links do they contain? I will recall Lee's deformation of Khovanov homology and sketch how it generalizes to the case of colored sl(N) link homology. The result is a decomposition theorem for deformed colored sl(N) knot homologies, which leads to new spectral sequences between knot homologies and to new concordance invariants in the spirit of Rasmussen's concordance invariant. Part of this is joint work with David E. V. Rose.

Short bio: Paul Wedrich obtained his PhD at the University of Cambridge in 2015 under the supervision of Jake Rasmussen. See

https://www.dpmms.cam.ac.uk/~

**Speaker: **Ajit Iqbal Singh, Indian National Science Academy

http://insaindia.org/detail.

Title: *Involutions and Trivolutions in Algebra and Analysis*

Date and Time: November 6, 2015; 1:00–2:00 pm

Place: Government 101

Abstract: The natural involutions in a group of taking inverse and in the complex plane of taking reflection in the real axis are usually combined to give an involution in the algebra of complex functions on groups thus forcing it to be conjugate linear. For finite or infinite matrices, taking inverse is replaced by taking transpose, the reflection in the diagonal, which forces it to be an anti-homomorphism as well. This is the basis of the definition of an involution in Algebra. Certain restrictions, continuity conditions and scaling are called for when we pass on to the context of Functional Analysis or Harmonic Analysis on groups, semi-groups and hypergroups. This opens up possibilities of many new involutions. However when we go to the biduals with Arens products, the availability starts being choosy. While the situation is fine for Arens regular algebras like C*-algebras, surprisingly so, it is impossible to have any involution for biduals of infinite amenable group algebras! Just like generalised inverses help in solving systems of equations, trivolutions T spring up as conjugate linear anti-homomorphisms T that are their own generalised inverses, i.e., T.T.T=T. This expository talk will give a gentle account including recent work by the speaker and her collaborators Mahmoud Filali and Mehdi Monfared.

**Short bio** at: https://en.wikipedia.org/wiki/

**Speaker: **Chris Laskowski, University of Maryland

http://www.math.umd.edu/~

Title: *Towers of Babel: What do probability, computer learning, combinatorial geometry, model theory, and neural networks have in common?*

Date and Time: October 30, 2015; 1:00–2:00 pm

Place: Government 101

Abstract: This will be a rambling talk that highlights a very attractive, naturally occurring polynomial/exponential growth dichotomy that keeps getting discovered over and over in various fields of math and computer science. Absolutely no knowledge of any of the fields mentioned in the title is assumed.

**Short bio:** Chris Laskowski is a professor of mathematics at University of Maryland. He is primarily interested in model theory, broadly defined. In addition to mathematics, he has co-authored papers in computational geometry, economics, and protein chemistry.

**Speaker: **Alissa Crans, Loyola Marymount University (Los Angeles)

Title: *Musical Actions of Dihedral Groups*

Date and Time: October 16, 2015; 1:00–2:00 pm

Place: Government 101**Abstract**: Can we hear an action of a group? Or a centralizer? In the same way it is possible to see group structure in a crystal, it is also possible to hear group structure in music. We will investigate two ways that the dihedral group of order 24 acts on the set of major and minor chords and illustrate both geometrically and algebraically how these two actions are dual. Both actions and their duality have been used to analyze works of music as diverse as that of Beethoven and the Beatles. (This is joint work with Thomas M. Fiore and Ramon Satyendra.)

**Bio** at: http://myweb.lmu.edu/acrans/

## Spring 2015

**speaker: **Robert L. Devaney, Boston University

http://math.bu.edu/people/bob/

**Title: ***Cantor and Sierpinski, Julia and Fatou: crazy topology in complex dynamics*

**Date and Time: ****Thursday, **April 23, 2015 4:00–5:00pm**Place:** Government Hall, Room 104

**Abstract**: In this talk, we shall describe some of the rich topological structures that arise as Julia sets of certain complex functions including the exponential and rational maps. These objects include Cantor bouquets, indecomposable continua, and Sierpinski curves. No real background in either complex dynamics or planar topology is necessary to follow this talk.

**Short Bio** at: http://math.bu.edu/people/

**Date and Time**: Wednesday, April 8, 2015 10:00-11:00am

**Place**: Government Hall, Room 104

### Crowdmark: Online Collaborative Grading at GWU?

### Crowdmark is a collaborative online grading and analytics platform that helps instructors and teaching assistants evaluate student work more effectively than ever before. Experiments involving thousands of students and more than a million exam pages have shown that Crowdmark cuts grading time in half. Audience members are encouraged to bring their laptops to participate in an interactive demonstration.

Professor James Colliander, University of Toronto and

CEO, Crowdmark, Inc.

Short bio:

(Distinguished Speculative First of April Talk)

**Speaker: **Scott Aaronson, MIT

**Title: **How Pervasive Is Incompleteness?

**Date and Time: Friday, **April 3, 2015 1:00–2:00pm

**Place:** Government Hall, Room 101

**Abstract**: I was asked to give a “speculative” math talk. So, I'll discuss the question of just how much “normal, finitary” math the Gödel incompleteness phenomenon might infest. I’ll first survey the types of independence and undecidability results that are known, and explain why in my view, none of them give a fully satisfactory answer. I’ll then speculate about the question, which I’m often asked, of whether the P vs. NP problem might turn out to be formally undecidable. Finally, I’ll discuss the Busy Beaver function, and its amazing ability to “concretize” questions of mathematical logic. I’ll mention some ongoing work with Adam Yedidia that aims to construct a small Turing machine whose (non-)halting is provably independent of the ZFC axioms.

**Short Bio**: Scott Aaronson is an Associate Professor of Electrical Engineering and Computer Science at MIT. He studied at Cornell and UC Berkeley, and did postdocs at the Institute for Advanced Study as well as the University of Waterloo. His research focuses on the capabilities and limits of quantum computers, and more generally on computational complexity and its relationship to physics. His first book, *Quantum Computing Since Democritus*, was published in 2013 by Cambridge University Press. Aaronson has written about quantum computing for Scientific American and the New York Times, and writes a popular blog at www.scottaaronson.com/blog. He’s received the National Science Foundation’s Alan T. Waterman Award, the United States PECASE Award, and MIT's Junior Bose Award for Excellence in Teaching.

**Math Colloquium**

**Speaker:** Yanping Ma, Loyola Marymount University

**Title:** Injury-initiated clot formation under flow: a mathematical model with treatment

**Date and Time: Friday,** March 27, 2015, 1:00–2:00pm

**Place:** Government Hall, Room 101

**Abstract**: When an individual at risk for forming a thrombus is treated with anticoagulant medication, the International Normalized Ratio (INR) must be measured regularly. We explore the conditions under which an injury-induced thrombus may form *in vivo* but not *in vitro*. We extend previous models and present numerical simulations that compare scenarios in which drug doses and flow rates are modified. Our results indicate that traditional INR measurements may not accurately reflect *in vivo* clotting times.

**Short Bio**: Yanping Ma obtained her PhD in math at Penn State University with minor in statistics, and her B.S. from the University of Science and Technology of China in math and applied math. She is currently working at Loyola Marymount University as an assistant professor. Her research interest is in bio mathematics modeling with simulations.

**Mathematics Colloquium (Jointly with ****Knots in Washington XL)**

**Speaker: **Sergei Chmutov, Ohio State University, Mansfield

https://people.math.osu.edu/

**Title: ***In memory of Sergei Duzhin* (1956–2015)**Date and Time: ****Tuesday,**March 10, 2015

10:00–11:00am**Place:** Duques Hall, Room 251

**Abstract**: I will recall life and work of my lifelong friend Sergei Duzhin who suddenly passed away on February 1, 2015. The main topic of my collaboration with Sergei Duzhin was Vassiliev knot invariants. Thus the mathematical part of my talk will concentrate on the theory of these invariants. I will first give definitions, survey the theory, and then explain our results and their further developments. I will then briefly talk about Duzhin’s life and some other of his results.

**Short Bio**: Sergei Chmutovis a professor of Mathematics at Ohio State University, Mansfield. He received his PhD from Moscow State University in 1985. His research interests include Vassiliev theory of knot invariants, knot theory, low-dimensional topology, theory of critical points of functions, combinatorics, (topological) graph theory, theory of singularities of algebraic varieties, and algebraic geometry. He authored 48 research papers and a book (jointly with S. Duzhin and Y. Mostovoy),*Introduction to Vassiliev Knot Invariants,* published by the Cambridge University Press in 2012.

**Speaker: **Gadi Fibich, Tel Aviv University, Israel

http://www.math.tau.ac.il/~

**Title: ***Is heterogeneity important?*

**Date and Time: Friday, **February 13, 2015, 1:00–2:00pm**Place:** Government Hall, Room 101

**Abstract**: Typically, a model with a heterogeneous property is considerably harder to analyze than the corresponding homogeneous model. In this talk I will show that any outcome of a heterogeneous model that satisfies the two properties of differentiability and symmetry is O(ε2) equivalent to the outcome of the corresponding homogeneous model, where ε is the level of heterogeneity. In such cases, therefore, the effect of heterogeneity is minor. Applications of this “averaging principle’’ to problems in queuing theory, game theory (auctions), and marketing (diffusion of new products in social networks) will be presented.

**Short Bio**: Gadi Fibich got his PhD from NYU in 1994. He is a Professor of applied math at Tel Aviv University and is currently on sabbatical at the University of Maryland. He has numerous publications in various areas of applied math, including nonlinear optics, perturbations theory, applications to marketing, biochemistry, and medicine.

**Title: **Planar graphs are 9/2-colorable and have independence ratio at least 3/13**Speaker:** Dan Cranston, Virginia Commonwealth University**Date and Time:** Friday February 6, 1:00-2:00pm

**Place:** Government 101

**Abstract:** For nearly a century, one of the major open questions in graph theory was the Four Color Conjecture: Every planar graph can be properly colored with four colors. In 1976, this conjecture was resolved (in the affirmative) by Appel and Haken. Their result is called the 4 Color Theorem. Unfortunately, their proof (as well as later proofs of this theorem) relies heavily on computers. In contrast, the 5 Color Theorem is easy to prove. In this talk we look at a 9/2 Color Theorem, which we can prove by hand.

A 2-fold coloring assigns to each vertex 2 colors, such that adjacent vertices get disjoint sets of colors. We show that every planar graph *G* has a 2-fold 9-coloring. In particular, this implies that *G* has fractional chromatic number at most 9/2. This is the first proof (independent of the 4 Color Theorem) that there exists a constant *k*<5 such that every planar *G* has fractional chromatic number at most *k*. We also show that every *n*-vertex planar graph has an independent set of size at least 3n/13. This improves on Albertson's bound of 2n/9, which was the best result independent of the 4 Color Theorem.

This is joint work with Landon Rabern.

**Short Bio: **Daniel Cranston earned his PhD in 2007 from University of Illinois, under the direction of Douglas West. From September 2007 to August 2009, Cranston was a postdoctoral fellow at the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) and Bell Labs, Rutgers University and Murray Hill, NJ. Cranston is currently assistant professor in the Department of Mathematics and Applied Mathematics at Virginia Commonwealth University. His research interests are mainly in graph theory and algorithms, but he is also interested in most areas of discrete math. He has been awarded NSA Young Investigator’s Award for the next academic year.

**Title: **The continued fractions, Sturmian and Ostrowski numeration systems**Speaker:** Abraham Bourla, American University**Date and Time:** Friday, January 23, 1:00-2:00pm**Place:** Government 101

**Abstract:** We will survey these three important non-fixed-radix numeration systems, each with a rich history and plenty of applications. We will present the built in connections between these systems and illustrate their geometric connections with the cutting sequences of geodesics and the rotation map on the circle.

**Short Bio:** Abraham Bourla worked as a computer programmer for the Israeli Defense Force and the private sector before coming to the US and studying mathematics. He has a Ph.D. from UConn and is currently teaching at AU.

**Speaker: **Rumen Dimitrov, Western Illinois University

**Title: **The Rich Structure of Modular Lattices Arising from Computably Enumerable Vector Spaces**Date and Time: **January 16, 2015; 1:00–2:00 pm**Place:** Monroe 250**Abstract:**

Post’s problem in computability theory, dating back to 1944, is whether there exist a computably enumerable (c.e.) Turing degree that is neither computable nor the degree of the halting problem. His strategy was to find a non-computable co-infinite c.e. set with a “thin” complement. The original notion of thinness was called“simplicity.” A c.e. set the complement of which is infinite but has no infinite c.e. subset is called simple. Different, ever-stronger, notions of thinness were defined, but none of them gave a solution to Post’s problem. These notions, however, revealed some fascinating structural properties of the lattice E of c.e. sets under inclusion, and its factor lattice E* (E modulo finite sets). In the talk we will introduce the lattice L of c.e. subspaces of the fully algorithmic infinite dimensional vector space and its factor lattice L* (L modulo finite dimension). We will explore some important similarities and differences between E* and L*.

**Short Bio:**

Rumen Dimitrov received PhD in mathematics at GWU in 2002, where he also spent 2002–03 as a visiting assistant professor of mathematics. He has been with the Department of Mathematics at Western Illinois University, as an assistant professor during 2003–08, and as an associate professor since 2008. His interests are in mathematical logic, computability theory, and computable model theory. His work in modular computability theory (in particular, computable algebras and closure systems) revolves around the open problems posed in the *Handbook of Recursive Mathematics*. In summer 2014, he presented a related paper at the *Computability in Europe* meeting in Budapest, Hungary. He has been a member of the senior personnel for the research collaboration with Russia and Kazakhstan funded by the NSF bi-national grants since 2002. He has co-organized two special sessions at AMS meetings in Washington.

Fall 2014

This event is co-sponsored by the GW Confucius Institute

**Speaker:**Cheng Chong-Qing, Nanjing University

**Title:**Is the Solar system stable? — a historical topic revisited

**Date and Time:**Friday, September 26, 1:00-2:00pm

**Place:**Duques 152

**Abstract: **The system I am going to talk about is an idealized model: to study n mass points which move in 3 dimensional space according to Newton’s law. We assume further that n-1 of these fictions mass points havevery small masses compared to the remaining one, which plays the role of the sun. I shall introduce some ideas to study this problem and give a brief review on new progress in the field.

**Short Bio:**Dr. Cheng Chong-Qing received his Ph,D. from Northwestern Polytechnical University in China. Currently, he is the Cheunkong Professor of Mathematics of Nanjing University, where he also serves as the Vice-President of the University. His research interests are in the field of dynamical systems, in particular, of Hamiltonian dynamics. Dr. Cheng has received numerous research awards including the National Young Investigate Awards (1995), Qiu-Shi Prize (1997), the Morningside Medal (1998), Prize for Natural Science, Education Ministry (2000), the National Second Prize for Natural Sciences (2001), and he was invited to give a 45-minute talk at the 26-th International Congress of Mathematicians in Hyderbad, India (2010).

**Time:** Friday, 10/10, 1-2pm**Location:** DUQUES 152**Speaker**: Xuhua He (University of Maryland)**Title:** Minimal length elements: some interaction between combinatorics, representation theory, and arithmetic geometry**Abstract:** The study of minimal length elements in a conjugacy class of a Weyl group arises in the study of representation theory. Minimal length elements have many remarkable combinatorial properties. The proof, however, is inspired by arithmetic geometry. In the first half of this talk, I will discuss these combinatorial properties, and some stories which lead to the discovery of the proof.

In the second half of this talk, I will talk about some applications of these combinatorial properties to representation theory and arithmetic geometry. I will explain how some ideas in arithmetic geometry lead to new discoveries in representation theory, and vice versa.**Bio: P**rof Xuhua He received his PhD in mathematics from Massachusetts Institute of Technology in 2005. He worked for the Institute for Advanced Study and Stony Brook University from 2005-2008. After that, he moved to Hong Kong and stayed there for six years. He is currently a Professor of Mathematics at University of Maryland.

Prof He's research interests lie at the crossroads of algebraic group theory, representation theory, combinatorics, algebraic geometry, and arithmetic geometry. He received the Morningside Gold Medal at the 6th International Congress of Chinese Mathematicians in 2013 for "his contributions to several fundamental problems in arithmetic geometry, algebraic groups, and representation theory".

**Time**: Thursday, October 16, 2014, 3pm**Location: **Phillips Hall 736**Speaker:** David Kopriva (Florida State University)**Title: **Spectral Methods in Motion**Abstract: **Accurate computation of wave scattering from moving, perfectly reflecting objects, or embedded objects with materialproperties that differ from the surrounding medium, requires methods that accurately represent the boundary location and motion, propagate the scattered waves with low dissipation and dispersion errors, and don't introduce errors or artifacts from the movement of a mesh. Discontinuous Galerkin spectral element methods are especially suited to problems where wave propagation accuracy is needed and the locations of material discontinuities are known. Applying the methods to an ALE (Arbitrary Lagrangian-Eulerian) formulation extends them to moving boundary problems. In this talk, we discuss the issues and choices for the development of a DGSEM-ALE approximation for the accurate approximation of wave propagation problems with moving boundaries. Examples from acoustics, fluid dynamics and electromagnetics will be presented to illustrate the application of the methods.**Bio: **David Kopriva is Professor of Mathematics at The Florida State University, where he has taught since 1985. He is an expert in the development, implementation and application of high order spectral multi-domain methods for time dependent problems. In 1986 he developed the first multi-domain spectral method for hyperbolic systems, which was applied to the Euler equations of gas dynamics. Though a multi-domain or spectral element approach is common now, at that time the idea of breaking up a computation into multiple spectral approximations was considered a radical idea. That original work led to the development of new multidimensional characteristic boundary conditions, spectral multi-domain methods for the compressible Navier-Stokes equations and multi-domain spectral versions of shock fitting algorithms for high speed flows. In the 1990's Kopriva developed a robust staggered grid Chebyshev spectral method that simplified the connectivity of subdomains and simplified parallel implementations. This work included the development of a non-conforming spectral method that enables the refinement of a mesh either by increasing the spectral order or decreasing the subdomain size locally. Most recently he has concentrated on the development of a discontinuous Galerkin form of the spectral element method for the solution of time-dependent systems. Kopriva has applied multi-domain spectral methods to time dependent problems in compressible flow, aeroacoustics and electromagnetics. Spectral multi-domain methods were used to solve problems in hypersonic flows over blunt bodies, in both the inviscid and viscous limits. Most recently he has applied the techniques he has developed to problems in electromagnetic scattering, problems in particulate transport, cryogenics and computational finance.

**Speaker: **Andrei Vesnin (Novosibirsk)**Title: **Knot groups and discreteness conditions**Date and time: **Friday, November 7, 1-2pm**Place: **Duques 152**Abstract:** There are various discreteness conditions for subgroups of PSL(2,C) acting on a hyperbolic 3-space. Most of conditions are related either to algebraic structure of a group or to its geometric action. It was shown by T. Jorgensen that a subgroup of PSL(2,C) is discrete if and only if any its 2-generated subgroup is discrete. Some of necessary conditions for 2-generated groups, obtained by T. Jorgensen, F. Gehring, G. Martin, and D. Tan, look as inequalities on traces of one generator and of a commutator of generators. We will say that a group is extreme if it gives the equality in such an inequality.

We will discuss hyperbolic knot groups and hyperbolic orbifold groups with are extreme groups for discreteness conditions (for example, the figure-eight knot and related orbifold groups). Also, we will discuss invariants of hyperbolic knots and links arising in this context.

**Bio: **Prof. Andrei Vesnin is head of the Laboratory of Applied Analysis, Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences and a professor of Geometry and Topology, Novosibirsk State University. He received a Candidate of Sciences in physics and mathematics is 1991 from Sobolev Institute of Mathematics for the thesis ”Discrete groups of reflections and three-dimensional manifolds”, and a Doctor of Sciences in physics in mathematics in 2005 for the thesis ”Volumes and isometries of three-dimensional hyperbolic manifolds and orbifolds”. He was a visiting professor in Seoul National University in 2002 – 2004. Prof. Vesnin's reseach interests include low-dimensional topology, knot theory, hyperbolic geometry, combinatorial group theory, graph theory and applications.

He is the editor-in-chief of Siberian Electronic Mathematics Reports and a member of editorial boards of Siberian Mathematical Journal and Scientiae Mathematicae Japonicae. In 2008 Prof. Vesnin was elected to corresponding member of the Russian Academy of Sciences.

Special Colloquium Talk**Speaker: **Uwe Kaiser (Boise State University)**Title: T**opology from the Quantum Computation Viewpoint**Time: **Tuesday, November 11, 11:10am -- 12:25pm (note the special time)**Location:** Monroe 115

**Abstract:** The talk will give an elementary introduction into the models of classical respectively quantum computation as information processing by classical logic gates respectively quantum gates. Quantum information processing is distinguished by interference and entanglement in informationally isolated systems. These properties give rise to the well known "quantum weirdness". I will briefly discuss the mathematical description of quantum information processing (the axioms of quantum mechanics) by unitary operators acting on complex vector spaces. Some examples for the resulting apparent improvement in computational power of quantum over classical computation will be described. Quantum information processing systems involve the wave functions of composite system and the statistics of the particle exchange of identical particles. Understanding this particle exchange is been known for a long time to be related to the topology of particles moving in space. Interesting examples are so called anyons, quasi-particles moving in 2-space and known to appear e.g. in the fractional quantum Hall effect. Then quantum computation naturally asks to understand the mathematical model of anyons, which is a well-known subject in the field of quantum topology.**Bio:** Dr. Uwe Kaiser received his PhD and habilitation from the University of Siegen in Germany. Additionally he also holds a K12-teaching certificate for Mathematics and Physics in Germany. Currently he is Associate Professor in the Mathematics Department at Boise State University, where he also serves as Associate Chair. His research interests are in Geometric and Algebraic Topology, more recently in Low Dimensional Topology and Quantum Topology, in particular in theory of skein modules. He is also working on several projects and grants related to STEM Education at Boise State University.

**Speaker:** Pavel Lushnikov (University of New Mexico)**Title: **Finite time singularities, rogue waves and strong collapse turbulence**Date and time:** Friday, November 21, 1-2pm.**Abstract: **Many nonlinear systems of partial differential equations have a striking phenomenon of spontaneous formation of singularities in a finite time (blow up). Blow up is often accompanied by a dramatic contraction of the spatial extent of solution, which is called by collapse. Near singularity point there is a qualitative change in underlying nonlinear phenomena, reduced models loose their applicability and other mechanisms become important such as inelastic collisions in the Bose-Einstein condensate, optical breakdown and dissipation in nonlinear optical media and plasma, wave breaking in hydrodynamics. Collapses occur in numerous reduced physical and biological systems including a nonlinear Schrodinger quation (NLSE) and a Keller-Segel equation (KSE). We will focus on the collapse in the critical spatial dimension two (2D) which has numerous applications. For instance, 2D NLSE describes the propagation of the intense laser beam in nonlinear Kerr media (like usual glass) which results in the catastrophic self-focusing (collapse) eventually causing optical damage as was routinely observe in experiment since 1960-es. Recently such events have been also often referred as optical rogue waves. Another dramatic NLSE application is the formation of rogue waves in ocean. 2D KSE collapse describes the bacterial aggregation in Petri dish as well as the gravitational collapse of Brownian particles. We study the universal self-similar scaling near collapse, i.e. the spatial and temporal structures near blow up point. In the critical 2D case all these collapses share a strikingly common feature that the collapsing solutions have a form of either rescaled soliton (for NLSE) or rescaled stationary solution (for KSE). The time dependence of that scale determines the time-dependent collapse width L(t) and amplitude ~1/L(t). At leading order L(t)~ (t_c-t)^{1/2} for all mentioned equations, where t_c is the collapse time. Collapse

however requires the modification of that scaling which in NLSE has the well-known loglog type ~ (\ln|\ln(t_c-t)|)^{-1/2} as well as KSE has another well-known type of logarithmic scaling modification. Loglog scaling for NLSE was first obtained asymptotically in 1980-es and later proven in 2006. However, it remained a puzzle that this scaling was never clearly observed in simulations or experiment. Similar situation existed for KSE. Here solved that puzzle by developing a perturbation theory beyond the leading order logarithmic corrections for both NLSE and KSE. We found that the classical loglog modification NLSE requires double-exponentially large amplitudes of the solution ~10^10^100, which is unrealistic to achieve in either physical experiments or numerical simulations. In contrast, we found that our new theory is valid starting from quite moderate (about 3 fold) increase of the solution amplitude compare with the initial conditions. We obtained similar results for KSE. In both cases new scalings are in excellent agreement with simulations. This efficiency of analytical results also allowed to study 2D NLSE-type dissipative system in the conditions of multiple random spontaneous formation of collapses in space and time. Dissipation ensures collapse regularization while collapses are responsible for non-Gaussian tails in the probability density function of amplitude fluctuations which makes turbulence strong. Power law of non-Gaussian tails is obtained for strong NLSE turbulence which is a characteristic feature of rogue waves. We suggest the spontaneous formation optical rogue from turbulent as a perspective route to the combing of multiple laser beams, generated by a number of fiber lasers, into a single coherent powerful laser beam.**Short bio:** Pavel Lushnikov received PhD in theoretical physics from the Landau Institute of Theoretical Physics. He moved to the postoctoral postion at the Los Alamos National Laboratory and later became the assistant professor at the University of Notre Dame. He joined UNM Department of Mathematics and Statistics in 2006 as the associate professor

and has been serving as the full professor since 2012. Since 2006 he has been awarded by 5 NSF and NSF/DOE grants. In 2008 he received Doctor of Science Degree in Physical and Mathematical Sciences, highest scientific degree in Russia, awarded for major scientific achievements beyond PhD by the Landau Institute. His interests include a wide range of topics in applied mathematics, nonlinear waves and theoretical physics. Among them are laser fusion and laser-plasma interaction; dynamics of fluids with free surface and nonlinear interactions of surface waves; theory of the wave collapse, singularity formation and its application to plasma physics, hydrodynamics, biology and nonlinear optics; high-bit-rate optical communication; dispersion-managed optical fiber systems; solution propagation in optical systems; high performance parallel simulations of optical fiber systems; Bose-Einstein condensation of ultracold dipolar gases. His recent Optics Letters paper on nonlinear beam combining, published in June 2014, has been in the top download of Optics Letters since then.

**Speaker:** Archana Khurana (University of Baltimore)**Date and time:** Friday, December 5, 1-2pm.**Place: **Duques 152

Title: On multi-index fixed charge bi-criterion transportation problem

Abstract:In this talk I would discuss an algorithm for solving a multi-index fixed charge bi-criterion transportation problem and also present a method for finding the optimum trade-off pair among the efficient cost-time trade-off pairs. The solution method would be useful when we need to transport heterogeneous commodities. The proposed algorithm minimizes variable and fixed costs simultaneously to yield an optimal basic feasible solution. I would also provide an algorithm to obtain an initial basic feasible solution of the multi-index transportation problem that may be used as a superior initial solution with any other existing procedure to enhance convergence to the optimal solution.

Bio:

Archana Khurana has obtained her Masters and Ph.D degree from Department of Mathematics, University of Delhi, Delhi, India. She was awarded Junior and Senior research fellowship from Council of Scientific and Industrial Research, Delhi, India during her Ph.D. After completion of her doctorate in 2004, she worked as a Research Engineer at Logistics Institute of Asia Pacific, National University of Singapore, Singapore for 1 year .

In September 2006, she joined Guru Gobind Singh Indraprastha University, Delhi, India and worked there till July 2013 where she taught undergraduate and graduate students. Thereafter she moved to USA and since August 2013, she is doing research at Merrick School of Business, University of Baltimore, Maryland, USA.

Her research interests are Linear and Non-linear programming, Transportation problems, Transshipment problems and Integer programming problems. Her thesis and ongoing research work has led to many publications in reputed International Journals. She was also sponsored a Major Research Project from University Grant Commission, Delhi, India of 3 years duration which was completed successfully. She loves travelling and playing Table tennis.

## Spring 2014

**Time: **Friday, May 9, 2014 1:00-2:00**Place: **GOV 102**Speaker:** Neil J. A. Sloane, Mathematics Department, Rutgers University, Piscataway, NJ.**Abstract**: The On-Line Encyclopedia of Integer Sequences is a database of number sequences, which in its fiftieth year now contains nearly a quarter of a million entries. This talk will describe some of the highlights, including the toothpick sequence, curling numbers, ``lunar'' arithmetic, and some very unusual recurrences. There will be several unsolved problems, music, and a movie.

**Title: **Diffusions, Fractional Laplacians and Traveling Waves**Speaker: **Changfeng Gui, University of Connecticut and NSF**Time: **Friday, March 21, 2014 1:00-2:00**Place: **GOV 102

Abstract: Fractional Laplacians can be used to model physical phenomena involving abnormal diffusions. In this talk, I will discuss how abnormal diffusions may affect the propagation of certain materials/species. In particular, the effects of abnormal diffusions on the existence of traveling wave will be examined. For three important classes of diffusion-reaction models with monostable, combustion and bistable nonlinearities, we will show rigorous results for abnormal diffusions and compare them with the results for the classical models. The talk is based on recent results obtained jointly with Tingting Huan and with Mingfeng Zhao

**Speaker:** Michael Baake, University of Bielefeld, Germany**Time: **Monday, March 31, 2014 2:45-3:45**Place: **Monroe 267

The discovery of quasicrystals by Dan Shechtman in 1982 has shown that there are interesting systems beyond perfect crystals with pure point diffraction spectra, and also that we still have a rather limited understanding of what `order' is supposed to mean, both mathematically and physically.

In this talk, basic structures with aperiodic order are reviewed from the point of view of mathematical diffraction theory, with focus on classic and paradigmatic examples. The talk is directed towards a general mathematical audience. Further details will later be discussed in the talk by Uwe Grimm.

** ****Distinguished Speculative First of April Talk**

**Title: **Topological, quantum and categorification invariants in 4D, unrealized opportunities**Speaker**: Samuel J. Lomonaco Jr, (UMBC __http://www.csee.umbc.edu/~ lomonaco/__),

**Time:**Thursday April 3, 2014 5:15pm

**Place:**Phil 108

Previous talks in the

**Distinguished Speculative First of April Talk**series:

**Title:**I. Speculative, Distinguished First of April Talk

**Speaker:**Oleg Viro (Stony Brook University)

**Time:**Friday, April 1, 2011 3:45-4:45 pm

**Place:**Media & Public Affairs Building (21st & H), Room 310

II. Distinguished speculative April first talk

**Title:**The Four Color Theorem

**Speaker: Louis Kauffman**(University of Illinois at Chicago)

**Time:**Tuesday, April 3, 2012 4:00pm

**Place:**1957 E Street, Room 111

III. Distinguished Speculative First of April Talk

**Title:**Quantum machine learning

**Speaker:**Seth Lloyd, MIT

**Time:**April 1, 2013,

__http://www.rle.mit.edu/people/__directory/seth-lloyd/

__http://en.wikipedia.org/wiki/__Seth_Lloyd

**joint Colloquium and JUMP seminar**

**Title:** Genome rearrangements: when intuition fails**Speaker**: Max Alekseyev, George Washington Univ.**Time:** Monday, April 7, 2014 11:10-12:10pm**Place:** Monroe 353

(* The JUMP seminar is part of the Joint Undergraduate Mathematics & Physics (JUMP) Scholarship program. See more info at__http://math.columbian.gwu.edu/ jump-scholarship__)

**Abstract:**

Genome rearrangements are genomic "earthquakes" that change the chromosomal architectures. The minimum number of rearrangements between two genomes (called "genomic distance") represents a rather accurate measure for the evolutionary distance between them and is often used as such in comparative genomics studies.

In this talk I shall describe two rather unexpected phenomena in genome rearrangements analysis. First, the weighted genomic distance designed to bound the proportion of transpositions (that are complex rearrangements rarely happening in reality) in rearrangement scenarios between two genomes does not actually achieve this goal. Second, while the median score of three genomes can be approximated by the sum of their pairwise genomic distances (up to a constant factor), these two measures of evolutionary distance of genomes are no so much correlated as one's intuition may suggest.**Bio:**

Dr. Max Alekseyev is an associate professor at the Department of Mathematics & Computational Biology Institute, George Washington University. He received a Ph.D. in computer science from the University of California, San Diego, and in 2009-2013 was an assistant professor of computer science at University of South Carolina. In 2011, Dr. Alekseyev served as a scientific director for the Algorithmic Biology Laboratory at St. Petersburg Academic University, Russia, where he led development of genome assembler SPAdes. He received an NSF CAREER award in 2013. Dr. Alekseyev's research interests range from discrete mathematics (particularly, combinatorics and graph theory) to bioinformatics (particularly, comparative genomics and phylogenomics). His research is focused on the development and application of new methods of discrete mathematics to solve old and recently emerged open biological problems.

Speaker:

Dr. Hans Kaper, Georgetown University

Abstract: Climate is an emerging area of research in the mathematical sciences, part of a broader portfolio that addresses issues of complexity and sustainability. So far, the climate system has received relatively little attention in the mathematical sciences community, despite the fact that the stakes are high, decision makers have more questions than we can answer, and mathematical models and statistical arguments play a central role in assessment exercises. In this talk I will identify some problems of current interest in climate science and indicate how, as mathematicians, we can find inspiration for new applications.

Bio: Dr. Hans Kaper is an applied mathematician and co-director of the Mathematics and Climate Research Network (http://www.mathclimate.org), an NSF funded virtual organization to develop the mathematics needed to better understand the Earth's climate. He is the (co) author of four books and more than 100 articles in refereed journals. His most recent book "Mathematics and Climate" (with Dr. Hans Engler) was published by the Society for Industrial and Applied Mathematics (SIAM) and was named“ASLI's Choice 2013” by the Atmospheric Science Librarians International (ASLI) as the best book of 2013 in the fields of meteorology/climatology/

**A joint talk with AMW Chapter of GWU**

Speaker: Sarah Raynor is an associate professor of Mathematics at Wake Forest University in Winston-Salem, NC

Friday, February 21, 2014 1:00pm - 2:00pm

Room: Government 102

Title: Stability of Soliton Solutions to the Korteweg-deVries Equation

Abstract: In this talk, we introduce the Korteweg-deVries Equation, a canonical nonlinear differential equation modelling the behavior of surface water waves in a long, narrow, shallow canal. We study special solutions to this equation, known as solitons. We are particularly interested in the stability of these special solutions. Several concepts of stability will be introduced and explained.

Bio: Sarah Raynor is an associate professor of Mathematics at Wake Forest University in Winston-Salem, NC. After finishing her Ph.D. at MIT in 2003, she spent a year at the Fields Institute in Toronto before beginning her position at Wake Forest. Dr. Raynor is interested in partial differential equations, and particularly in dispersive equations, which model wave phenomena in mathematical physics.

**Speaker: Juncheng Wei**

Date and Time: Thursday, February 13, 2014; 2:20pm - 3:35pm

Place: **Goverment **#227

**Title**: Geomterization Program of Semilinear Elliptic PDEs

Abstract: Understanding the entire solutions of nonlinear elliptic equations in $R^N$ such as $Δu + f(u) = 0$ is a basic problem in PDE research. This is the context of various classical results in literature like the Gidas-Ni-Nirenberg theorems on radial symmetry, Liouville type theorems, or the achievements around De Giorgi’s conjecture. In those results, the geometry of level sets of the solutions turns out to be a posteriori very simple (planes or spheres). On the other hand, problems of this form do have solutions with more interesting patterns, and the structure of their solution sets has remained mostly a mystery. A major aspect of our research program is to bring ideas from Differential Geometry into the analysis and construction of entire solutions for two important equations: (1) the Allen-Cahn equation and (2) the nonlinear Schrodinger equation. Though simple-looking, they are typical representatives of two classes of semilinear elliptic problems. The structure of entire solutions is quite rich. In this talk, we shall establish an intricate correspondence between the study of entire solutions of some scalar equations and the theories of minimal surfaces and constant mean curvature surfaces (CMC).

**Bio:** Prof. Juncheng Wei at University of British Columbia is a Canada Research Chair in Partial Differential Equations. He is a prolific researcher who has written over 280 articles since 1995. His paper coauthored with M. Del Pino and M. Kowalczyk (Annals of Mathematics 174 (2011)) resolved the De Giorgi’s Conjecture in dimensions greater than 8. For this and other significant works, he is invited to give a lecture at 2014 International Congress of Mathematicians.

**Title: Presentation about the Colonial One High Performance Cluster**

Speaker:Glen MacLachlan from the CCAS Office of Technology Services

Friday, January 31, at 1-2pm

Place: # Gov 102

A presentation about the Colonial One High Performance Cluster next , our standard colloquium time. Colonial One has recently been procured by the GW and everyone working for CCAS can now get access to it in order to perform large-scale computations. You can read more about it here:__http://columbian.gwu.edu/ots/hpc__

Glen's presentation will focus on how to start working with the Colonial One, which administrative and technical steps need to be completed, which types of queues exist, and so on. I've met with Glen today and he proposed to devote a portion of his time to a hands-on demonstration of the typical workflow involved in preparing and submitting cluster jobs.

## Fall 2013

Speaker: Dr. Max Alekseyev (University of South Carolina)

Date and Time: Monday, October 21, 2013 11:30am-12:30pm

Place: Monroe 267

Title: Challenges in Comparative Genomics: from Biological Problems to Combinatorial Algorithms (and back)

ABSTRACT: Recent large-scale sequencing projects fueled the comparative genomics studies and heightened the need for algorithms to extract valuable information about genetic and phylogenomic variations. Since the most dramatic genomic changes are caused by genome rearrangement events (which shuffle genomic material), it becomes extremely important to understand their mechanism and reconstruct the sequence of such events (evolutionary history) between genomes of interest. In this talk I shall describe several controversial and hotly debated topics in evolutionary biology (chromosome breakage models, mammalian phylogenomics, prediction of future rearrangements) and formulate related combinatorial challenges (rearrangement and breakpoint re-use analysis, ancestral genomes reconstruction problem). I shall further present my recent theoretic and algorithmic advances in addressing these challenges and their biological implications.

BIO: Dr. Max Alekseyev is an assistant professor at the Department of Computer Science and Engineering, University of South Carolina. He received a Ph.D. in computer science (2007) from the University of California, San Diego. In 2011, Dr. Alekseyev served as a scientific director for the Algorithmic Biology Laboratory at St. Petersburg Academic University, Russia, where he led development of genome assembler SPAdes. He received an NSF CAREER award in 2013. Dr. Alekseyev's research interests range from discrete mathematics (particularly, combinatorics and graph theory) to bioinformatics (particularly, comparative genomics and phylogenomics). His research is focused on the development and application of new methods of discrete mathematics to solve old and recently emerged open biological problems.

Speaker: Professor Anna Mazzuccato from Penn State

Date and Time: Friday, September 27, 2013 1pm

Place: Goverment #102

Title: Fluids flow at high Reynolds numbers Abstract: I will discuss how to model (incompressible) fluid flows at low viscosity or high Reynolds numbers. The Reynolds number measures the relative strength of convection with respect to dissipation. Such flows model turbulence phenomena. In particular, I will discuss whether enstrophy, the energy associated to vortices, is dissipated in the limit of vanishing viscosity in 2D flows. Enstrophy dissipation is a key aspect of the Kraichnan-Batchelor theory of turbulence. I will also discuss the zero-viscosity limit, that is, whether inviscid flows can approximate well viscous flows, in the presence of walls. No slip at rigid walls for viscous flows leads to the appearance of boundary layers. Layer separation and production of vorticity at walls is one of the most important mechanisms for forcing and mixing in flows.

Speaker: Jennifer Chubb (University of San Francisco)

Date and Time: Friday, September 20, 2013 1pm

Place: Government #102

Title: Quantum computing today

Abstract: The notion of quantum computing is not a very old one. It was Richard Feynman who, in 1981, first put forth the idea that computers designed to exploit the principles of quantum physics might have a leg up on classical computers. Since that time, loads of researchers have worked on

developing the theories of quantum computing, information, and cryptography, and many more are attempting to implement their discoveries. In this talk, we will survey the (brief) history of the subject, in addition to seeing something about what quantum computing is, and what makes quantum algorithms different from the programs we write every day for our classical machines.

Bio: Jennifer Chubb received her PhD in Mathematics from George Washington University in 2009 and is currently a member of the USF Math Department faculty. Her main research area is in mathematical logic specifically computability theory, and she has a particular interest in computable mathematical structures. Chubb also holds a BS in Physics & Applied Mathematics and an MS in Applied Mathematics from George Mason University. While pursuing those degrees, she worked in experimental physics and studied chaos and nonlinear dynamics. She is currently co-editing a volume on Logic and algebraic structures in quantum computing and quantum information.

Speaker: Dillon Mayhew, School of Mathematics, Statistics and Operations Research, Victoria University, Wellington, New Zealand.

Date and Time: Friday, September 13, 1pm

Place: Goverment #102

Title: Characterizing representable matroids

Abstract: Matroids abstract the notions of linear/geometric/algebraic dependence. More specifically, a matroid consists of a finite collection of points, and a distinguished family of dependent subsets. If we take a finite collection of vectors from a vector space, and distinguish the linearly dependent