All Seminars & Colloquia
The magic behind quantum computing: Square Root of (-1)
Jerzy Kocik, Southern Illinois University
Sunday, 12/4/2011, 7:00pm - Thursday, 1/30/2014, 11:59pm
Abstract: The soothingly graspable formalism of Quantum Mechanics (comprising of quite elementary concepts of linear algebra) contrasts strongly with profound interpretational problems of this formalism. Hence, not to discourage a reader, most expositions quickly move to the formalism and technical description of quantum algorithms, leaving a mathematician not trained in physics somewhat perplexed. This gentler introduction to quantum computing honestly presents the strangeness of quantum nature of reality and is aimed to a non-physicist who ponders why quantum computers are possible.
Homology of a Small Category with Functor Coefficients and Barycentric Subdivision.
Speaker: Jing Wang (GWU)
Thursday, 12/1/2011, 6:00pm - 11:59pm
Abstract: We will introduce the definition of homology of a small category with functor coefficients and then compare two different homologies when we take the category of a simplical complex. We analyze the classical result that barycentric subdivision preserves homology and generalize it to the context of a small category with coefficients in a functor to R-modules.
Character Varieties of surfaces as completely integrable systems
Adam Sikoa, University at Buffalo.
Tuesday, 11/22/2011, 4:10pm - 11:59pm
Abstract: It is known that the trace functions of a maximal set of disjoint simple closed curves on a closed surface make its SU(2)-character variety into an (almost) completely integrable dynamical system. We prove an analogous statement for all rank 2 Lie groups. We will discuss the possible generalizations of this result to higher ranks and,
if time permits, its applications to quantization of character varieties.
Adiabatic quantum computing: equivalence with quantum computing
William de la Cruz, Center of Research and Advanced Studies of IPN, Mexico Cit
Thursday, 11/3/2011, 5:00pm - 11:59pm
Abstract: The adiabatic quantum computing (AQC) was originally introduced to solve optimization problems by constructing two Hamiltonian operators where the first one is easy to prepare and the second one codifies the solution of the considered problem. Van Dam et al. (2001) proved that AQC performs universal computing by showing that the adiabatic evolution can be simulated with quantum circuits of polynomial size. In this talk we review van Dam's construction in order to understand the complexity of AQC and its limitations
The Bonahon Metric and Topology
Speaker: Mark Kidwell (U.S. Naval Academy and GWU)
Wednesday, 10/26/2011, 10:06pm - 11:59pm
Abstract: In his book “Low-Dimensional Geometry: From Euclidean Spaces to Hyperbolic Knots”, Francis
Bonahon considers no structure more abstract than a metric space. He then needs to define a metric
on a quotient space, such as the torus obtained by identifying opposite sides of a rectangle. We explore
some quirky consequences of Bonahon’s definition of a (pseudo)-metric on a quotient space. We then
answer the question: does the topology defined by the Bohahon metric on a quotient space coincide
with the quotient topology?
Mochizuki's quandle 3-cocycle invariant of links S^3 is one of the Dijkgraaf-Witten invariants
Speaker: Takefumi Nosaka, RIMS at Kyoto University
Friday, 10/7/2011, 9:11pm - 11:59pm
Abstract: Let p be an odd prime, and \phi the Mochizuki 3-cocycle of "the
dihedral quandle" of order p. Using the 3-cocycle, Carter-Kamada-Saito
combinatorially defined a shadow quandle cocycle invariant of links in
S^3. Let M_L be the double covering branched along a link L. Our main
result is that the cocycle invariant of L equals the Dijkgraaf-Witten
invariant of M_L with respect to the group Z/pZ. We further compute
Dijkgraaf-Witten invariants of some 3-manifolds. In this talk, I
Jointly with Math Colloquium and Applied Math Seminar: Topological Quantum Computation
Zhenghan Wang, Microsoft Research
Thursday, 10/6/2011, 7:45pm - 11:59pm
Modified right-angled Artin groups.
Speaker: Noel Brady, NSF and University of Oklahoma
Tuesday, 9/27/2011, 3:00pm - 11:59pm
Abstract: The family of right-angled Artin groups (RAAGs) interpolates between the family of finitely generated free groups on one hand and the family of finitely generated free abelian groups on the other. RAAGs are easy to define (their definition can be encoded in a finite graph) and have very nice geometric and topological properties (they have non-positively curved cubical classifying spaces). There is a standard map from a RAAG to the integers, and the topological properties of the kernel is reflected in the topology of the clique complex associated to the defining finite graph.
Adiabatic quantum computing: application to NP-hard problems
William de la Cruz, Center of Research and Advanced Studies of IPN, Mexico City
Thursday, 9/22/2011, 5:04pm - 11:59pm
Abstract: Adiabatic quantum computing (AQC) have been shown to be a useful tool for approximating optimization problems. We show an experimental study of the AQC applied to the MaxSat problem.
Homology of Distributive Lattice
Jozef Przytycki, GW
Tuesday, 9/20/2011, 3:14pm - 11:59pm
Abstract: While homology theory of associative structures, such as groups and rings, was extensively studied in the past, beginning with the work of Hopf, Eilenberg, and Hochschild, homology of non-associative distributive structures, such as quandles, has been neglected until recently. Distributive structures have been studied for a long time. In 1880, C.S. Peirce emphasized the importance of (right-) self-distributivity in algebraic structures. However, homology for these universal algebras was introduced only sixteen years ago by Fenn, Rourke, and Sanderson.