All Seminars & Colloquia
C.e. and co-c.e. structures and their isomorphism
Valentina Harizanov, GWU
Thursday, 11/21/2013, 9:49pm - 11:59pm
Abstract: Computable structures and their isomorphisms have been studied extensively in computable structure theory. Here, we investigate the complexity of isomorphisms of computably enumerable (c.e.) and co-computably enumerable (co-c.e.) structures with a single equivalence relation and structures with a single injective function. This is joint work with Doug Cenzer and Jeff Remmel.
Finite Difference Methods for Nonlinear Elliptic Equations with Application to Optimal Transport
Speaker: Brittney Froese, University of Texas, Austin.
Friday, 11/8/2013, 6:00pm - 11:59pm
Abstract: We describe the use of finite difference methods for solving nonlinear elliptic partial differential equations (PDEs). We show that simple techniques, which work for linear equations, may fail for nonlinear equations. We describe a framework for developing convergent finite difference methods for nonlinear degenerate elliptic equations.
Connections between Complex Dynamics and Ergodic Theory
Speaker: Jane Hawkins - NSF and UNC Chapel Hill
Friday, 10/25/2013, 7:00pm - 11:59pm
Abstract: While the Julia sets of rational maps of the sphere usually conjure up images of interesting topological features, they also possess many measure theoretic properties worth studying. Every rational map has several distinguished invariant measures: one is the unique invariant measure of maximal entropy and the other is a more geometric measure called conformal measure. Only in rare instances do they coincide. There is often a nonatomic invariant measure equivalent to conformal measure, sometimes infinite and sometimes finite. We give families of examples of these.
Contact Lenses and Tear Film Evolution
Speaker: Matthew Gerhart. (George Mason University)
Thursday, 10/24/2013, 7:00pm - 11:59pm
Abstract: The tears that surround your eye are an integral part of proper eye function. Dry-eye is a condition when the tear film thins to a point where the tear film loses its ability function properly. The use of contact lenses in some patients can increase the likelihood of this condition. Through this talk, I will introduce the mechanics of the tear film (Navier-Stokes Equations) and the mechanics of the motion of the tears in the contact lens (Darcy's Equations), both of which are coupled together, in a thin film, lubrication theory setting.
Recent Topics in Integro-Differential Equations
Speaker: Russell Schwab, Michigan State University.
Friday, 10/18/2013, 5:00pm - 11:59pm
Abstract: We will give a brief overview of some recent results on the analysis of elliptic integro-differential equations (which are the natural class of generators of Markov processes) from the perspective of nonlinear elliptic equations. We will discuss some regularity results and possibly some applications to Neumann homogenization.
Orderable groups and their spaces of order
Speaker: Mietek Dabkowski, University of Texas at Dallas
Friday, 10/11/2013, 8:30pm - 11:59pm
Abstract: A left order on a group G is a linear order of the domain of G, which is left-invariant under the group operation. Right orders and bi-orders are defined similarly. We investigate computability theoretic and topological properties of spaces of left orders on computable orderable groups. Topological properties of spaces of orders on groups were first studied by A. Sikora who showed that for free abelian groups of finite rank n >1 the space of orders is homeomorphic to the Cantor set.
Norm Approximation in Ergodic Theory
Speaker: Joseph Rosenblatt, University of Illinois, Urbana
Friday, 10/11/2013, 7:00pm - 11:59pm
Abstract: Classical ergodic averages give good norm approximations, but these averages are not necessarily giving the best norm approximation among all possible averages.
Topological transitivity for interval map
Speaker: Robbie Robinson, GWU
Friday, 10/4/2013, 8:00pm - 11:59pm
Abstract: Topological transitivity is one of the three pillars of Bob Devaney's definition of chaos, along with sensitive dependence on initial conditions, and dense periodic points. In this talk we study the dynamics of piecewise continuous, piecewise monotonic maps of the interval. We discuss several notions of topological transitivity, including an unusual one from the 1960's due to Bill Parry, and discuss the inter-relations between these various notions.
Orderings of algebraic structures on trees
Jennifer Chubb, University of San Francisco
Thursday, 9/19/2013, 9:30pm - 11:59pm
Abstract: A partial left ordering or bi-ordering of an algebraic structure is a partial ordering of the elements of the structure, which is invariant under the structure acting on itself on the left or, respectively, both on the left and on the right. I will discuss algorithmic properties of the orderings admitted by a computable structure, and consider some general questions
Quandles and codimension two embeddings
Jozef Przytycki, GWU
Thursday, 9/5/2013, 9:30pm - 11:59pm
Abstract: Distributivity has been an integral part of logic for a long time. An attempt to decouple them in linear logic applied to quantum mechanics was not successful. Distributivity in topology is a more recent development and can be dated to the PhD dissertation of Joyce in 1979, in which quandles were applied to knot theory. The next push came with construction of homology theory for quandles by Fenn, Rourke, and Sanderson (between 1990 and 1995). In 1998, Carter, Kamada, and Saito