Distinguished Women in Mathematics Lecture Series Home Upcoming Speakers Past Speakers Horton-Jacobs/Wins Lecture Series UT Math Department Contact Us Past Speakers Fall 2009 This semester the talks and preparatory lectures were organized by Aynur Bulut, Orit Davidovich, Brandy Guntel, Kim Hopkins, and Heather Van Ligten, and the invited speakers were Susan Friedlander and Dusa McDuff. Susan Friedlander, University of Southern California Topic: Mathematical Fluid Dynamics Title: Instabilities in fluid motion Abstract: Instabilities in fluid motion are ubiquitous and yet instabilities come in various "flavors". The partial differential equations of fluid dynamics are very challenging nonlinear systems. A classical approach to detecting instabilities is to study the spectral problem associated with the linearized equations. We will discuss how in some situations it is possible to prove that linear instability implies instability for the full nonlinear equations. Examples where this can be proved include the cases of the 2-dimensional Euler equations, the 3-dimensional Navier-Stokes equation and an interesting equation arising in oceanography called the surface quasi-geostrophic equation. Spring 2009 This semester the talks and preparatory lectures were organized by Orit Davidovich, Brandy Guntel, Adriana Salerno, and Elizabeth Thoren, and the invited speakers were Abigail Thompson, Ruth Charney, Gigliola Staffilani.  Abigail Thompson, University of California, Davis Topic Knot Theory; 3-Manifolds Title: The stabilization problem for 3-manifolds Abstract: Surprisingly, any closed orientable 3-manifold can be split into two simple pieces, called handlebodies. The simplicity stops there, sadly, and understanding the relationships among different splittings of the same manifold is an ongoing task. I'll describe the stabilization problem for such splittings of 3-manifolds, and some recent examples which underscore the difficulty of the problem. This is joint work with Joel Hass and William Thurston. Ruth Charney, Brandeis University Topic: Geometric Group Theory Title: Groups and their automorphisms, from free to free abelian. Abstract: Automorphism groups of free groups and free abelian groups play an important role in mathematics. Surprisingly, they share much in common. Between free groups and free abelian groups lies a large class of groups known as right-angled Artin groups. We investigate which of these properties hold for automorphisms of all such groups. This presentation was the first in the Horton-Jacobs/WINS Lecture Series. Gigliola Staffilani, Massachusetts Institute of Technology Topic: Partial Differential Equations and Harmonic Analysis Title: On Dispersive Waves Fall 2008 This semester the talks and preparatory lectures were organized by Orit Davidovich, Brandy Guntel, Adriana Salerno, and Elizabeth Thoren, and the invited speakers were Eleny Ionel and Catharina Stroppel. Eleny Ionel, Universität Bonn Topic : Symplectic Geometry Title: Gromov-Witten invariants and symplectic degenerations Abstract: The moduli spaces of holomorphic curves have an intriguing structure, which is reflected in the structure of the Gromov-Witten invariants. One way to get a glimpse into it is to follow what happens to the moduli spaces during (symplectic) degenerations, like those coming from a (generalized) symplectic sum. This in particular involves extending the notion of Gromov-Witten invariants to (mildly) singular settings. I will survey what is known so far about this problem, mention some of its applications and discuss some of the current open problems. Catharina Stroppel, Universität Bonn Topic: Representation Theory Title: Crystal bases, Hecke algebras and equivalences of categories Abstract: The classical Schur-Weyl duality relates modules for the general linear Lie algebra with modules over the symmetric group. I first explain a higher level version of this where cyclotomic versions of degenerate Hecke algebras occur. Afterwords I will indicate how this picture can be categorified. The combinatorics of crystal graphs plays an important role here. Finally I want to illustrate in two examples how this setup can be used to derive equivalences of categories where the aforementioned Hecke algebras play the key role. This was a joint presentation with the GRASP Colloquium and they have posted a video of the lecture. Spring 2008 This semester the talks and preparatory lectures were organized by Orit Davidovich, Adriana Salerno, and Andrea Young, and the invited speakers were Vyjayanthi Chari, Panagiota Dakalopoulos, and Paula Tretkoff. Vyjayanthi Chari, University of California, Riverside Topic: Representation Theory Title: Affine Algebras, Quivers and Koszulity Abstract: The representation theory of the affine Lie algebras and their quantum analogs have been intensively studied in recent years. The subject has connections with number theory, topology and mathematical physics. The study of finite dimensional representations of these algebras is surprisingly complex, and is related to the mathematical structures which arise from solvable models in statistical mechanics. There are a number of different approaches to this study: a geometric approach via quiver varieties, a combinatorial approach using crystal bases and an algebraic approach using the classical methods of representation theory. In this talk, I will discuss some of these ideas and formulate some recent results which establish a connection between these representations and those of finite dimensional associative algebras. Panagiota Dakalopoulos, Columbia University Topic: Geometric Flow Title: Surface Evolution under Curvature Flows: Existence and Optimal Regularity Abstract: We will discuss the evolution of a hyper-surface in R^{n+1} by functions of its principal curvatures. Typical examples include the Mean Curvature flow, the Gauss Curvature flow, the Inverse Mean Curvature flow and the Harmonic Mean Curvature flow. These flows are described by non-linear parabolic equations for the local embedding map. We will discuss the existence and optimal regularity for such equations as well as the formation of singularities in certain cases. Paula Tretkoff, Texas A&M University Topic: Number Theory Title: Aspects of transcendental number theory Abstract: We discuss an assortment of results on the transcendence properties of special values of modular and hypergeometric functions. The emphasis will be on open problems and connections with other branches of mathematics.