Distinguished Women in Mathematics Lecture Series Home Upcoming Speakers Past Speakers Horton-Jacobs/Wins Lecture Series AWM - UT Student Chapter UT Math Department Contact Us Past Speakers Spring 2013 This semester the talks and preparatory lectures were organized by Allison Moore, Verónica Quítalo, Alice Mark, Laura Starkston, Laura Fredrickson, Maja Taskovic, and Karin Knudson. Rachel Pries, Colorado State University Topic: Arlgebraic Geometry and Number Theory Title: The boundary of the moduli space of curves and arithmetic applications Abstract: This talk is about the pivotal role played by topology and geometry in the proofs of arithmetic results about curves in positive characteristic. I will describe some background about the boundary of the moduli space of curves and about the action of fundamental groups on torsion points of abelian varieties. These were key concepts used in results such as Deligne and Mumford's proof of the irreducibility of the moduli space of curves and Harbater and Raynaud's proof of Abhyankar's Conjecture about Galois covers of curves. I will finish by talking about how these concepts were used in my result with Achter about the monodromy of the p-rank strata of the moduli space of curves. The talk will include a lot of background and motivating examples. Fall 2012 This semester the talks and preparatory lectures were organized by Allison Moore, Verónica Quítalo, Alice Mark, Laura Starkston, Laura Fredrickson, Maja Taskovic, and Karin Knudson. Ingrid Daubechies, Duke University Topic: Applied Analysis Title: The talk will describe wavelets, a mathematical tool used for the analysis and compression of images (including for digital cinema). Then it will go on to discuss how they have been used recently for the study of paintings by e.g. Van Gogh, Goossen van der Weyden, Gauguin and Giotto. This presentation was also the Horton-Jacobs/WINS Lecture for the 2012 - 2013 year.  Irene Fonseca, Carnegie Mellon University Topic: Applied Analysis Title: Variational Methods in Materials and Image Processing Abstract: Several questions in applied analysis motivated by issues in computer vision, physics, materials sciences and other areas of engineering may be treated variationally leading to higher order problems and to models involving lower dimension density measures. Their study often requires state-of-the-art techniques, new ideas, and the introduction of innovative tools in partial differential equations, geometric measure theory, and the calculus of variations. In this talk it will be shown how some of these questions may be reduced to well understood first order problems, while in others the higher order terms play a fundamental role. Applications to phase transitions, to the equilibrium of foams under the action of surfactants, imaging, micromagnetics, thin films, and quantum dots will be addressed. Spring 2012 This semester the talks and preparatory lectures were organized by Allison Moore, Verónica Quítalo, Alice Mark, Laura Starkston, Laura Fredrickson, Maja Taskovic, and Michelle Chu. Gordana Matic, The University of Georgia Topic: Low Dimensional Topology Title: Contact Invariant in Sutured Floer Homology Abstract: In the 70's Thurston and Winkelnkemper showed that an open book decomposition of a 3-manifold can be used to construct a contact structure. In 2000 Giroux showed that every contact structure on a 3-manifold can be obtained from that process. Ozsvath and Szabo used this fact to define an invariant for a contact structure in their Heegaard Floer Homology, providing an important new tool to study contact 3-manifolds. We will describe a simple way to visualize this contact invariant and talk about applications and generalizations. In particular, when the contact manifold has boundary we can define an invariant in Sutured Floer Homology, a variant of Heegard Floer homology for a manifold with boundary due to Andras Juhasz, and use it to answer some questions about fillability of contact structures. This presentation was also the Horton-Jacobs/WINS Lecture for the 2011 - 2012 year.  Spring 2011 This semester the talks and preparatory lectures were organized by Orit Davidovich, Brandy Guntel, Karin Knudson, Alice Mark, Allison Moore, Verónica Quítalo, and Sarah Rich. Alice Chang, Princeton University Topic: Geometry and PDE Title: Fully non-linear PDE in conformal geometry Abstract: I will discuss a class of integral conformal invariants and the role they have played in a special case of a uniformization theorem for 4-spheres. The main tool is a study of fully non-linear elliptic PDE of Monge-Amphere type. I will also discuss the connection of these conformal invariants to geometric invariants on conformal compact Einstein manifolds in the CFT/ADS setting. This presentation was also the Horton-Jacobs/WINS Lecture for the 2010 - 2011 year.  Winnie Li, Pennsylvania State University Topic: Number Theory Title: Zeta Functions in Combinatorics and Number Theory Abstract: Roughly speaking, a zeta function is a counting function. Well-known zeta functions in number theory include the Riemann zeta function and the zeta function attached to an algebraic variety defined over a finite field. The former counts integral ideals of a given norm, while the latter counts solutions over a finite field. A combinatorial zeta function counts tailless geodesic cycles of a given length in a finite simplicial complex. One-dimensional complexes are graphs; attached to graphs are the well-studied Ihara zeta functions. Zeta functions attached to 2-dimensional complexes are recently obtained by myself and students Ming-Hsuan Kang and Yang Fang by considering finite quotients of the Bruhat-Tits buildings associated to SL(3) and Sp(4) over a p-adic field. The purpose of this talk is to show connections between combinatorics and number theory, using zeta functions as a theme. We shall give closed form expressions of the combinatorial zeta functions mentioned above, and compare their features, in particular, the role of the Riemann Hypothesis, with those of the zeta functions for varieties over finite fields. Spring 2010 This semester the talks and preparatory lectures were organized by Orit Davidovich, Brandy Guntel, Kim Hopkins and Heather Van Ligten. Antonella Grassi, University of Pennsylvania Topic: Algebraic Geometry Title: A, D, E (B and C etc.) Abstract: I will give an overview of certain singularities arising in algebraic geometry (like in elliptic fibrations) and in other contexts including the physics of string theory. Kristin Lauter, Microsoft Research Topic: Cryptography Title: Expander graphs and their applications to cryptography Abstract: Hash functions are ubiquitous in cryptography: they are used in encryption, key exchange, signatures and more. We will review these functions and discuss the requirement that they be resistant to collision. We will then recall the notion of expander graphs and explain how to construct collision-resistant hash functions from graphs in which it is hard to find cycles. Finally, we will discuss a family of graphs that were constructed by A. Pizer: the vertices of Pizer's graphs are supersingular elliptic curves in characteristic p, while the edges are n-isogenies between supersingular elliptic curves. (Here, n is a fixed integer prime to p.) For Pizer's graphs, cycles are hard to find because it is difficult to compute isogenies between supersingular elliptic curves. 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. Dusa McDuff, Columbia University Topic: Symplectic Geometry Title: Symplectic embedding of ellipsoids and continued fractions This presentation was also the Horton-Jacobs/WINS Lecture for the 2009 - 2010 year.  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.