Seminars and Colloquia Schedule

Exact Theory of Solitary Waves on Water with Surface Tension

Series: CDSNS Colloquium
Time: Monday, November 8, 2010 - 11:00 for 1 hour (actually 50 minutes)
Location: Skiles 169
Speaker: Shu-Ming Sun – Virginia Tech

The talk concerns the mathematical aspects of solitary waves (i.e. single hump waves) moving with a constant speed on water of finite depth with surface tension using fully nonlinear Euler equations governing the motion of the fluid flow. The talk will first give a quick formal derivation of the solitary-wave solutions from the Euler equations and then focus on the mathematical theory of existence and stability of two-dimensional solitary waves. The recent development on the existence and stability of various three-dimensional waves will also be discussed.

A General Framework for a Class of First Order Primal Dual Algorithms for Convex Optimization in Imaging Science

Series: Applied and Computational Mathematics Seminar
Time: Monday, November 8, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location: Skiles 002
Speaker: Ernie Esser – University of California, Irvine

In this talk, based on joint work with Xiaoqun Zhang and Tony Chan, we showhow to generalize the primal dual hybrid gradient (PDHG) algorithm proposedby Zhu and Chan to a broader class of convex optimization problems. A mainfocus will also be to survey several closely related methods and explain theconnections to PDHG. We point out convergence results for some modifiedversions of PDHG that have similarly good empirical convergence rates fortotal variation (TV) minimization problems. We also show how to interpretPDHG applied to TV denoising as a projected averaged gradient method appliedto the dual functional. We present some numerical comparisons of thesealgorithms applied to TV denoising and discuss some novel applications suchas convexified multiphase segmentation.

Homology torsion growth, hyperbolic volume, and Mahler measure

Series: Geometry Topology Seminar
Time: Monday, November 8, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location: Skiles 269
Speaker: Thang Le – GaTech

We prove a conjecture of K. Schmidt in algebraic dynamical system theory onthe growth of the number of components of fixed point sets. We also prove arelated conjecture of Silver and Williams on the growth of homology torsions offinite abelian covering of link complements. In both cases, the growth isexpressed by the Mahler measure of the first non-zero Alexander polynomial ofthe corresponding modules. In the case of non-ablian covering, the growth of torsion is less thanor equal to the hyperbolic volume (or Gromov norm) of the knot complement.

On evolution equations with fractional diffusion

Series: PDE Seminar
Time: Tuesday, November 9, 2010 - 15:05 for 1 hour (actually 50 minutes)
Location: Skiles 255
Speaker: Prof. Luis Silvestre – University of Chicago – luis@math.uchicago.edu

We prove a new Holder estimate for drift-(fractional)diffusion equations similar to the one recently obtained by Caffarelli and Vasseur, but for bounded drifts that are not necessarily divergence free. We use this estimate to study the regularity of solutions to either the Hamilton-Jacobi equation or conservation laws with critical fractional diffusion.

Combinatorics of the tropical Torelli map

Series: Tropical Geometry Seminar
Time: Wednesday, November 10, 2010 - 10:05 for 1 hour (actually 50 minutes)
Location: Skiles 114
Speaker: Melody Chan – UC Berkeley

The Torelli map, taking an algebraic curve to its Jacobian, has a tropical analogue, developed in recent work by Brannetti, Melo, and Viviani. I will discuss the tropical Torelli map, with a focus on combinatorics and computations in low genus. Metric graphs, positive semidefinite forms, and regular matroids all play a role.

Teaching jobs for mathematicians

Series: Research Horizons Seminar
Time: Wednesday, November 10, 2010 - 12:00 for 1 hour (actually 50 minutes)
Location: Skiles 171
Speaker: Richard Millman – CEISMC and School of Mathematics

Hosts: Yao Li and Ricardo Restrepo.

Dr. Millman is the Director of the Center for Education Integrating Science, Mathematics & Computing (CEISMC) and professor of mathematics at the Georgia Institute of Technology. He is a first hand expert in mathematics education and K-12 mathematics teacher education. Complementing the previous panel discussion on jobs in academia and industry, Dr. Milman will lead the discussion on teaching jobs.

Quartic Curves and their Bitangents

Series: Algebra Seminar
Time: Wednesday, November 10, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location: D.M. Smith Room 015
Speaker: Bernd Sturmfels – University of California, Berkeley

A smooth quartic curve in the projective plane has 36 representations as a symmetric determinant of linear forms and 63 representations as a sum of three squares. We report on joint work with Daniel Plaumann and Cynthia Vinzant regarding the explicit computation of these objects. This lecture offers a gentle introduction to the 19th century theory of plane quartics from the current perspective of convex algebraic geometry.

Weighted estimates for quasilinear equations with BMO coefficients on Reifenberg flat domains and their applications

Series: Analysis Seminar
Time: Wednesday, November 10, 2010 - 15:00 for 1 hour (actually 50 minutes)
Location: Skiles 269
Speaker: Nguyen Cong Phuc – LSU

We discuss a global weighted estimate for a class of divergence form elliptic operators with BMO coefficients on Reifenbergflat domains. Such an estimate implies new global regularity results in Morrey, Lorentz, and H\"older spaces for solutionsof certain nonlinear elliptic equations. Moreover, it can also be used to obtain a capacitary estimate to treat a measuredatum quasilinear Riccati type equations with nonstandard growth in the gradient.

Convex Algebraic Geometry

Series: School of Mathematics Colloquium
Time: Thursday, November 11, 2010 - 11:05 for 1 hour (actually 50 minutes)
Location: Skiles 269
Speaker: Bernd Sturmfels – UC Berkeley – bernd@math.berkeley.edu

Convex algebraic geometry is an emerging ﬁeld at the interface of convex optimizationand algebraic geometry. A primary focus lies on the mathematical underpinnings ofsemidefinite programming. This lecture oﬀers a self-contained introduction. Startingwith elementary questions concerning multifocal ellipses in the plane, we move on todiscuss the geometry of spectrahedra and orbitopes, and we end with recent resultson the convex hull of a real algebraic variety.

Kelly width

Series: Graph Theory Seminar
Time: Thursday, November 11, 2010 - 12:05 for 1 hour (actually 50 minutes)
Location: Skiles 114
Speaker: Nishad Kothari – CS, GT

Tree-width is a well-known metric on undirected graphs that measures how tree-like a graph is and gives a notion of graph decomposition that proves useful in fixed-parameter tractable (FPT) algorithm development. In the directed setting, many similar notions have been proposed - none of which has been accepted widely as a natural generalization of tree-width. Among the many suggested equivalent parameters were the "directed tree-width" by Johnson et al, and DAG-width by Berwanger et al and Odbrzalek. In this talk, I will present a recent paper by Hunter and Kreutzer, that defines another such directed width parameter, celled "kelly-width". I will discuss the equivalent complexity measures for graphs such as elimination orderings, k-trees and cops and robber games and study their natural generalizations to digraphs. I will discuss its usefulness by discussing potential applications including polynomial-time algorithms for NP-complete problems on graphs of bounded Kelly-width (FPT). I will also briefly discuss our work in progress (joint with Shiva Kintali) towards designing an approximation algorithm for Kelly Width.

Random matrices with independent log-concave columns

Series: Stochastics Seminar
Time: Thursday, November 11, 2010 - 15:05 for 1 hour (actually 50 minutes)
Location: Skiles 002
Speaker: Radoslaw Adamczak – University of Warsaw and Fields Institute

I will discuss certain geometric properties of random matrices with independent logarithmically concave columns, obtained in the last several years jointly with O. Guedon, A. Litvak, A. Pajor and N. Tomczak-Jaegermann. In particular I will discuss estimates on the largest and smallest singular values of such matrices and rates on convergence of empirical approximations to covariance matrices of log-concave measures (the Kannan-Lovasz-Simonovits problem).

A Minimax Problem in Almost Axisymmetric Flows

Series: SIAM Student Seminar
Time: Friday, November 12, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location: Skiles 255
Speaker: Mark Sedjro – School of Mathematics, Georgia Tech

Almost axisymmetric flows are derived from Boussinesq equations for incompressible fluids. They are supposed to capture special features in tropical cyclones. We establish an unusual minimax equality as the first step towards studying this challenging problem. I will review some basic techniques of the calculus of variations.

Non-commutative Geometry IV - Crossed products: the noncommutative torus

Series: Geometry Topology Working Seminar
Time: Friday, November 12, 2010 - 14:00 for 2 hours
Location: Skiles 171
Speaker: Jean Bellissard – Ga Tech

Note this is a 2 hour talk.

In this lecture, we will look at the notion of crossed product by a group action. The example of the non commutative torus will be considered in detail. The analog of vector fields, vector bundle and connection will be introduced from this example. Some example of connection will be described and the curvature will be computed.

Sequences of problems, matrices, and solutions

Series: Other Talks
Time: Friday, November 12, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location: Klaus 1447
Speaker: Eric de Sturler – Department of Mathematics, Virginia Tech – sturler@vt.edu

In a wide range of applications, we deal with long sequences of slowly changing matrices or large collections of related matrices and corresponding linear algebra problems. Such applications range from the optimal design of structures to acoustics and other parameterized systems, to inverse and parameter estimation problems in tomography and systems biology, to parameterization problems in computer graphics, and to the electronic structure of condensed matter. In many cases, we can reduce the total runtime significantly by taking into account how the problem changes and recycling judiciously selected results from previous computations. In this presentation, I will focus on solving linear systems, which is often the basis of other algorithms. I will introduce the basics of linear solvers and discuss relevant theory for the fast solution of sequences or collections of linear systems. I will demonstrate the results on several applications and discuss future research directions.

Cycles in sparse graphs

Series: Combinatorics Seminar
Time: Friday, November 12, 2010 - 14:05 for 1 hour (actually 50 minutes)
Location: Skiles 255
Speaker: Jacques Verstraete – University of California, San Diego

**PLEASE NOTE SPECIAL TIME**

Let C(G) denote the set of lengths of cycles in a graph G. In this talk I shall present the recent proofs of two conjectures of P. Erdos on cycles in sparse graphs. In particular, we show that if G is a graph of average degree d containing no cycle of length less than g, then as d -> \infty then |C(G)| = \Omega(d^{\lfloor (g - 1)/2 \rfloor}). The proof is then adapted to give partial results on three further conjectures of Erdos on cycles in graphs with large chromatic number. Specifically, Erd\H{o}s conjectured that a triangle-free graph of chromatic number k contains cycles of at least k^{2 - o(1)} different lengths as k \rightarrow \infty. We define the {\em independence ratio} of a graph G by \iota(G) := \sup_{X \subset V(G)} \frac{|X|}{\alpha(X)}, where \alpha(X) is the independence number of the subgraph of G induced by X. We show that if G is a triangle free graph and \iota(G) \geq k, then |C(G)| = \Omega(k^2 \log k). This result is sharp in view of Kim's probabilistic construction of triangle-free graphs with small independence number. A number of salient open problems will be presented in conclusion. This work is in part joint with B. Sudakov. Abstract

Georgia Institute of Technology College of Sciences

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