Seminars and Colloquia by Series

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 SedjroSchool 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.

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 AdamczakUniversity 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).

Kelly width

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

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 SturmfelsUC Berkeley
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.

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 PhucLSU
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.

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 SturmfelsUniversity 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.

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 MillmanCEISMC and School of Mathematics

Please Note: 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.

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 ChanUC 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.

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 SilvestreUniversity of Chicago
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.

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 LeGaTech
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.

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