Seminars and Colloquia by Series

Global Weak Solutions for an Incompressible Charged Fluid with Multi-Scale Couplings - Initial-Boundary Value Problem

Series
PDE Seminar
Time
Tuesday, April 7, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
Location
Skiles 255
Speaker
Joseph Jerome Northwestern University, Evanston
The Cauchy problem for the Poisson-Nernst-Planck/Navier-Stokes model was investigated by the speaker in [Transport Theory Statist. Phys. 31 (2002), 333-366], where a local existence-uniqueness theory was demonstrated, based upon Kato's framework for examining evolution equations. In this talk, the existence of a global distribution solution is proved to hold for the model, in the case of the initial-boundary value problem. Connection of the above analysis to significant applications is discussed. The solution obtained is quite rudimentary, and further progress would be expected in resolving issues of regularity.

Entropy and Sumsets

Series
Combinatorics Seminar
Time
Tuesday, April 7, 2009 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Adam MarcusYale University
The entropy function has a number of nice properties that make it a useful counting tool, especially when one wants to bound a set with respect to the set's projections. In this talk, I will show a method developed by Mokshay Madiman, Prasad Tetali, and myself that builds on the work of Gyarmati, Matolcsi and Ruzsa as well as the work of Ballister and Bollobas. The goal will be to give a black-box method for generating projection bounds and to show some applications by giving new bounds on the sizes of Abelian and non-Abelian sumsets.

Dispersive properties of surface water waves

Series
CDSNS Colloquium
Time
Monday, April 6, 2009 - 16:30 for 2 hours
Location
Skiles 255
Speaker
Vera Mikyoung HurMIT
I will speak on the dispersive character of waves on the interface between vacuum and water under the influence of gravity and surface tension. I will begin by giving a precise account of the formulation of the surface water-wave problem and discussion of its distinct features. They include the dispersion relation, its severe nonlinearity, traveling waves and the Hamiltonian structure. I will describe the recent work of Hans Christianson, Gigliola Staffilani and myself on the local smoothing effect of 1/4 derivative for the fully nonlinear problem under surface tension with some detail of the proof. If time permits, I will explore some open questions regarding long-time behavior and stability.

Density of isoperimetric spectra

Series
Geometry Topology Seminar
Time
Monday, April 6, 2009 - 16:00 for 1 hour (actually 50 minutes)
Location
Emory, W306 MSC (Math and Science Center)
Speaker
Noel BradyUniversity of Oklahoma

Please Note: Joint meeting at Emory

A k--dimensional Dehn function of a group gives bounds on the volumes of (k+1)-balls which fill k--spheres in a geometric model for the group. For example, the 1-dimensional Dehn function of the group Z^2 is quadratic. This corresponds to the fact that loops in the euclidean plane R^2 (which is a geometric model for Z^2) have quadratic area disk fillings. In this talk we will consider the countable sets IP^{(k)} of numbers a for which x^a is a k-dimensional Dehn function of some group. The situation k \geq 2 is very different from the case k=1.

Contact geometry, open books and monodromy

Series
Geometry Topology Seminar
Time
Monday, April 6, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Emory, W306 MSC (Math and Science Center)
Speaker
John EtnyreSchool of Mathematics, Georgia Tech

Please Note: Joint meeting at Emory

Recall that an open book decomposition of a 3-manifold M is a link L in M whose complement fibers over the circle with fiber a Seifert surface for L. Giroux's correspondence relates open book decompositions of a manifold M to contact structures on M. This correspondence has been fundamental to our understanding of contact geometry. An intriguing question raised by this correspondence is how geometric properties of a contact structure are reflected in the monodromy map describing the open book decomposition. In this talk I will show that there are several interesting monoids in the mapping class group that are related to various properties of a contact structure (like being Stein fillable, weakly fillable, . . .). I will also show that there are open book decompositions of Stein fillable contact structures whose monodromy cannot be factored as a product of positive Dehn twists. This is joint work with Jeremy Van Horn-Morris and Ken Baker.

Graph Patches (Partial Sparsifiers) and their applications to designing cost-effective, expanding networks

Series
Combinatorics Seminar
Time
Friday, April 3, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Alexandra KollaUC Berkeley
I will present an approximation algorithm for the following problem: Given a graph G and a parameter k, find k edges to add to G as to maximize its algebraic connectivity. This problem is known to be NP-hard and prior to this work no algorithm was known with provable approximation guarantee. The algorithm uses a novel way of sparsifying (patching) part of a graph using few edges.

Small random perturbation of ODE around hyperbolic points

Series
SIAM Student Seminar
Time
Friday, April 3, 2009 - 12:30 for 2 hours
Location
Skiles 269
Speaker
Sergio AlmadaSchool of Mathematics, Georgia Tech
Suppose b is a vector field in R^n such that b(0) = 0. Let A = Jb(0) the Jacobian matrix of b at 0. Suppose that A has no zero eigenvalues, at least one positive and at least one negative eigenvalue. I will study the behavior of the stochastic differential equation dX_\epsilon = b(X_\epsilon) + \epsilon dW as \epsilon goes to 0. I will illustrate the techniques done to deal with this kind of equation and make remarks on how the solution behaves as compared to the deterministic case.

The power of LP and SDP hierarchies and integrality gaps through semidefinite programming duality

Series
ACO Student Seminar
Time
Thursday, April 2, 2009 - 13:30 for 2 hours
Location
Skiles 255
Speaker
Alexandra KollaUC Berkeley
In the first part of the talk, I am going to give an introduction and overview of linear and semidefinite programming hierarchies. I will mostly review known integrality gaps for such programs and try to give an intuition of why we currently lack strong techniques for designing rounding algorithms. In the second part of the talk I will focus on the stronger SDP Lasserre hierarchy. In contrast with the previous LP and SDP hierarchies, very few examples of integrality gap instances are known to date. I will present a recent technique for designing such instances and discuss open problems in the area.

Compensated compactness and isometric embedding

Series
School of Mathematics Colloquium
Time
Thursday, April 2, 2009 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Marshall SlemrodDepartment of Mathematics, University of Wisconsin
In this talk I will outline recent results of G-Q Chen, Dehua Wang, and me on the problem of isometric embedding a two dimensional Riemannian manifold with negative Gauss curvature into three dimensional Euclidean space. Remarkably there is very pretty duality between this problem and the equations of steady 2-D gas dynamics. Compensated compactness (L.Tartar and F.Murat) yields proof of existence of solutions to an initial value problem when the prescribed metric is the one associated with the catenoid.

The Linear Complementarity Problem, Lemke Algorithm, Perturbation, and the Complexity Class PPAD

Series
ACO Colloquium
Time
Wednesday, April 1, 2009 - 16:30 for 2 hours
Location
Klaus 1116E
Speaker
Ilan AdlerUC Berkeley
One of the most interesting aspects of the Linear Complementarity Problem (LCP) is its range from relatively easy problems such as linear and convex quadratic programming problems to NP-hard problems. A major effort in LCP theory had been the study of the Lemke algorithm, a simplex-like algorithm which is guaranteed to terminate in finite number of iterations but not necessarily with a solution (or a certificate that no solution exists). Over the years, many subclasses of LCP were proven to be workable by the Lemke algorithm. Those subclasses were often characterized as ‘nice’ even when no polynomial upper bound for the algorithm was known to exist. In fact, for most of these classes, instances with exponential number of steps had been discovered. In this talk, I’ll discuss the close connection between these classes and the PPAD (Polynomial-time Parity Argument Directed) complexity class. The discovery that computing Nash equilibrium (which is an LCP) is PPAD complete is particularly significant in analyzing the complexity of LCP. I’ll also discuss the LCP reduction-via-perturbation technique and its relation to the PPAD class and the Lemke Algorithm. This talk is based on a joint work with Sushil Verma.

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