Seminars and Colloquia by Series

Dilute Quantum Gases

Series
Math Physics Seminar
Time
Monday, January 12, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Robert SeiringerPrinceton University
We present an overview of mathematical results on the low temperature properties of dilute quantum gases, which have been obtained in the past few years. The discussion includes, for instance, results on the free energy in the thermodynamic limit, and on Bose-Einstein condensation, Superfluidity and quantized vortices in trapped gases. All these properties are intensely being studied in current experiments on cold atomic gases. We will give a brief description of the mathematics involved in understanding these phenomena, starting from the underlying many-body Schroedinger equation.

Electro-Optics for Beach Zone Observation

Series
Applied and Computational Mathematics Seminar
Time
Monday, January 12, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Frank CrosbyNaval Surface Warfare Center, Panama City
Several imaging innovations have been designed to find hidden objects in coastal areas of entry, such as beaches and ports. Each imaging device is designed to exploit particular distinguishing characteristics. This talk with cover using a tunable multi-spectral camera for polarization based detection and object identification with a flash LIDAR camera that produces three-dimensional imagery.

Some random matrix problems in high-dimensional statistics

Series
Job Candidate Talk
Time
Thursday, January 8, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Noureddine El KarouiUC Berkeley
It is now increasingly common in statistical practice to encounter datasets in which the number of observations, n, is of the same order of magnitude as the number of measurements, p, we have per observation. This simple remark has important consequences for theoretical (and applied) statistics. Namely, it suggests on the theoretical front that we should study the properties of statistical procedures in an asymptotic framework where p and n both go to infinity (and p/n has for instance a finite non-zero limit). This is drastically different from the classical theory where p is held fixed when n goes to infinity. Since a number of techniques in multivariate statistics rely fundamentally on sample covariance matrices and their eigenvalues and eigenvectors, the spectral properties of large dimensional covariance matrices play a key role in such "large n, large p" analyses. In this talk, I will present a few problems I have worked on, concerning different aspects of the interaction between random matrix theory and multivariate statistics. I will discuss some fluctuation properties of the largest eigenvalue of sample covariance matrices when the population covariance is (fairly) general, talk about estimation problems for large dimensional covariance matrices and, time permitting, address some applications in a classic problem of mathematical finance. The talk will be self-contained and no prior knowledge of statistics or random matrix theory will be assumed.

Polynomial mappings

Series
Job Candidate Talk
Time
Wednesday, January 7, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Mike ZieveIAS
I will present properties of polynomials mappings and generalizations. I will first describe all polynomials f and g for which there is a complex number c such that the orbits {c, f(c), f(f(c)), ...} and {c, g(c), g(g(c)), ...} have infinite intersection. I will also discuss a common generalization of this result and Mordell's conjecture (Faltings' theorem). After this I will move to polynomial mappings over finite fields, with connections to curves having large automorphism groups and instances of a positive characteristic analogue of Riemann's existence theorem.

An Approach to the Gaussian Correlation Conjecture

Series
Stochastics Seminar
Time
Friday, December 12, 2008 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Joel ZinnTexas A&M University
In this approach to the Gaussian Correlation Conjecture we must check the log-concavity of the moment generating function of certain measures pulled down by a particular Gaussian density.

Southeast Geometry Seminar

Series
Other Talks
Time
Friday, December 12, 2008 - 09:00 for 8 hours (full day)
Location
Skiles 243
Speaker
Various SpeakersVarious Universities
The Southeast Geometry Seminar (SGS) is a semiannual series of one day events organized by Vladimir Oliker (Emory), Mohammad Ghomi and John McCuan (Georgia Tech) and Gilbert Weinstein (UAB). See http://www.math.uab.edu/sgs for details

Maximum principle and gradient bounds for stationary solutions of the Navier-Stokes equations; a computer aided approach

Series
PDE Seminar
Time
Thursday, December 11, 2008 - 15:15 for 1.5 hours (actually 80 minutes)
Location
Skiles 255
Speaker
Robert FinnStanford University
We calculate numerically the solutions of the stationary Navier-Stokes equations in two dimensions, for a square domain with particular choices of boundary data. The data are chosen to test whether bounded disturbances on the boundary can be expected to spread into the interior of the domain. The results indicate that such behavior indeed can occur, but suggest an estimate of general form for the magnitudes of the solution and of its derivatives, analogous to classical bounds for harmonic functions. The qualitative behavior of the solutions we found displayed some striking and unexpected features. As a corollary of the study, we obtain two new examples of non-uniqueness for stationary solutions at large Reynolds numbers.

Expanders via Random Spanning Trees

Series
Combinatorics Seminar
Time
Friday, December 5, 2008 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Luis RademacherSchool of Computer Science, Georgia Tech
Expanders via Random Spanning Trees Motivated by the problem of routing reliably and scalably in a graph, we introduce the notion of a splicer, the union of spanning trees of a graph. We prove that for any bounded-degree n-vertex graph, the union of two random spanning trees approximates the expansion of every cut of the graph to within a factor of O(log n). For the random graph G_{n,p}, for p > c (log n)/n, two spanning trees give an expander. This is suggested by the case of the complete graph, where we prove that two random spanning trees give an expander. The construction of the splicer is elementary — each spanning tree can be produced independently using an algorithm by Aldous and Broder: a random walk in the graph with edges leading to previously unvisited vertices included in the tree. A second important application of splicers is to graph sparsification where the goal is to approximate every cut (and more generally the quadratic form of the Laplacian) using only a small subgraph of the original graph. Benczur-Karger as well as Spielman-Srivastava have shown sparsifiers with O(n log n/eps^2) edges that achieve approximation within factors 1+eps and 1-eps. Their methods, based on independent sampling of edges, need Omega(n log n) edges to get any approximation (else the subgraph could be disconnected) and leave open the question of linear-size sparsifiers. Splicers address this question for random graphs by providing sparsifiers of size O(n) that approximate every cut to within a factor of O(log n). This is joint work with Navin Goyal and Santosh Vempala.

Transient (Electro)Chemical Imaging of Reacting Interfaces - Physical Concepts and Mathematical Challenges

Series
Mathematical Biology Seminar
Time
Wednesday, December 3, 2008 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Andrei FedorovSchool of Mechanical Engineering, Georgia Tech
In this presentation I will outline physical principles of two analytical techniques, the Scanning ElectroChemical Microscopy (SECM) and Scanning Mass Spectrometry (SMS), which can be used to obtain the spatially resolved images of (bio/electro)chemically active interfaces. The mathematical models need to be employed for image interpretation and mapping measured quantities (e.g., an electrode current in SECM) to biochemically relevant quantities (e.g., kinetics of exocytotic signaling events in cellular communications), and I will review the key ideas/assumptions used for the model formulation and the main results of analysis and simulations. In conclusion, an alternative approach to spatially-resolved imaging based on the multi-probe array will be introduced along with intriguing opportunities and challenges for mathematical interpretation of such images.

Oblique derivative problems for elliptic equations

Series
PDE Seminar
Time
Tuesday, December 2, 2008 - 15:15 for 1.5 hours (actually 80 minutes)
Location
Skiles 255
Speaker
Gary M. LiebermanIowa State University
The usual boundary condition adjoined to a second order elliptic equation is the Dirichlet problem, which prescribes the values of the solution on the boundary. In many applications, this is not the natural boundary condition. Instead, the value of some directional derivative is given at each point of the boundary. Such problems are usually considered a minor variation of the Dirichlet condition, but this talk will show that this problem has a life of its own. For example, if the direction changes continuously, then it is possible for the solution to be continuously differentiable up to a merely Lipschitz boundary. In addition, it's possible to get smooth solutions when the direction changes discontinuously as well.

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