Seminars and Colloquia by Series

Comparison Methods and Eigenvalue Problems in Cones

Series
Other Talks
Time
Monday, April 5, 2010 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Guy Degla – Institute of Mathematics and Physical Sciences, Benin
The purpose of this talk is to highlight some versions of the Krein-Rutman theorem which have been widely and deeply applied in many fields (e.g., Mathematical Analysis, Geometric Analysis, Physical Sciences, Transport theory and Information Sciences). These versions are motivated by optimization theory, perturbation theory, bifurcation theory, etc. and give rise to some simple but useful comparison methods, in ordered Banach spaces, such as the Dodds-Fremlin theorem and the De Pagter theorem.

Orbitopes

Series
Algebra Seminar
Time
Monday, April 5, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Frank Sottile – Texas A&M
An orbitope is the convex hull of an orbit of a compact group acting linearly on a vector space. Instances of these highly symmetric convex bodies have appeared in many areas of mathematics and its applications, including protein reconstruction, symplectic geometry, and calibrations in differential geometry.In this talk, I will discuss Orbitopes from the perpectives of classical convexity, algebraic geometry, and optimization with an emphasis on motivating questions and concrete examples. This is joint work with Raman Sanyal and Bernd Sturmfels.

Extrapolation of Carleson measures

Series
Analysis Seminar
Time
Monday, April 5, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Steven Hofmann – University of Missouri
We discuss joint work with J.-M. Martell, in which werevisit the ``extrapolation method" for Carleson measures, originallyintroduced by John Lewis to proveA_\infty estimates for certain caloric measures, and we present a purely real variable version of the method. Our main result is a general criterion fordeducing that a weight satisfies a ReverseHolder estimate, given appropriate control by a Carleson measure.To illustrate the useof this technique,we reprove a well known theorem of R. Fefferman, Kenig and Pipherconcerning the solvability of the Dirichlet problem with data in some L^p space.

Tight frame, Sparsity and Bregman algorithms

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 5, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Jianfeng Cai – Dep. of Math. UCLA
 Tight frame is a generalization of orthonormal basis. It  inherits most good properties of orthonormal basis but gains more  robustness to represent signals of intrests due to the redundancy. One can  construct tight frame systems under which signals of interests have sparse  representations. Such tight frames include translation invariant wavelet,  framelet, curvelet, and etc. The sparsity of a signal under tight frame systems has three different formulations, namely, the analysis-based sparsity, the synthesis-based one, and the balanced one between them. In this talk, we discuss Bregman algorithms for finding signals that are sparse under tight frame systems with the above three different formulations. Applications of our algorithms include image inpainting, deblurring, blind deconvolution, and cartoon-texture decomposition. Finally, we apply the linearized Bregman, one of the Bregman algorithms, to solve the problem of matrix completion, where we want to find a low-rank matrix from its incomplete entries. We view the low-rank matrix as a sparse vector under an adaptive linear transformation which depends on its singular vectors. It leads to a singular value thresholding (SVT) algorithm.

Two Problems in Asymptotic Combinatorics

Series
Combinatorics Seminar
Time
Friday, April 2, 2010 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Rodney Canfield – Professor, University of Georgia, Athens, GA
I will divide the talk between two topics. The first is Stirling numbers of the second kind, $S(n,k)$. For each $n$ the maximum $S(n,k)$ is achieved either at a unique $k=K_n$, or is achieved twice consecutively at $k=K_n,K_n+1$. Call those $n$ of the second kind {\it exceptional}. Is $n=2$ the only exceptional integer? The second topic is $m\times n$ nonnegative integer matrices all of whose rows sum to $s$ and all of whose columns sum to $t$, $ms=nt$. We have an asymptotic formula for the number of these matrices, valid for various ranges of $(m,s;n,t)$. Although obtained by a lengthy calculation, the final formula is succinct and has an interesting probabilistic interpretation. The work presented here is collaborative with Carl Pomerance and Brendan McKay, respectively.

From concentration to isoperimetry by semigroup proofs

Series
Probability Working Seminar
Time
Friday, April 2, 2010 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 169
Speaker
Linwei Xin – Georgia Tech
 It is well known that isoperimetric type inequalities can imply concentration inequalities, but the reverse is not true generally. However, recently E Milman and M Ledoux proved that under some convex assumption of the Ricci curvature, the reverse is true in the Riemannian manifold setting. In this talk, we will focus on the semigroup tools in their papers. First, we introduce some classic methods to obtain concentration inequalities, i.e. from isoperimetric inequalities, Poincare's inequalities, log-Sobolev inequalities, and transportation inequalities. Second, by using semigroup tools, we will prove some kind of concentration inequalities, which then implies linear isoperimetry and super isoperimetry. 

The topology at infinity of real algebraic manifolds

Series
Geometry Topology Seminar
Time
Friday, April 2, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Clint McCrory – UGA –
A noncompact smooth manifold X has a real algebraic structure if and only if X is tame at infinity, i.e. X is the interior of a compact manifold with boundary. Different algebraic structures on X can be detected by the topology of an algebraic compactification with normal crossings at infinity. The resulting filtration of the homology of X is analogous to Deligne's weight filtration for nonsingular complex algebraic varieties.

A brief introduction to copulas and related problems

Series
SIAM Student Seminar
Time
Friday, April 2, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Ruodu Wang – School of Mathematics, Georgia Tech
A copula C of n arbitrary random variables X_1, ..., X_n contains all the information about their dependence. First I will briefly introduce the definition, basic properties and elementary examples of copulas, as well as Sklar's Theorem (1959). Then I will present a family of multivariate copulas whose marginal copula belongs to a family of extreme copulas. Finally I will discuss a minimization problem related to copula, which is still open. The talk should be easy to understand for all level audience who have knowledge of basic probability theory

[Special day and location] Electrostatic effects on DNA dynamics in fluid by the generalized immersed boundary method

Series
Applied and Computational Mathematics Seminar
Time
Friday, April 2, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Sookkyung Lim – Department of Mathematical Sciences, University of Cincinnati
We investigate the effects of electrostatic and steric repulsion on thedynamics of pre-twisted charged elastic rod, representing a DNA molecule,immersed in a viscous incompressible fluid. Equations of motion of the rod, whichinclude the fluid-structure interaction, rod elasticity, and electrostatic interaction, are solved by the generalized immersed boundary method. Electrostatic interaction is treated using a modified Debye-Huckel repulsive force in which the electrostatic force depends on the salt concentration and the distance between base pairs, and a close range steric repulsion force to prevent self-penetration. After perturbation a pretwisted DNA circle collapses into a compact supercoiled configuration. The collapse proceeds along a complex trajectory that may pass near several equilibrium configurations of saddle type, before it settles in a locally stable equilibrium. We find that both the final configuration and the transition path are sensitive to the initial excess link, ionic stregth of the solvent, and the initial perturbation.

Goodness-of-fit testing under long memory

Series
Stochastics Seminar
Time
Thursday, April 1, 2010 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Hira Koul – Michigan State University
In this talk we shall discuss the problem of fitting a distribution function to the marginal distribution of a long memory process. It is observed that unlike in the i.i.d. set up, classical tests based on empirical process are relatively easy to implement. More importantly, we discuss fitting the marginal distribution of the error process in location, scale and linear regression models. An interesting observation is that the first order difference between the residual empirical process and the null model can not be used to asymptotically to distinguish between the two marginal distributions that differ only in their means. This finding is in sharp contrast to a recent claim of Chan and Ling to appear in the Ann. Statist. that such a process has a Gaussian weak limit. We shall also proposes some tests based on the second order difference in this case and analyze some of their properties. Another interesting finding is that residual empirical process tests in the scale problem are robust against not knowing the scale parameter. The third finding is that in linear regression models with a non-zero intercept parameter the first order difference between the empirical d.f. of residuals and the null d.f. can not be used to fit an error d.f. This talk is based on ongoing joint work with Donatas Surgailis.

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