Seminars and Colloquia by Series

Athens/Atlanta Number Theory Seminar - Lecture 1 - Degree three cohomology of function fields of surfaces

Series
Other Talks
Time
Tuesday, April 13, 2010 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Venapally Suresh – University of Hyderabad / Emory University
Let k be a global field or a local field. Class field theory says that every central division algebra over k is cyclic. Let l be a prime not equal to the characteristic of k. If k contains a primitive l-th root of unity, then this leads to the fact that every element in H^2(k, µ_l ) is a symbol. A natural question is a higher dimensional analogue of this result: Let F be a function field in one variable over k which contains a primitive l-th root of unity. Is every element in H^3(F, µ_l ) a symbol? In this talk we answer this question in affirmative for k a p-adic field or a global field of positive characteristic. The main tool is a certain local global principle for elements of H^3(F, µ_l ) in terms of symbols in H^2(F µ_l ). We also show that this local-global principle is equivalent to the vanishing of certain unramified cohomology groups of 3-folds over finite fields.

Fokker-Planck equation on graphs with finite number of vertices

Series
PDE Seminar
Time
Tuesday, April 13, 2010 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Yao Li – Georgia Tech
Fokker-Planck equation is a linear parabolic equation which describes the time evolution of of probability distribution of a stochastic process defined on a Euclidean space. Moreover, it is the gradient flow of free energy functional. We will present a Fokker-Planck equation which is a system of ordinary differential equations and describes the time evolution of probability distribution of a stochastic process on a graph with a finite number of vertices. It is shown that there is a strong connection but also substantial differences between the ordinary differential equations and the usual Fokker-Planck equation on Euclidean spaces. Furthermore, the ordinary differential equation is in fact a gradient flow of free energy on a Riemannian manifold whose metric is closely related to certain Wasserstein metrics. Some examples will also be discussed.

A parametrization of the two variable trigonometric moment problem

Series
Research Horizons Seminar
Time
Tuesday, April 13, 2010 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Jeff Geronimo – Professor, School of Mathematics

Please Note: Hosted by: Huy Huynh and Yao Li

A useful parametrization of the one variable trigonometric moment problem is given in terms of polynomials orthogonal on the unit circle. A description of this parameterization will be given as well as some of its uses. We will then describe a possible two variable extension.

How to get far with only a small effort

Series
Job Candidate Talk
Time
Tuesday, April 13, 2010 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Rafael de le Llave – Department of Mathematics, University of Texas, Austin
Many mechanical systems have the property that some small perturbations can accumulate over time to lead to large effects. Other perturbations just average out and cancel. It is interesting in applications to find out what systems have these properties and which perturbations average out and which ones grows. A complete answer is far from known but it is known that it is complicated and that, for example, number theory plays a role. In recent times, there has been some progress understanding some mechanisms that lead to instability. One can find landmarks that organize the long term behavior and provide an skeleton for the dynamics. Some of these landmarks provide highways along which the perturbations can accumulate.

General Audience Lecture - Spaces of positive curvature

Series
Other Talks
Time
Monday, April 12, 2010 - 17:00 for 1 hour (actually 50 minutes)
Location
Klaus 1116W
Speaker
Richard Schoen – Stanford University
In 1854 Riemann extended Gauss' ideas on curved geometries from two dimensional surfaces to higher dimensions. Since that time mathematicians have tried to understand the structure of geometric spaces based on their curvature properties. It turns out that basic questions remain unanswered in this direction. In this lecture we will give a history of such questions for spaces with positive curvature, and describe the progress that has been made as well as some outstanding conjectures which remain to be settled.

Twists of elliptic curves with a large set of integral points over function fields

Series
Algebra Seminar
Time
Monday, April 12, 2010 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Ricardo Conceicao – Oxford College of Emory University –
We will explicitly construct twists of elliptic curves with an arbitrarily large set of integral points over $\mathbb{F}_q(t)$. As a motivation to our main result, we will discuss a conjecture of Vojta-Lang concerning the behavior of integral points on varieties of log-general type over number fields and present a natural translation to the function field setting. We will use our construction to provide an isotrivial counter-example to this conjecture. We will also show that our main result also provides examples of elliptic curves with arbitrarily large set of independent points and of function fields with large $m$-class rank.

Influence of Cellular Substructure on Gene Expression and Regulation

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 12, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Samuel Isaacson – Boston University Mathematics Dept.
We will give an overview of our recent work investigating the influence of incorporating cellular substructure into stochastic reaction-diffusion models of gene regulation and expression. Extensions to the reaction-diffusion master equation that incorporate effects due to the chromatin fiber matrix are introduced. These new mathematical models are then used to study the role of nuclear substructure on the motion of individual proteins and mRNAs within nuclei. We show for certain distributions of binding sites that volume exclusion due to chromatin may reduce the time needed for a regulatory protein to locate a binding site.

Southeast Geometry Seminar

Series
Other Talks
Time
Monday, April 12, 2010 - 08:00 for 8 hours (full day)
Location
Skiles 269
Speaker
Southeast Geometry Seminar – School of Mathematics, Georgia Tech
The Southeast Geometry Seminar is a series of semiannual one-day events focusing on geometric analysis. These events are hosted in rotation by the following institutions: The University of Alabama at Birmingham; The Georgia Institute of Technology; Emory University; The University of Tennessee Knoxville. The presentations will include topics on geometric analysis, and related fields, such as partial differential equations, general relativity, and geometric topology. See the Schedule for times and abstracts of talks.

Monomer correlations on the square lattice

Series
Combinatorics Seminar
Time
Friday, April 9, 2010 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Mihai Ciucu – Professor, Indiana University, Bloomington
In 1963 Fisher and Stephenson conjectured that the correlation function of two oppositely colored monomers in a sea of dimers on the square lattice is rotationally invariant in the scaling limit. More precisely, the conjecture states that if one of the monomers is fixed and the other recedes to infinity along a fixed ray, the correlation function is asymptotically $C d^(-1/2)$, where $d$ is the Euclidean distance between the monomers and $C$ is a constant independent of the slope of the ray. Shortly afterward Hartwig rigorously determined $C$ when the ray is in a diagonal direction, and this remains the only direction settled in the literature. We generalize Hartwig's result to any finite collection of monomers along a diagonal direction. This can be regarded as a counterpart of a result of Zuber and Itzykson on n-spin correlations in the Ising model. A special case proves that two same-color monomers interact the way physicists predicted.

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