Seminars and Colloquia by Series

Regularity of Solutions of Hamilton-Jacobi Equation on a Domain

Series
PDE Seminar
Time
Tuesday, October 28, 2014 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Albert FathiÉcole Normale Supérieure de Lyon, France
In this lecture, we will explain a new method to show that regularity on the boundary of a domain implies regularity in the inside for PDE's of the Hamilton-Jacobi type. The method can be applied in different settings. One of these settings concerns continuous viscosity solutions $U : T^N\times [0,+\infty[ \rightarrow R$ of the evolutionary equation $\partial_t U(x, t) + H(x, \partial_x U(x, t) ) = 0,$ where $T^N = R^N / Z^N$, and $H: T^N \times R^N$ is a Tonelli Hamiltonian, i.e. H(x, p) is $C^2$, strictly convex superlinear in p. Let D be a compact smooth domain with boundary $\partial D$ contained in $T^N \times ]0,+\infty[$ . We show that if U is differentiable at each point of $\partial D$, then this is also the case on the interior of D. There are several variants of this result in different settings. To make the result accessible to the layman, we will explain the method on the function distance to a closed subset of an Euclidean space. This example contains all the ideas of the general case.

Intuitive Dyadic Calculus

Series
Analysis Working Seminar
Time
Monday, October 27, 2014 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Robert RahmSchool of Math
We discuss an approach to dyadic lattices (and their applications to harmonic analysis) presented by Lerner and Nazarov in their manuscript, Intutive Dyadic Calculus.

On complexity of 3-manifolds/On coordinates on virtual braid groups

Series
Geometry Topology Seminar
Time
Monday, October 27, 2014 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Evgeny Fominykh and Andrei VesninChelyabinsk State University
These are two half an hour talks.Evgeny's abstract: The most useful approach to a classication of 3-manifolds is the complexity theory foundedby S. Matveev. Unfortunately, exact values of complexity are known for few infinite seriesof 3-manifold only. We present the results on complexity for two infinite series of hyperbolic3-manifolds with boundary.Andrei's abstract: We define coordinates on virtual braid groups. We prove that these coordinates are faithful invariants of virtual braids on two strings, and present evidence that they are also very powerful invariants for general virtual braids.The talk is based on the joint work with V.Bardakov and B.Wiest.

Southeast Geometry Seminar XXV

Series
Other Talks
Time
Sunday, October 26, 2014 - 08:30 for 8 hours (full day)
Location
University of Tennessee Knoxville
Speaker
Southeast Geometry SeminarUniversity of Tennessee Knoxville
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: Emory University; Georgia Institute of Technology; University of Alabama at Birmingham; University of Tennessee Knoxville. The following five speakers will give presentations: Sigurd Angenent (University of Wisconsin-Madison); Omer Bobrowski (Duke University); Tom Ivey (College of Charleston); Ken Knox (University of Tennessee); Facundo Memoli (Ohio State University). Please email oliker@mathcs.emory.edu if you plan to attend and wish to request support.

Embeddings of manifolds and contact manifolds II

Series
Geometry Topology Working Seminar
Time
Friday, October 24, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
John EtnyreGeorgia Tech
This is the second of several talks discussing embeddings of manifolds. I will discuss some general results for smooth manifolds, but focus on embeddings of contact manifolds into other contact manifolds. Particular attention will be paid to embeddings of contact 3-manifolds in contact 5-manifolds. I will discuss two approaches to this last problem that are being developed jointly with Yanki Lekili.

Singularity formation in Compressible Euler equations

Series
PDE Working Seminar
Time
Thursday, October 23, 2014 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Ronghua PanGeorgiaTech
Compressible Euler equations describe the motion of compressible inviscid fluid. Physically, it states the basic conservation laws of mass, momentum, and energy. As one of the most important examples of nonlinear hyperbolic conservation laws, it is well-known that singularity will form in the solutions of Compressible Euler equations even with small smooth initial data. This talk will discuss some classical results in this direction, including some most recent results for the problem with large initial data.

Zeros of random polynomials

Series
School of Mathematics Colloquium
Time
Thursday, October 23, 2014 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Professor Igor PritskerOklahoma State University
The area was essentially originated by the general question: How many zeros of a random polynomials are real? Kac showed that the expected number of real zeros for a polynomial with i.i.d. Gaussian coefficients is logarithmic in terms of the degree. Later, it was found that most of zeros of random polynomials are asymptotically uniformly distributed near the unit circumference (with probability one) under mild assumptions on the coefficients. Thus two main directions of research are related to the almost sure limits of the zero counting measures, and to the quantitative results on the expected number of zeros in various sets. We give estimates of the expected discrepancy between the zero counting measure and the normalized arclength on the unit circle. Similar results are established for polynomials with random coefficients spanned by various bases, e.g., by orthogonal polynomials. We show almost sure convergence of the zero counting measures to the corresponding equilibrium measures for associated sets in the plane, and quantify this convergence. Random coefficients may be dependent and need not have identical distributions in our results.

The Loop Theorem

Series
Geometry Topology Student Seminar
Time
Wednesday, October 22, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Sudipta KolayGeorgia Tech

Please Note: This is a project for Prof. Margalit's course on Low-dimensional Topology and Hyperbolic Geometry.

In this talk we will discuss the Loop Theorem, which is a generalization of Dehn's lemma. We will outline a proof using the "tower construction".

Band Operators on Matrix Weighted L^2 Spaces

Series
Analysis Seminar
Time
Wednesday, October 22, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Kelly BickelBucknell University
In this talk, we will discuss a T1 theorem for band operators (operators with finitely many diagonals) in the setting of matrix A_2 weights. This work is motivated by interest in the currently open A_2 conjecture for matrix weights and generalizes a scalar-valued theorem due to Nazarov-Treil-Volberg, which played a key role in the proof of the scalar A_2 conjecture for dyadic shifts and related operators. This is joint work with Brett Wick.

Modeling Avian Influenza and Control Strategies in Poultry

Series
Mathematical Biology Seminar
Time
Wednesday, October 22, 2014 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Hayriye GulbudakSchool of Biology, GaTech
The emerging threat of a human pandemic caused by high-pathogenic H5N1 avian in uenza virus magnifies the need for controlling the incidence of H5N1 in domestic bird populations. The two most widely used control measures in poultry are culling and vaccination. In this talk, I will discuss mathematical models of avian in uenza in poultry which incorporate culling and vaccination. First, we consider an ODE model to understand the dynamics of avian influenza under different culling approaches. Under certain conditions, complex dynamical behavior such as bistability is observed and analyzed. Next, we model vaccination of poultry by formulating a coupled ODE-PDE model which takes into account vaccine-induced asymptomatic infection. In this study, the model can exhibit the "silent spread" of the disease through asymptomatic infection. We analytically and numerically demonstrate that vaccination can paradoxically increase the total number of infected when the efficacy is not sufficiently high.

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