Seminars and Colloquia by Series

Synchronization of Cows

Series
Mathematical Biology Seminar
Time
Tuesday, September 7, 2010 - 17:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Mason Porter – Oxford University
The study of collective behavior---of animals, mechanical systems, or even abstract oscillators---has fascinated a large number of researchers from observational geologists to pure mathematicians. We consider the collective behavior of herds of cattle. We first consider some results from an agent-based model and then formulate a mathematical model for the daily activities of a cow (eating, lying down, and standing) in terms of a piecewise affine dynamical system. We analyze the properties of this bovine dynamical system representing the single animal and develop an exact integrative form as a discrete-time mapping. We then couple multiple cow "oscillators" together to study synchrony and cooperation in cattle herds, finding that it is possible for cows to synchronize less when the coupling is increased. [This research is in collaboration with Jie Sun, Erik Bollt, and Marian Dawkins.]

Curve complexes and mapping class groups

Series
Geometry Topology Working Seminar
Time
Friday, September 3, 2010 - 13:00 for 2 hours
Location
Skiles 114
Speaker
Dan Margalit – Georgia Tech
The mapping class group is the group of symmetries of a surface (modulo homotopy). One way to study the mapping class group of a surface S is to understand its action on the set of simple closed curves in S (up to homotopy). The set of homotopy classes of simple closed curves can be organized into a simplicial complex called the complex of curves. This complex has some amazing features, and we will use it to prove a variety of theorems about the mapping class group. We will also state some open questions. This talk will be accessible to second year graduate students.

The number of vertices in a 6-critical graph is linear in its genus

Series
Graph Theory Seminar
Time
Thursday, September 2, 2010 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Luke Postle – Math, GT
A deep theorem of Thomassen shows that for any surface there are only finitely many 6-critical graphs that embed on that surface. We give a shorter self-contained proof that for any 6-critical graph G that embeds on a surface of genus g, that |V(G)| is at most linear in g. Joint work with Robin Thomas.

The Aleksandrov problem and optimal transport on $S^n$

Series
School of Mathematics Colloquium
Time
Thursday, September 2, 2010 - 11:00 for 1 hour (actually 50 minutes)
Location
249 Skiles
Speaker
Vladimir Oliker – Emory University –
The purpose of this talk is to describe a variational approach to the problemof A.D. Aleksandrov concerning existence and uniqueness of a closed convexhypersurface in Euclidean space $R^{n+1}, ~n \geq 2$ with prescribed integral Gauss curvature. It is shown that this problem in variational formulation is closely connected with theproblem of optimal transport on $S^n$ with a geometrically motivated cost function.

A Variational Estimate for Paraproducts

Series
Analysis Seminar
Time
Wednesday, September 1, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Yen Do – Georgia Tech
We show variational estimates for paraproducts, which can be viewed as bilinear generalizations of L\'epingle’s variational estimates for martingale averages or scaled families of convolution operators. The heart of the matter is the case of low variation exponents. Joint work with Camil Muscalu and Christoph Thiele.

Universality Limits for Random Matrices and orthogonal Polynomials

Series
Research Horizons Seminar
Time
Wednesday, September 1, 2010 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Doron Lubinsky – School of Mathematics - Georgia Tech
Orthogonal Polynomials play a key role in analysis of random matrices. We discuss universality limits in the so-called unitary case, showing how the universality limit reduces to an asymptotic involving reproducing kernels associated with orthogonal polynomials. As a consequence, we show that universality holds in measure for any compactly supported measure.

What is a tropical variety?

Series
Tropical Geometry Seminar
Time
Wednesday, September 1, 2010 - 10:05 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Josephine Yu – Georgia Tech
Tropical varieties are polyhedral objects that behave like algebraic varieties. They arise in a few different ways -- from polynomials with (max,+) operations, from study of Groebner bases, and from non-archimedean valuations of algebraic varieties. In this expository talk, I will introduce the tropical varieties of ideals in a polynomial ring from the point of view of (max,+) algebra and show how they are related to Groebner theory, Newton polytopes and their subdivisions. I will also discuss their properties and give some examples.

Small solutions of nonlinear Schrodinger equations near first excited states

Series
PDE Seminar
Time
Tuesday, August 31, 2010 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Professor Tai-Peng Tsai – Department of Mathematics, University of British Columbia –
Consider a nonlinear Schrodinger equation in $R^3$ whose linear part has three or more eigenvalues satisfying some resonance conditions. Solutions which are initially small in $H^1 \cap L^1(R^3)$ and inside a neighborhood of the first excited state family are shown to converge to either a first excited state or a ground state at time infinity. An essential part of our analysis is on the linear and nonlinear estimates near nonlinear excited states, around which the linearized operators have eigenvalues with nonzero real parts and their corresponding eigenfunctions are not uniformly localized in space. This is a joint work with Kenji Nakanishi and Tuoc Van Phan.The preprint of the talk is available at http://arxiv.org/abs/1008.3581

Spherical images of hypersurfaces

Series
Geometry Topology Seminar
Time
Monday, August 30, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Mohammad Ghomi – Ga Tech
We discuss necessary and sufficient conditions of a subset X of the sphere S^n to be the image of the unit normal vector field (or Gauss map) of a closed orientable hypersurface immersed in Euclidean space R^{n+1}.

Pages