Seminars and Colloquia by Series

Some Results in Sums and Products

Series
Dissertation Defense
Time
Thursday, November 13, 2014 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Chris Pryby – School of Mathematics, Georgia Tech
We demonstrate new results in additive combinatorics, including a proof of the following conjecture by J. Solymosi: for every epsilon > 0, there exists delta > 0 such that, given n^2 points in a grid formation in R^2, if L is a set of lines in general position such that each line intersects at least n^{1-delta} points of the grid, then |L| < n^epsilon. This result implies a conjecture of Gy. Elekes regarding a uniform statistical version of Freiman's theorem for linear functions with small image sets.

Variational inequalities related to the Monge-Ampere equation

Series
Analysis Seminar
Time
Wednesday, November 12, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Diego Maldonado – Kansas State University
We will start with a description of geometric and measure-theoretic objects associated to certain convex functions in R^n. These objects include a quasi-distance and a Borel measure in R^n which render a space of homogeneous type (i.e. a doubling quasi-metric space) associated to such convex functions. We will illustrate how real-analysis techniques in this quasi-metric space can be applied to the regularity theory of convex solutions u to the Monge-Ampere equation det D^2u =f as well as solutions v of the linearized Monge-Ampere equation L_u(v)=g. Finally, we will discuss recent developments regarding the existence of Sobolev and Poincare inequalities on these Monge-Ampere quasi-metric spaces and mention some of their applications.

Fenchel-Nielsen Coordinates on Teichmüller Space

Series
Geometry Topology Student Seminar
Time
Wednesday, November 12, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jamie Conway – Georgia Tech
A surface with negative Euler characteristic has a hyperbolic metric. However, this metric is not unique. We will consider the Teichmüller space of a surface, which is the space of hyperbolic structures up to an equivalence relation. We will discuss the topology of and how to put coordinates on this space. If there is time, we will see that the lengths of 9g-9 curves determine the hyperbolic structure.

Grothendieck's anabelian conjectures

Series
Research Horizons Seminar
Time
Wednesday, November 12, 2014 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dr. Kirsten Wickelgren – Georgia Tech Math Department
We will discuss methods for solving polynomial equations with integer solutions using the loops on the space of all complex solutions to the same equations. We will then state generalizations of this method due to A. Grothendieck.

Intuitive Dyadic Calculus

Series
Analysis Working Seminar
Time
Monday, November 10, 2014 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Robert Rahm – School 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.

Torsion of curves on locally convex surfaces

Series
Geometry Topology Seminar
Time
Monday, November 10, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Mohammad Ghomi – Georgia Tech –
We prove that the torsion of any smooth closed curve in Euclidean space which bounds a simply connected locally convex surface vanishes at least 4 times (vanishing of torsion means that the first 3 derivatives of the curve are linearly dependent). This answers a question of Rosenberg related to a problem of Yau on characterizing the boundary of positively curved disks in 3-space. Furthermore, our result generalizes the 4 vertex theorem of Sedykh for convex space curves, and thus constitutes a far reaching extension of the classical 4 vertex theorem for planar curves. The proof follows from an extensive study of the structure of convex caps in a locally convex surface.

Embeddings of manifolds and contact manifolds IV

Series
Geometry Topology Working Seminar
Time
Friday, November 7, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
John Etnyre – Georgia Tech
This is the fourth 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.

Frontiers in Science - Bionic Knees and Elephant Nerves

Series
Other Talks
Time
Thursday, November 6, 2014 - 19:00 for 2 hours
Location
Clary Theatre
Speaker
Max Donelan – Simon Fraser University, Department of Biomedical Physiology and Kinesiology

Please Note: 
After the talk there will be a reception and time for visitors to chat with Donelan and each other.

Professor Max Donelan talks about the bionic energy harvester, which uses energy generated from walking to power portable devices. He also discusses his research on the reflexes and nerves of animals, from elephants to shrews.

Singularity formation in Compressible Euler equations (Part II)

Series
PDE Working Seminar
Time
Thursday, November 6, 2014 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Ronhua Pan – GeorgiaTech –
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.

Mixing rates of interacting particle systems

Series
Math Physics Seminar
Time
Thursday, November 6, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Yao Li – Courrant Institute, NY –
In this talk I will begin with our recent results on non-equilibrium steady states (NESS) of a microscopic heat conduction model, which is a stochastic particle system coupled to unequal heat baths. This stochastic model is derived from a mechanical chain model (Eckmann and Young 2006) by randomizing certain quantities while retaining the other features. We proved various results including the existence and uniqueness of NESS and the exponential rate of mixing. Then I will follow with an energy dependent Kac-type model that is obtained from an improved version of randomization of the “local" dynamics. We rigorously proved that this Kac-type model has a mixing rate $\sim t^{-2}$. In the end, I will show that slow (polynomial) mixing rates appear in a large class of statistical mechanics models.

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