Seminars and Colloquia by Series

Chern-Simons theory and knot invariants

Series
Geometry Topology Student Seminar
Time
Wednesday, September 10, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jonathan Paprocki – Georgia Tech
We will present an introduction to gauge theory and classical Chern-Simons theory, a 3-dimensional topological gauge field theory whose quantization yields new insights about knot invariants such as the Jones polynomial. Then we will give a sketch of quantum Chern-Simons theory and how Witten used it as a 3-dimensional method to obtain the Jones polynomial, as well as how it may be used to obtain other powerful knot and 3-manifold invariants. No physics background is necessary.

Existence of strong solutions to Compressible Navier-Stokes equations with degenerate viscosities and vacuum

Series
PDE Seminar
Time
Tuesday, September 9, 2014 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Shengguo Zhu – Georgia Tech
We identify sufficient conditions on initial data to ensure the existence of a unique strong solution to the Cauchy problem for the Compressible Navier-Stokes equations with degenerate viscosities and vacuum (such as viscous Saint-Venants model in $\mathbb{R}^2$). This is a recent work joint with Yachun Li and Ronghua Pan.

Variable Selection Consistency of Linear Programming Discriminant Estimator

Series
High-Dimensional Phenomena in Statistics and Machine Learning Seminar
Time
Tuesday, September 9, 2014 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dong Xia – School of Mathematics, Georgia Tech
The linear programming discriminant(LPD) estimator is used in sparse linear discriminant analysis for high dimensional classification problems. In this talk we will give a sufficient condition for the variable selection property of the LPD estimator and our result provides optimal bound on the requirement of sample size $n$ and magnitude of components of Bayes direction.

Log-Sobolev Inequalities and Their Applications

Series
Analysis Working Seminar
Time
Monday, September 8, 2014 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
George Kerchev – School of Math –
This talk will concern Log-Sobolev inequalities and their applications. We will discuss connections to exponential convergence of Markov semigroups, the Poincare inequality and Gaussian concentration. It's the first part of a series.

Computation of normally hyperbolic invariant manifolds

Series
Applied and Computational Mathematics Seminar
Time
Monday, September 8, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dr. Marta Canadell – Georgia Tech Mathematics
We explain a method for the computation of normally hyperbolic invariant manifolds (NHIM) in discrete dynamical systems.The method is based in finding a parameterization for the manifold formulating a functional equation. We solve the invariance equation using a Newton-like method taking advantage of the dynamics and the geometry of the invariant manifold and its invariant bundles. The method allows us to compute a NHIM and its internal dynamics, which is a-priori unknown.We implement this method to continue the invariant manifold with respect to parameters, and to explore different mechanisms of breakdown. This is a joint work with Alex Haro.

A Central Limit Theorem for the Length of the Longest Common Subsequence in Random Words

Series
Stochastics Seminar
Time
Thursday, September 4, 2014 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Christian Houdre – School of Mathematics, Georgia Tech
Let (X_k)_{k \geq 1} and (Y_k)_{k\geq1} be two independent sequences of independent identically distributed random variables having the same law and taking their values in a finite alphabet \mathcal{A}_m. Let LC_n be the length of the longest common subsequence of the random words X_1\cdots X_n and Y_1\cdots Y_n. Under assumptions on the distribution of X_1, LC_n is shown to satisfy a central limit theorem. This is in contrast to the Bernoulli matching problem or to the random permutations case, where the limiting law is the Tracy-Widom one. (Joint with Umit Islak)

Exams: the devil is in the details

Series
Professional Development Seminar
Time
Wednesday, September 3, 2014 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Brett Wick and Rafael de la Llave – Georgia Tech
A discussion of case studies on the making, giving, grading, etc. of exams, followed by course group meetings for 2401 and 2403.

Reconstruction Problems in Geometry

Series
Research Horizons Seminar
Time
Wednesday, September 3, 2014 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dr. Dan Margalit – Georgia Tech Math Department
Here is a classical theorem. Consider a bijection (just a set map!) from the Euclidean plane to itself that takes 0 to 0 and takes the points on an arbitrary line to the points on a (possibly different line). The theorem is that such a bijection always comes from a linear map. I'll discuss various generalizations of this theorem in geometry, topology, and algebra, ending with a discussion of some recent, related research on the topology of surfaces.

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