Seminars and Colloquia by Series

Maximum height of low-temperature 3D Ising interfaces

Series
Stochastics Seminar
Time
Thursday, October 10, 2019 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Reza GheissariUniversity of California, Berkeley

Consider the random surface given by the interface separating the plus and minus phases in a low-temperature Ising model in dimensions $d\geq 3$. Dobrushin (1972) famously showed that in cubes of side-length $n$ the horizontal interface is rigid, exhibiting order one height fluctuations above a fixed point. 

We study the large deviations of this interface and obtain a shape theorem for its pillar, conditionally on it reaching an atypically large height. We use this to analyze the law of the maximum height $M_n$ of the interface: we prove that for every $\beta$ large, $M_n/\log n \to c_\beta$, and $(M_n - \mathbb E[M_n])_n$ forms a tight sequence. Moreover, even though this centered sequence does not converge, all its sub-sequential limits satisfy uniform Gumbel tail bounds. Based on joint work with Eyal Lubetzky. 

Stochastic analysis and geometric functional inequalities

Series
High Dimensional Seminar
Time
Wednesday, October 9, 2019 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Masha GordinaUniversity of Connecticut

We will survey different methods of proving functional inequalities for hypoelliptic  diffusions and the corresponding heat kernels. Some of these methods rely on geometric methods such as curvature-dimension inequalities (due to Baudoin-Garofalo), and some are probabilistic  such as coupling, and finally some use structure  theory and a Fourier transform on Lie groups. This is based on joint work with M. Asaad, F. Baudoin, B. Driver, T. Melcher, Ph. Mariano et al.

Obstructions to nice branch sets for branched coverings

Series
Geometry Topology Student Seminar
Time
Wednesday, October 9, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Sudipta KolayGeorgia Tech

It is a classical theorem of Alexander that every closed oriented manifold is a piecewise linear branched covering of the sphere. In this talk, we will discuss some obstructions to realizing a manifold as a branched covering of the sphere if we require additional properties (like being a submanifold) on the branch set.

 

A random walk through sub-riemanian geometry

Series
Analysis Seminar
Time
Wednesday, October 9, 2019 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Masha GordinaUniversity of Connecticut

A sub-Riemannian manifold M is a connected smooth manifold such that the only smooth curves in M which are admissible are those whose tangent vectors at any point are restricted to a particular subset of all possible tangent vectors.  Such spaces have several applications in physics and engineering, as well as in the study of hypo-elliptic operators.  We will  construct a random walk on M which converges to a process whose infinitesimal generator  is  one of the natural sub-elliptic  Laplacian  operators.  We will also describe these  Laplacians geometrically and discuss the difficulty of defining one which is canonical.   Examples will be provided.  This is a joint work with Tom Laetsch.

Geometric Approaches for Metastability in Stochastic Dynamical Systems with Applications

Series
Research Horizons Seminar
Time
Wednesday, October 9, 2019 - 13:10 for
Location
Skiles 005
Speaker
Larissa SerdukovaGeorgia Tech

Please Note: NOTE THE UNUSUAL TIME: This seminar takes place from 1:10-1:50 for THIS WEEK ONLY.

Basin of attraction for a stable equilibrium point is an effective concept for stability in deterministic systems. However, it does not contain information on the external perturbations that may affect it. The concept of stochastic basin of attraction (SBA) is introduced by incorporating a suitable probabilistic notion of basin. The criteria for the size of the SBA is based on the escape probability, which is one of the deterministic quantities that carry dynamical information and can be used to quantify dynamical behavior of the corresponding stochastic basin of attraction. SBA is an efficient tool to describe the metastable phenomena complementing the known exit time, escape probability, or relaxation time. Moreover, the geometric structure of SBA gives additional insight into the system's dynamical behavior, which is important for theoretical and practical reasons. This concept can be used not only in models with small intensity but also with whose amplitude is proportional or in general is a function of an order parameter. The efficiency of the concept is presented through two applications.

Partially ordered Reeb graphs, tree decompositions, and phylogenetic networks

Series
Mathematical Biology Seminar
Time
Wednesday, October 9, 2019 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Anastasios StefanouMathematical Biosciences Institute, Ohio State University

Inspired by the interval decomposition of persistence modules and the extended Newick format of phylogenetic networks, we show that, inside the larger category of partially ordered Reeb graphs, every Reeb graph with n leaves and first Betti number s, is equal to a coproduct of at most 2s trees with (n + s) leaves. An implication of this result, is that Reeb graphs are fixed parameter tractable when the parameter is the first Betti number. We propose partially ordered Reeb graphs as a natural framework for modeling time consistent phylogenetic networks.  We define a notion of interleaving distance on partially ordered Reeb graphs which is analogous to the notion of interleaving distance for ordinary Reeb graphs. This suggests using the interleaving distance as a novel metric for time consistent phylogenetic networks.

Deterministic algorithms for counting bases of a matroid

Series
Lorentzian Polynomials Seminar
Time
Tuesday, October 8, 2019 - 14:50 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Mohit SinghGeorgia Tech

We will discuss a deterministic, polynomial (in the rank) time approximation algorithm for counting the bases of a given matroid and for counting common bases between two matroids of the same rank. This talk follows the paper (https://arxiv.org/abs/1807.00929) of Nima Anari, Shayan Oveis Gharan, and Cynthia Vinzant.

Efficient Representations of Correlated Data as Tensor Networks

Series
Math Physics Seminar
Time
Monday, October 7, 2019 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Glen EvenblySchool of Physics, Georgia Tech
Tensors networks are a formalism for expressing high-order tensors as networks of low-order tensors, thus can offer a compact representation of certain high-dimensional datasets. Originally developed in the context of quantum many-body theory, where they are used to efficiently represent quantum wave-functions, tensor networks have since found application in big data analytics, error correction, classical data compression and machine learning.
 
In this talk I will provide a brief introduction to the theory and application of tensor networks, and outline some of the current research directions in the tensor network program.    
 

Joint UGA-GT Topology Seminar at GT: Upper bounds on the topological slice genus via twisting operations

Series
Geometry Topology Seminar
Time
Monday, October 7, 2019 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Duncan McCoyUQAM
I will explain how null-homologous twisting operations can be used to obtain bounds on the topological slice genus. In particular, I will discuss how one can obtain upper bounds on the topological slice genera of torus knots and satellite knots using these operations.

Pages