Seminars and Colloquia by Series

Portraits of RIFs: their singularities and unimodular level sets on T^2

Series
Analysis Seminar
Time
Wednesday, November 7, 2018 - 10:14 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Kelly Bickel – Bucknell University
This talk concerns two-variable rational inner functions phi with singularities on the two-torus T^2, the notion of contact order (and related quantities), and its various uses. Intuitively, contact order is the rate at which phi’s zero set approaches T^2 along a coordinate direction, but it can also be defined via phi's well-behaved unimodular level sets. Quantities like contact order are important because they encode information about the numerical stability of phi, for example when it belongs to Dirichlet-type spaces and when its partial derivatives belong to Hardy spaces. The unimodular set definition is also useful because it allows one to “see” contact order and in some sense, deduce numerical stability from pictures. This is joint work with James Pascoe and Alan Sola.

Inviscid damping near Couette flow in a finite channel

Series
PDE Seminar
Time
Tuesday, November 6, 2018 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Hao Jia – University of Minnesota –
The two dimensional Euler equation is globally wellposed, but the long time behavior of solutions is not well understood. Generically, it is conjectured that the vorticity, due to mixing, should weakly but not strongly converge as $t\to\infty$. In an important work, Bedrossian and Masmoudi studied the perturbative regime near Couette flow $(y,0)$ on an infinite cylinder, and proved small perturbation in the Gevrey space relaxes to a nearby shear flow. In this talk, we will explain a recent extension to the case of a finite cylinder (i.e. a periodic channel) with perturbations in a critical Gevrey space for this problem. The main interest of this extension is to consider the natural boundary effects, and to ensure that the Couette flow in our domain has finite energy. Joint work with Alex Ionescu.

The extremal function for $K_p$ minors

Series
Other Talks
Time
Tuesday, November 6, 2018 - 12:30 for 30 minutes
Location
Skiles 006
Speaker
Dantong Zhu – Georgia Tech –

Please Note: This talk is organized by the Association for Women in Math (AWM). Everyone is welcome to attend.

In 1968, Mader showed that for every integer $p = 1, 2, …, 7$, agraph on $n \geq p$ vertices and at least $(p-2)n - \binom{p-1}{2} + 1$ edgeshas a $K_p$ minor. However, this result is false for $p = 8$ with the counter-example K2,2,2,2,2. In this talk, we will discuss this function presented byMader for $K_p$ where $p$ is bigger. We will also discuss related resultsproved using probabilistic methods and the relation of this problem toHadwiger’s conjecture.

Quantum Chaos, Thermalization, and Localization

Series
Other Talks
Time
Tuesday, November 6, 2018 - 11:00 for 1 hour (actually 50 minutes)
Location
Howey N110
Speaker
Brian Swingle – Univ of Maryland
I will discuss chaos in quantum many-body systems, specifically how it is relates to thermalization and how it fails in many-body localized states. I will conjecture a new universal form for the spreading of chaos in local systems, and discuss evidence for the conjecture from a variety of sources including new large-scale simulations of quantum dynamics of spin chains.

A family of freely slice good boundary links

Series
Geometry Topology Seminar
Time
Monday, November 5, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Min Hoon Kim – Korea Institute for Advanced Study
The still open topological 4-dimensional surgery conjecture is equivalent to the statement that all good boundary links are freely slice. In this talk, I will show that every good boundary link with a pair of derivative links on a Seifert surface satisfying a homotopically trivial plus assumption is freely slice. This subsumes all previously known methods for freely slicing good boundary links with two or more components, and provides new freely slice links. This is joint work with Jae Choon Cha and Mark Powell.

High-dimensional Covariance Structure Testing using Maximum Pairwise Bayes Factors

Series
Applied and Computational Mathematics Seminar
Time
Monday, November 5, 2018 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Lizhen Lin – University of Notre Dame –
Hypothesis testing of structure in covariance matrices is of significant importance, but faces great challenges in high-dimensional settings. Although consistent frequentist one-sample covariance tests have been proposed, there is a lack of simple, computationally scalable, and theoretically sound Bayesian testing methods for large covariance matrices. Motivated by this gap and by the need for tests that are powerful against sparse alternatives, we propose a novel testing framework based on the maximum pairwise Bayes factor. Our initial focus is on one-sample covariance testing; the proposed test can optimally distinguish null and alternative hypotheses in a frequentist asymptotic sense. We then propose diagonal tests and a scalable covariance graph selection procedure that are shown to be consistent. Further, our procedure can effectively control false positives. A simulation study evaluates the proposed approach relative to competitors. The performance of our graph selection method is demonstrated through applications to a sonar data set.

Introduction to Freedman's disk embedding conjecture

Series
Geometry Topology Seminar Pre-talk
Time
Monday, November 5, 2018 - 12:45 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Min Hoon Kim – Korea Institute for Advanced Study
In 1982, by using his celebrated disk embedding theorem, Freedman classified simply connected topological 4-manifolds up to homeomorphism. The disk embedding conjecture says that the disk embedding theorem holds for general 4-manifolds with arbitrary fundamental groups. The conjecture is a central open question in 4-manifold topology. In this introductory survey talk, I will briefly discuss Freedman's disk embedding conjecture and some related conjectures (the topological 4-dimensional surgery conjecture and the s-cobordism conjecture). I will also explain why the disk embedding conjecture implies that all good boundary links are freely slice.

A Simple Analytic Proof for the Shadowing Lemma

Series
Dynamical Systems Working Seminar
Time
Friday, November 2, 2018 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 156
Speaker
Yian Yao – GT Math
The Shadowing lemma describes the behaviour of pseudo-orbits near a hyperbolic invariant set. In this talk, I will present an analytic proof of the shadowing lemma for discrete flows. This is a work by K. R. Meyer and George R. Sell.

A splitter theorem for large 3-connected graphs

Series
Combinatorics Seminar
Time
Friday, November 2, 2018 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Guoli Ding – Louisiana State University
The purpose of this talk is to explain the following result. Let n > 2 be an integer. Let H be a 3-connected minor of a 3-connected graph G. If G is sufficiently large (relative to n and the size of H) then G has a 3-connected minor obtained from H by “adding” K_{3,n} or W_n.

Accelerating the Convergence Rate of Distributed Subgradient Methods with Adaptive Quantization

Series
ACO Student Seminar
Time
Friday, November 2, 2018 - 12:20 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Thinh Doan – ISyE/ECE, Georgia Tech –
Abstract In this talk, I will present a popular distributed method, namely, distributed consensus-based gradient (DCG) method, for solving optimal learning problems over a network of agents. Such problems arise in many applications such as, finding optimal parameters over a large dataset distributed among a network of processors or seeking an optimal policy for coverage control problems in robotic networks. The focus is to present our recent results, where we study the performance of DCG when the agents are only allowed to exchange their quantized values due to their finite communication bandwidth. In particular, we develop a novel quantization method, which we refer to as adaptive quantization. The main idea of our approach is to quantize the nodes' estimates based on the progress of the algorithm, which helps to eliminate the quantized errors. Under the adaptive quantization, we then derive the bounds on the convergence rates of the proposed method as a function of the bandwidths and the underlying network topology, for both convex and strongly convex objective functions. Our results suggest that under the adaptive quantization, the rate of convergence of DCG with and without quantization are the same, except for a factor which captures the number of quantization bits. To the best of the authors’ knowledge, the results in this paper are considered better than any existing results for DCG under quantization. This is based on a joint work with Siva Theja Maguluri and Justin Romberg. Bio Thinh T. Doan is a TRIAD postdoctoral fellow at Georgia Institute of Technology, joint between the School of Industrial and Systems Engineering and the School of Electrical and Computer Engineering (ECE). He was born in Vietnam, where he got his Bachelor degree in Automatic Control at Hanoi University of Science and Technology in 2008. He obtained his Master and Ph.D. degrees both in ECE from the University of Oklahoma in 2013 and the University of Illinois at Urbana-Champaign in 2018, respectively. His research interests lie at the intersection of control theory, optimization, distributed algorithms, and applied probability, with the main applications in machine learning, reinforcement learning, power networks, and multi-agent systems.

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