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Series: PDE Seminar

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.

Series: Other Talks

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.

Series: Other Talks

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.

Series: Geometry Topology Seminar

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.

Monday, November 5, 2018 - 13:55 ,
Location: Skiles 005 ,
Lizhen Lin ,
University of Notre Dame ,
lizhen.lin@nd.edu ,
Organizer: Wenjing Liao

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.

Monday, November 5, 2018 - 12:45 ,
Location: Skiles 006 ,
Min Hoon Kim ,
Korea Institute for Advanced Study ,
Organizer: Jennifer Hom

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.

Friday, November 2, 2018 - 15:05 ,
Location: Skiles 156 ,
Yian Yao ,
GT Math ,
Organizer: Jiaqi Yang

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.

Series: Combinatorics Seminar

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.

Series: ACO Student Seminar

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.

Series: Graph Theory Seminar

Let X denote the number of triangles in the random graph G(n, p). The problem of determining the asymptotics of the rate of the upper tail of X, that is, the function f_c(n,p) = log Pr(X > (1+c)E[X]), has attracted considerable attention of both the combinatorics and the probability communities. We shall present a proof of the fact that whenever log(n)/n << p << 1, then f_c(n,p) = (r(c)+o(1)) n^2 p^2 log(p) for an explicit function r(c). This is joint work with Matan Harel and Frank Mousset.