Seminars and Colloquia Schedule

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.

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.

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.

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.

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 –

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.

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.

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.

From Atoms to Fluids: an introduction to Statistical Mechanics

Series
Research Horizons Seminar
Time
Wednesday, November 7, 2018 - 12:20 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Federico Bonetto – Georgia Tech
We all know that the air in a room is made up by a huge number of atoms that zip around at high velocity colliding continuously. How is this consistent with our observation of air as a thin and calm fluid surrounding us? This is what Statistical Mechanics try to understand. I'll introduce the basic examples and ideas of equilibrium and non equilibrium Statistical Mechanics showing that they apply well beyond atoms and air.

Analysis and recovery of high-dimensional data with low-dimensional structures

Series
High Dimensional Seminar
Time
Wednesday, November 7, 2018 - 12:52 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Wenjing Liao – Georgia Tech –

High-dimensional data arise in many fields of contemporary science and introduce new challenges in statistical learning and data recovery. Many datasets in image analysis and signal processing are in a high-dimensional space but exhibit a low-dimensional structure. We are interested in building efficient representations of these data for the purpose of compression and inference, and giving performance guarantees depending on the intrinsic dimension of data. I will present two sets of problems: one is related with manifold learning; the other arises from imaging and signal processing where we want to recover a high-dimensional, sparse vector from few linear measurements. In the first problem, we model a data set in $R^D$ as samples from a probability measure concentrated on or near an unknown $d$-dimensional manifold with $d$ much smaller than $D$. We develop a multiscale adaptive scheme to build low-dimensional geometric approximations of the manifold, as well as approximating functions on the manifold. The second problem arises from source localization in signal processing where a uniform array of sensors is set to collect propagating waves from a small number of sources. I will present some theory and algorithms for the recovery of the point sources with high precision.

Transition lines for Almost Mathieu Operator

Series
Math Physics Seminar
Time
Wednesday, November 7, 2018 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Fan Yang – Georgia Tech
I will talk about what happens on the spectral transition lines for the almost Mathieu operator. This talk is based on joint works with Svetlana Jitomirskaya and Qi Zhou. For both transition lines \{\beta(\alpha)=\ln{\lambda}\} and \{\gamma(\alpha,\theta)=\ln{\lambda}\} in the positive Lyapunov exponent regime, we show purely point spectrum/purely singular continuous spectrum for dense subsets of frequencies/phases.

Finding small simple cycle separators for 2-connected planar graphs

Series
Graph Theory Working Seminar
Time
Wednesday, November 7, 2018 - 16:30 for 1.5 hours (actually 80 minutes)
Location
Skiles 006
Speaker
Michael Wigal – Georgia Tech
For a graph on $n$ vertices, a vertex partition $A,B,C$ is a $f(n)$-vertex separator if $|C| \le f(n)$ and $|A|,|B| \le \frac{2}{3}n$ and $(A,B) = \emptyset$. A theorem from Gary Miller states for an embedded 2-connected planar graph with maximum face size $d$ there exists a simple cycle such that it is vertex separator of size at most $2\sqrt{dn}$. This has applications in divide and conquer algorithms.

The Clemens conjecture

Series
Student Algebraic Geometry Seminar
Time
Thursday, November 8, 2018 - 13:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Stephen McKean – Georgia Tech
In 1986, Herb Clemens conjectured that on a general quintic threefold, there are finitely many rational curves of any given degree. In this talk, we will give a survey of what is known about this conjecture. We will also highlight the connections between enumerative geometry and physics that arise in studying the quintic threefold.

Randomness vs Quantumness

Series
ACO Student Seminar
Time
Friday, November 9, 2018 - 13:05 for 30 minutes
Location
Skiles 005
Speaker
Lance Fortnow – School of Computer Science, Georgia Tech –
Often the popular press talks about the power of quantum computing coming from its ability to perform several computations simultaneously. We’ve already had a similar capability from probabilistic machines. This talk will explore the relationship between quantum and randomized computation, how they are similar and how they differ, and why quantum can work exponentially faster on some but far from all computational problems. We’ll talk about some open problems in quantum complexity that can help shed light on the similarities and differences between randomness and “quantumness”. This talk will not assume any previous knowledge of quantum information or quantum computing.

Locally decodable codes and arithmetic progressions in random settings

Series
Combinatorics Seminar
Time
Friday, November 9, 2018 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Sivakanth Gopi – Microsoft Research Redmond
(1) A set D of natural numbers is called t-intersective if every positive upper density subset A of natural numbers contains a (t+1)-length arithmetic progression (AP) whose common differences is in D. Szemeredi's theorem states that the set of all natural numbers is t-intersective for every t. But there are other non-trivial examples like {p-1: p prime}, {1^k,2^k,3^k,\dots} for any k etc. which are t-intersective for every t. A natural question to study is at what density random subsets of natural numbers become t-intersective? (2) Let X_t be the number of t-APs in a random subset of Z/NZ where each element is selected with probability p independently. Can we prove precise estimates on the probability that X_t is much larger than its expectation? (3) Locally decodable codes (LDCs) are error correcting codes which allow ultra fast decoding of any message bit from a corrupted encoding of the message. What is the smallest encoding length of such codes? These seemingly unrelated problems can be addressed by studying the Gaussian width of images of low degree polynomial mappings, which seems to be a fundamental tool applicable to many such problems. Adapting ideas from existing LDC lower bounds, we can prove a general bound on Gaussian width of such sets which reproves the known LDC lower bounds and also implies new bounds for the above mentioned problems. Our bounds are still far from conjectured bounds which suggests that there is plenty of room for improvement. If time permits, we will discuss connections to type constants of injective tensor products of Banach spaces (or chernoff bounds for tensors in simpler terms). Joint work with Jop Briet.

A formula with some applications to the theory of Lyapunov exponents (Cancelled)

Series
Dynamical Systems Working Seminar
Time
Friday, November 9, 2018 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 156
Speaker
Rui Han – Georgia Tech
We prove an elementary formula about the average expansion of certain products of 2 by 2 matrices. This permits us to quickly re-obtain an inequality by M. Herman and a theorem by Dedieu and Shub, both concerning Lyapunov exponents. This is a work of A. Avila and J. Bochi. https://link.springer.com/article/10.1007/BF02785853