Seminars and Colloquia by Series

Optimal variance-reduced stochastic approximation in Banach spaces

Series
Applied and Computational Mathematics Seminar
Time
Monday, November 21, 2022 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005 and https://gatech.zoom.us/j/98355006347
Speaker
Wenlong Mou – UC Berkeley –

Please Note: Speaker will give the talk in person

Estimating the fixed-point of a contractive operator from empirical data is a fundamental computational and statistical task. In many practical applications including dynamic programming, the relevant norm is not induced by an inner product structure, which hinders existing techniques for analysis. In this talk, I will present recent advances in stochastic approximation methods for fixed-point equations in Banach spaces. Among other results, we discuss a novel variance-reduced stochastic approximation scheme, and establish its non-asymptotic error bounds. In contrast to worst-case guarantees, our bounds are instance-dependent, and achieve the optimal covariance structure in central limit theorems non-asymptotically.
Joint works with Koulik Khamaru, Martin Wainwright, Peter Bartlett, and Michael Jordan.

Naturality of Legendrian LOSS invariant under positive contact surgery

Series
Geometry Topology Seminar
Time
Monday, November 21, 2022 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Shunyu Wan – University of Virginia –

Given a Legendrian knot L in a contact 3 manifold, one can associate a so-called LOSS invariant to L which lives in the knot Floer homology group. We proved that the LOSS invariant is natural under the positive contact surgery. In this talk I will review some background and definition, try to get the ideal of the proof and talk about the application which is about distinguishing Legendrian and Transverse knot.

Algebraic and combinatorial problems arising from maximum likelihood estimation using small datasets

Series
Algebra Seminar
Time
Monday, November 21, 2022 - 13:30 for 1 hour (actually 50 minutes)
Location
Clough 125 Classroom
Speaker
Daniel Irving Bernstein – Tulane University Department of Mathematics –

Loosely speaking, the maximum likelihood threshold of a statistical model is the fewest number of data points needed to fit the model using maximum likelihood estimation. In this talk, I will discuss combinatorial and algebraic-geometric approaches to studying this poorly understood quantity for a certain class of Gaussian models. This is based on joint work with Sean Dewar, Steven Gortler, Tony Nixon, Meera Sitharam, and Louis Theran

Structure and computation of data-driven brain networks

Series
Time
Friday, November 18, 2022 - 16:30 for 1 hour (actually 50 minutes)
Location
Skiles 005 and Online
Speaker
Hannah Choi – Georgia Tech

https://gatech.zoom.us/j/95197085752?pwd=WmtJUVdvM1l6aUJBbHNJWTVKcVdmdz09

The complex connectivity structure unique to the brain network is believed to underlie its robust and efficient coding capability. One of many unique features of the mammalian brain network is its spatial embedding and hierarchical organization. I will discuss effects of these structural characteristics on network dynamics as well as their computational implications with a focus on the flexibility between modular and global computations and predictive coding.  

Markov chains and sampling methods for contiguous partitions

Series
Combinatorics Seminar
Time
Friday, November 18, 2022 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 202
Speaker
Wesley Pegden – Carnegie Mellon University

With applications in the analysis of political districtings, Markov chains have become and essential tool for studying contiguous partitions of geometric regions. Nevertheless, there remains a dearth of rigorous results on the mixing times of the chains employed for this purpose. In this talk we'll discuss a sub-exponential bound on the mixing time of the Glauber dynamics chain for the case of bounded-size contiguous partition classes on certain grid-like classes of graphs.

Using Morse homology to understand persistence modules I

Series
Geometry Topology Working Seminar
Time
Friday, November 18, 2022 - 14:00 for 1.5 hours (actually 80 minutes)
Location
Skiles 006
Speaker
Daniel Irvine – Georgia Tech –

Please Note: Part 1 of a multi-part discussion.

Morse theory and Morse homology together give a method for understanding how the topology of a smooth manifold changes with respect to a filtration of the manifold given by sub-level sets. The Morse homology of a smooth manifold can be expressed using an algebraic object called a persistence module. A persistence module is a module graded by real numbers, and in this setup the grading on the module corresponds to the aforementioned filtration on the smooth manifold.

This is the first of a series of talks that aims to explain the relationship between Morse homology and persistence modules. In the first talk, I will give a rapid review of Morse theory and a review of Morse homology. An understanding of singular homology will be assumed. 

Breaking the quadratic gap for strongly polynomial solvers to combinatorial linear programs

Series
ACO Student Seminar
Time
Friday, November 18, 2022 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Bento Natura – Georgia Tech ISyE –

Recent years have seen tremendous progress in high-accuracy solvers for Maximum Flow, Minimum-Cost Flow and general Linear Programs (LP). Progress on strongly polynomial solvers for combinatorial LP on the other hand has stalled. The computational gap between high-accuracy solvers and strongly polynomial solvers is linear in the number of variables only for combinatorial LP on directed graphs. For combinatorial LP beyond directed graphs this gap is currently quadratic and is known since the 1980s due to a seminal result by Tardos.

We finally break the quadratic gap and design a strongly polynomial interior-point-method for combinatorial LP, which reduces the gap to only a linear factor. Thus, we match the known linear gap for LP on directed graphs. Furthermore, we close the linear gap between feasibility and optimization of combinatorial LP.

Idylls and Baker-Lorscheid Multiplicities

Series
Algebra Student Seminar
Time
Friday, November 18, 2022 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Trevor Gunn – Georgia Tech

I will describe the arithmetic of polynomials over idylls and various division algorithms and rules. For instance, that arithmetic might capture a total order/sign or an absolute value. These division algorithms will relate, for instance, the number of positive roots of a polynomial to the signs of the coefficients (Descartes's Rule of Signs).

New bounds on the excess charge for bosonic systems interacting through Coulomb potentials

Series
Math Physics Seminar
Time
Thursday, November 17, 2022 - 16:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Rafael Benguria – Catholic University of Chile –

In this talk, using a technique introduced by P.~T.~Nam in 2012 and the Coulomb Uncertainty Principle, I will present the proof of new bounds on the excess charge for non relativistic  atomic systems, independent of the particle statistics. These new bounds are the best bounds to date for bosonic systems. This is joint work with Juan Manel González and Trinidad Tubino.

Join Zoom Meeting: https://gatech.zoom.us/j/94786316294

Large Dimensional Independent Component Analysis: Statistical Optimality and Computational Tractability

Series
Stochastics Seminar
Time
Thursday, November 17, 2022 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ming Yuan – Columbia University

Independent component analysis is a useful and general data analysis tool. It has found great successes in many applications. But in recent years, it has been observed that many popular approaches to ICA do not scale well with the number of components. This debacle has inspired a growing number of new proposals. But it remains unclear what the exact role of the number of components is on the information theoretical limits and computational complexity for ICA. Here I will describe our recent work to specifically address these questions and introduce a refined method of moments that is both computationally tractable and statistically optimal.

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