Seminars and Colloquia by Series

Inference, Computation, and Games

Series
Applied and Computational Mathematics Seminar
Time
Monday, September 20, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005 and https://bluejeans.com/457724603/4379
Speaker
Florian SchaeferGT CSE

Please Note: Note the hybrid mode. The speaker will be in person in Skiles 005.

In this talk, we develop algorithms for numerical computation, based on ideas from competitive games and statistical inference. 

 

In the first part, we propose competitive gradient descent (CGD) as a natural generalization of gradient descent to saddle point problems and general sum games. Whereas gradient descent minimizes a local linear approximation at each step, CGD uses the Nash equilibrium of a local bilinear approximation. Explicitly accounting for agent-interaction significantly improves the convergence properties, as demonstrated in applications to GANs, reinforcement learning, and computer graphics.

 

In the second part, we show that the conditional near-independence properties of smooth Gaussian processes imply the near-sparsity of Cholesky factors of their dense covariance matrices. We use this insight to derive simple, fast solvers with state-of-the-art complexity vs. accuracy guarantees for general elliptic differential- and integral equations. Our methods come with rigorous error estimates, are easy to parallelize, and show good performance in practice.

Mitsumatsu's Liouville domains are stably Weinstein

Series
Geometry Topology Seminar
Time
Monday, September 20, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Austin ChristianGeorgia Tech

In 1995, Mitsumatsu constructed a large family of Liouville domains whose topology obstructs the existence of a Weinstein structure.  Stabilizing these domains yields Liouville domains for which the topological obstruction is no longer in effect, and in 2019 Huang asked whether Mitsumatsu's Liouville domains were stably homotopic to Weinstein domains.  We answer this question in the affirmative.  This is joint work-in-progress with J. Breen.

Whitney Towers, Higher Order Intersections, and Tree-Valued Invariants

Series
Geometry Topology Working Seminar
Time
Friday, September 17, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Miriam KuzbaryGeorgia Tech

In this pair of talks I will survey some of the machinery developed by Conant, Schneiderman, and Teichner to study Whitney towers, and their applications to the study of knot and link concordance. Whitney towers can be thought of as measuring the failure of the Whitney trick in dimension 4 and can be used, in a sense, to approximate slice disks. The talks will be based on various papers of Schneiderman, Conant-Schneiderman-Teichner, Cochran-Orr-Teichner and lecture notes by those authors.

Stochastic Methods for Matrix Games and its Applications.

Series
ACO Student Seminar
Time
Friday, September 17, 2021 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 314
Speaker
Yujia JinStanford University

Please Note: Stream online at https://bluejeans.com/520769740/

In this talk, I will introduce some recent advances in designing stochastic primal-dual methods for bilinear saddle point problems, in the form of min_x max_y y^TAx under different geometries of x and y. These problems are prominent in economics, linear programming, machine learning and reinforcement learning. Specifically, our methods apply to Markov decision processes (MDPs), linear regression, and computational geometry tasks. 

 

In our work, we propose a variance-reduced framework for solving convex-concave saddle-point problems, given a gradient estimator satisfying some local properties. Further, we show how to design such gradient estimators for bilinear objectives under different geometry including simplex (l_2), Euclidean ball (l_1) or box (l_inf) domains. For matrix A with larger dimension n, nonzero entries nnz and accuracy epsilon, our proposed variance-reduced primal dual methods obtain a runtime complexity of nnz+\sqrt{nnz*n}/epsilon, improving over the exact gradient methods and fully stochastic methods in the accuracy and/or the sparse regime (when epsilon < n/nnz). For finite-sum saddle-point problems sum_{k=1}^K f_k(x,y) where each f is 1-smooth, we show how to obtain an epsilon-optimal saddle point within gradient query complexity of K+\sqrt{K}/epsilon.

 

Moreover, we also provide a class of coordinate methods for solving bilinear saddle-point problems. These algorithms use either O(1)-sparse gradient estimators to obtain improved sublinear complexity over fully stochastic methods, or their variance-reduced counterparts for improved nearly-linear complexity, for sparse and numerically sparse instances A. 

 

This talk is based on several joint works with Yair Carmon, Aaron Sidford and Kevin Tian, with links of papers below:

Variance Reduction for Matrix Games

Coordinate Methods for Matrix Games

Efficiently Solving MDPs using Stochastic Mirror Descent

 

Bio of the speaker: Yujia Jin is a fourth-year Ph.D. student in Department of Management Science and Engineering, Stanford University, working with Aaron Sidford. She is interested in designing efficient continuous optimization methods, which often run in nearly linear / sublinear time and find vast applications in machine learning, data analysis, reinforcement learning, and graph problems.

The algebra of linear PDE

Series
Algebra Student Seminar
Time
Friday, September 17, 2021 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 005, or ONLINE
Speaker
Marc HärkönenGeorgia Tech

Please Note: Online link: https://teams.microsoft.com/l/meetup-join/19%3a3a9d7f9d1fca4f5b991b4029b09c69a1%40thread.tacv2/1631746973297?context=%7b%22Tid%22%3a%22482198bb-ae7b-4b25-8b7a-6d7f32faa083%22%2c%22Oid%22%3a%2206706002-23ff-4989-8721-b078835bae91%22%7d

This talk is meant to be a gentle introduction to the algebraic theory of linear PDE with constant coefficients. We will present the connection between submodules of free modules of polynomial rings and solution sets of PDEs, and establish certain results relating analytical properties of solutions with algebraic properties of polynomial modules. We will also review classical spaces of functions in distribution theory and Fourier analysis.

Towards robust and efficient mean estimation

Series
Stochastics Seminar
Time
Thursday, September 16, 2021 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Stas MinskerUniversity of Southern California

Several constructions of the estimators of the mean of a random variable that admit sub-Gaussian deviation guarantees and are robust to adversarial contamination under minimal assumptions have been suggested in the literature. The goal of this talk is to discuss the size of constants appearing in the bounds, both asymptotic and non-asymptotic, satisfied by the median-of-means estimator and its analogues. We will describe a permutation-invariant version of the median-of-means estimator and show that it is asymptotically efficient, unlike its “standard" version. Finally, applications and extensions of these results to robust empirical risk minimization will be discussed.

Enumerating Knots and Links

Series
Geometry Topology Student Seminar
Time
Wednesday, September 15, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Hugo ZhouGeorgia Tech

How do we build a knot table? We will discuss Conway’s paper “an enumeration of knots and links” and Hoste, Thistlethwaite and Weeks’ paper “the first 1701936 knots”.

Maximizing insight with minimal (and erroneous) information: The case of COVID-19

Series
Mathematical Biology Seminar
Time
Wednesday, September 15, 2021 - 11:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Juan B. GutiérrezUniversity of Texas at Saint Antonio

Please Note: Meeting Link: https://bluejeans.com/379561694/5031

This talk presents novel approaches to old techniques to forecast COVID-19: (i) a modeling framework that takes into consideration asymptomatic carriers and government interventions, (ii) a method to rectify daily case counts reported in public databases, and (iii) a method to study socioeconomic factors and propagation of disinformation. In the case of (i), results were obtained with a comprehensive data set of hospitalizations and cases in the metropolitan area of San Antonio through collaboration with local and regional government agencies, a level of data seldom studied in a disaggregated manner. In the case of (ii), results were obtained with a simple approach to data rectification that has not been exploited in the literature, resulting in a non-autonomous system that opens avenues of mathematical exploration. In the case of (iii), this talk presents a methodology to study the effect of socioeconomic and demographic factors, including the phenomenon of disinformation and its effect in public health; currently there are few mathematical results in this important area.

Induced subgraphs and treewidth

Series
Graph Theory Seminar
Time
Tuesday, September 14, 2021 - 15:45 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Sophie SpirklUniversity of Waterloo

Treewidth, introduced by Robertson and Seymour in the graph minors series, is a fundamental measure of the complexity of a graph. While their results give an answer to the question, “what minors occur in graphs of large treewidth?,” the same question for induced subgraphs is still open. I will talk about some conjectures and recent results in this area. Joint work with Tara Abrishami, Maria Chudnovsky, Cemil Dibek, Sepehr Hajebi, Pawel Rzazewski, Kristina Vuskovic.

(Differential) primary decomposition of modules

Series
Algebra Seminar
Time
Tuesday, September 14, 2021 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Justin ChenICERM/Georgia Tech

Primary decomposition is an indispensable tool in commutative algebra, both theoretically and computationally in practice. While primary decomposition of ideals is ubiquitous, the case for general modules is less well-known. I will give a comprehensive exposition of primary decomposition for modules, starting with a gentle review of practical symbolic algorithms, leading up to recent developments including differential primary decomposition and numerical primary decomposition. Based on joint works with Yairon Cid-Ruiz, Marc Harkonen, Robert Krone, and Anton Leykin.

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