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Series: Job Candidate Talk

Convex-geometric methods, involving random projection operators and coverings, have been successfully used in the study of the largest and smallest singular values, delocalization of eigenvectors,
and in establishing the limiting spectral distribution for certain random matrix models. Among
further applications of those methods in computer science and statistics are restricted invertibility
and dimension reduction, as well as approximation of covariance matrices of multidimensional distributions. Conversely, random linear operators play a very important role in geometric functional
analysis. In this talk, I will discuss some recent results (by my collaborators and myself) within convex geometry and the theory of random matrices, focusing on invertibility of square non-Hermitian
random matrices (with applications to numerical analysis and the study of the limiting spectral
distribution of directed d-regular graphs), approximation of covariance matrices (in particular, a
strengthening of the Bai–Yin theorem), as well as some applications of random operators in convex
geometry.

Series: Geometry Topology Seminar

Monday, January 22, 2018 - 13:55 ,
Location: Skiles 005 ,
Dr. Lee, Kiryung ,
GT ECE ,
Organizer: Sung Ha Kang

TBA by Kiryung Lee

Series: ACO Student Seminar

Studying random samples drawn from large, complex sets is one way to begin to learn about typical properties and behaviors. However, it is important that the samples examined are random enough: studying samples that are unexpectedly correlated or drawn from the wrong distribution can produce misleading conclusions. Sampling processes using Markov chains have been utilized in physics, chemistry, and computer science, among other fields, but they are often applied without careful analysis of their reliability. Making sure widely-used sampling processes produce reliably representative samples is a main focus of my research, and in this talk I'll touch on two specific applications from statistical physics and combinatorics.I'll also discuss work applying these same Markov chain processes used for sampling in a novel way to address research questions in programmable matter and swarm robotics, where a main goal is to understand how simple computational elements can accomplish complicated system-level goals. In a constrained setting, we've answered this question by showing that groups of abstract particles executing our simple processes (which are derived from Markov chains) can provably accomplish remarkable global objectives. In the long run, one goal is to understand the minimum computational abilities elements need in order to exhibit complex global behavior, with an eye towards developing systems where individual components are as simple as possible.This talk includes joint work with Marta Andrés Arroyo, Joshua J. Daymude, Daniel I. Goldman, David A. Levin, Shengkai Li, Dana Randall, Andréa Richa, William Savoie, and Ross Warkentin.

Series: Other Talks

This is a workshop designed to provide an introduction to the use of
modern tools from Dynamical Systems in the design of space exploration
missions. More details and a detailed schedule is found in http://people.math.gatech.edu/~rll6/JPL/jpl.html

Series: Other Talks

Series: Analysis Seminar

An overarching problem in matrix weighted theory is the so-called A2 conjecture, namely the question of whether the norm of a Calderón-Zygmund operator acting on a matrix weighted L2 space depends linearly on the A2 characteristic of the weight. In this talk, I will discuss the history of this problem and provide a survey of recent results with an emphasis on the challenges that arise within the setup.

Series: Other Talks

Series: Job Candidate Talk

Semiparametric regressions enjoy the flexibility of nonparametric models as well as the in-terpretability of linear models. These advantages can be further leveraged with recent ad-vance in high dimensional statistics. This talk begins with a simple partially linear model,Yi = Xi β ∗ + g ∗ (Zi ) + εi , where the parameter vector of interest, β ∗ , is high dimensional butsufficiently sparse, and g ∗ is an unknown nuisance function. In spite of its simple form, this highdimensional partially linear model plays a crucial role in counterfactual studies of heterogeneoustreatment effects. In the first half of this talk, I present an inference procedure for any sub-vector (regardless of its dimension) of the high dimensional β ∗ . This method does not requirethe “beta-min” condition and also works when the vector of covariates, Zi , is high dimensional,provided that the function classes E(Xij |Zi )s and E(Yi |Zi ) belong to exhibit certain sparsityfeatures, e.g., a sparse additive decomposition structure. In the second half of this talk, I discussthe connections between semiparametric modeling and Rubin’s Causal Framework, as well asthe applications of various methods (including the one from the first half of this talk and thosefrom my other papers) in counterfactual studies that are enriched by “big data”.Abstract as a .pdf

Series: School of Mathematics Colloquium

The probability of outcomes of repeated
fair coin tosses can be computed exactly using binomial coefficients.
Performing asymptotics on these formulas uncovers the Gaussian
distribution and the first instance of the central limit theorem. This
talk will focus on higher version of this story. We will consider random
motion subject to random forcing. By leveraging structures from representation theory and quantum integrable systems
we can compute the analogs of binomial coefficients and extract new and
different asymptotic behaviors than those of the Gaussian. This model
and its analysis fall into the general theory of "integrable
probability".