Seminars and Colloquia by Series

Hyperfields, Ordered Blueprints, and Moduli Spaces of Matroids

Series
Algebra Seminar
Time
Friday, October 19, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Matt Baker – Georgia Tech –
I will begin with a gentle introduction to hyperrings and hyperfields (originally introduced by Krasner for number-theoretic reasons), and then discuss a far-reaching generalization, Oliver Lorscheid’s theory of ordered blueprints. Two key examples of hyperfields are the hyperfield of signs S and the tropical hyperfield T. An ordering on a field K is the same thing as a homomorphism to S, and a (real) valuation on K is the same thing as a homomorphism to T. In particular, the T-points of an ordered blue scheme over K are closely related to Berkovich’s theory of analytic spaces.I will discuss a common generalization, in this language, of Descartes' Rule of Signs (which involves polynomials over S) and the theory of Newton Polygons (which involves polynomials over T). I will then introduce matroids over hyperfields (as well as certain more general kinds of ordered blueprints). Matroids over S are classically called oriented matroids, and matroids over T are also known as valuated matroids. I will explain how the theory of ordered blueprints and ordered blue schemes allow us to construct a "moduli space of matroids”, which is the analogue in the theory of ordered blue schemes of the usual Grassmannian variety in algebraic geometry. This is joint work with Nathan Bowler and Oliver Lorscheid.

The Price of Fair PCA: One Extra Dimension

Series
ACO Student Seminar
Time
Friday, October 19, 2018 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Samira Samadi – CS, Georgia Tech –
We investigate whether the standard dimensionality reduction techniques inadvertently produce data representations with different fidelity for two different populations. We show on several real-world datasets, PCA has higher reconstruction error on population A than B (for example, women versus men or lower versus higher-educated individuals). This can happen even when the dataset has similar number of samples from A and B . This motivates our study of dimensionality reduction techniques which maintain similar fidelity for A as B . We give an efficient algorithm for finding a projection which is nearly-optimal with respect to this measure, and evaluate it on several datasets. This is a joint work with Uthaipon Tantipongpipat, Jamie Morgenstern, Mohit Singh, and Santosh Vempala.

Lectures on Combinatorial Statistics: 2

Series
Stochastics Seminar
Time
Thursday, October 18, 2018 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Gabor Lugosi – Pompeu Fabra University, Barcelona –
In these lectures we discuss some statistical problems with an interesting combinatorial structure behind. We start by reviewing the "hidden clique" problem, a simple prototypical example with a surprisingly rich structure. We also discuss various "combinatorial" testing problems and their connections to high-dimensional random geometric graphs. Time permitting, we study the problem of estimating the mean of a random variable

Gabor Lugosi lectures on combinatorial statistics (2 of 3)

Series
Other Talks
Time
Thursday, October 18, 2018 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Lectures on Combinatorial Statistics – Pompeu Fabra University, Barcelona –

Please Note: Thanks are due to our colleague, Vladimir Koltchinskii, for arranging this visit. Please write to Vladimir if you would like to meet with Professor Gabor Lugosi during his visit, or for additional information.

In these lectures we discuss some statistical problems with an interesting combinatorial structure behind. We start by reviewing the "hidden clique" problem, a simple prototypical example with a surprisingly rich structure. We also discuss various "combinatorial" testing problems and their connections to high-dimensional random geometric graphs. Time permitting, we study the problem of estimating the mean of a random variable.

The Littlewood-Richardson Rule

Series
Student Algebraic Geometry Seminar
Time
Thursday, October 18, 2018 - 13:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Trevor Gunn – Georgia Tech
We will go over a short proof of the Littlewood-Richardson Rule due to Stembridge as well as some related combinatorics of tableaux.

Undergraduate Seminar (extra thursday lecture): When triangles turn square

Series
Other Talks
Time
Thursday, October 18, 2018 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Boris Bukh – Carnegie Mellon University
What to do if the measurements that you took were corrupted by a malicious spy? We will see how the natural geometric approach to the problem leads to a geometry where lines are crooked, and triangles are square.

Induced matching and strong chromatic index in bipartite graphs

Series
Graph Theory Working Seminar
Time
Wednesday, October 17, 2018 - 16:30 for 1.5 hours (actually 80 minutes)
Location
Skiles 006
Speaker
Chi-Nuo Lee – Georgia Tech
Erdős and Nešetřil conjectured in 1985 that every graph with maximum degree Δ can be strong edge colored using at most (5/4)Δ^2 colors. In this talk, we focus on a conjecture by R.J. Faudree et al, that Δ^2 holds as a bound for strong chromatic index in bipartite graphs, and related results where a bound is known.

Dynamical sampling

Series
Analysis Seminar
Time
Wednesday, October 17, 2018 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Longxiu Huang – Vanderbilt University
Dynamical sampling is a new area in sampling theory that deals with signals that evolve over time under the action of a linear operator. There are lots of studies on various aspects of the dynamical sampling problem. However, they all focus on uniform discrete time-sets $\mathcal T\subset\{0,1,2,\ldots, \}$. In our study, we concentrate on the case $\mathcal T=[0,L]$. The goal of the present work is to study the frame property of the systems $\{A^tg:g\in\mathcal G, t\in[0,L] \}$. To this end, we also characterize the completeness and Besselness properties of these systems.

Giannopolous’s upper bound for the Banach-Mazur distance to the cube

Series
High Dimensional Seminar
Time
Wednesday, October 17, 2018 - 12:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Christina Giannitsi – Georgia Institute of technology –

We already know that the Euclidean unit ball is at the center of the Banach-Mazur compactum, however its structure is still being explored to this day. In 1987, Szarek and Talagrand proved that the maximum distance $R_{\infty} ^n$ between an arbitrary $n$-dimensional normed space and $\ell _{\infty} ^n$, or equivalently the maximum distance between a symmetric convex body in $\mathbb{R} ^n$ and the $n$-dimensional unit cube is bounded above by $c n^{7/8}$. In this talk, we will discuss a related paper by A. Giannopoulos, "A note to the Banach-Mazur distance to the cube", where he proves that $R_{\infty} ^n < c n^{5/6}$.

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