Seminars and Colloquia Schedule

Complex curves through a contact lens

Series
Geometry Topology Seminar
Time
Monday, October 16, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Kyle Hayden – Boston College
Every four-dimensional Stein domain has a Morse function whoseregular level sets are contact three-manifolds. This allows us to studycomplex curves in the Stein domain via their intersection with thesecontact level sets, where we can comfortably apply three-dimensional tools.We use this perspective to understand links in Stein-fillable contactmanifolds that bound complex curves in their Stein fillings.

Approximation of Functions Over Manifolds by Moving Least Squares

Series
Applied and Computational Mathematics Seminar
Time
Monday, October 16, 2017 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dr. Barak Sober – Tel Aviv University –
We approximate a function defined over a $d$-dimensional manifold $M ⊂R^n$ utilizing only noisy function values at noisy locations on the manifold. To produce the approximation we do not require any knowledge regarding the manifold other than its dimension $d$. The approximation scheme is based upon the Manifold Moving Least-Squares (MMLS) and is therefore resistant to noise in the domain $M$ as well. Furthermore, the approximant is shown to be smooth and of approximation order of $O(h^{m+1})$ for non-noisy data, where $h$ is the mesh size w.r.t $M,$ and $m$ is the degree of the local polynomial approximation. In addition, the proposed algorithm is linear in time with respect to the ambient space dimension $n$, making it useful for cases where d is much less than n. This assumption, that the high dimensional data is situated on (or near) a significantly lower dimensional manifold, is prevalent in many high dimensional problems. Thus, we put our algorithm to numerical tests against state-of-the-art algorithms for regression over manifolds and show its dominance and potential.

Jensen-Pólya Criterion for the Riemann Hypothesis and Related Problems

Series
Algebra Seminar
Time
Monday, October 16, 2017 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Larry Rolen – Georgia Tech –
In this talk, I will summarize forthcoming work with Griffin, Ono, and Zagier. In 1927 Pólya proved that the Riemann Hypothesis is equivalent to the hyperbolicity of Jensen polynomials for Riemann's Xi-function. This hyperbolicity has been proved for degrees $d\leq 3$. We obtain an arbitrary precision asymptotic formula for the derivatives $\Xi^{(2n)}(0)$, which allows us to prove thehyperbolicity of 100% of the Jensen polynomials of each degree. We obtain a general theorem which models such polynomials by Hermite polynomials. This general condition also confirms a conjecture of Chen, Jia, and Wang.

Non-smooth dynamics in the environment and data science

Series
Research Horizons Seminar
Time
Wednesday, October 18, 2017 - 12:10 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Rachel Kuske – Georgia Tech
This talk will cover some recent and preliminary results in the area of non-smooth dynamics, with connections to applications that have been overlooked. Much of the talk will present open questions for research projects related to this area.

Lens space realization problem

Series
Geometry Topology Student Seminar
Time
Wednesday, October 18, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Sudipta Kolay – Georgia Tech
I will talk about the Berge conjecture, and Josh Greene's resolution of a related problem, about which lens spaces can be obtained by integer surgery on a knot in S^3.

Gabor bases and convexity

Series
Analysis Seminar
Time
Wednesday, October 18, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Alex Yosevich – University of Rochester
We are going to prove that indicator functions of convex sets with a smooth boundary cannot serve as window functions for orthogonal Gabor bases.

Sequential low-rank matrix completion and estimation: Uncertainty quantification and design

Series
Stochastics Seminar
Time
Thursday, October 19, 2017 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Yao Xie – ISyE, Georgia Institute of Technology
We present a unified framework for sequential low-rank matrix completion and estimation, address the joint goals of uncertainty quantification (UQ) and statistical design. The first goal of UQ aims to provide a measure of uncertainty of estimated entries in the unknown low-rank matrix X, while the second goal of statistical design provides an informed sampling or measurement scheme for observing the entries in X. For UQ, we adopt a Bayesian approach and assume a singular matrix-variate Gaussian prior the low-rank matrix X which enjoys conjugacy. For design, we explore deterministic design from information-theoretic coding theory. The effectiveness of our proposed methodology is then illustrated on applications to collaborative filtering.

Slack Matrices for Polytopes and Polyhedra

Series
Student Algebraic Geometry Seminar
Time
Friday, October 20, 2017 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Kisun Lee – Georgia Institute of Technology
We will introduce a class of nonnegative real matrices which are called slack matrices. Slack matrices provide the distance from equality of a vertex and a facet. We go over concepts of polytopes and polyhedrons briefly, and define slack matrices using those objects. Also, we will give several necessary and sufficient conditions for slack matrices of polyhedrons. We will also restrict our conditions for slack matrices for polytopes. Finally, we introduce the polyhedral verification problem, and some combinatorial characterizations of slack matrices.

The list chromatic number of graphs with small clique number (joint with ARC; note the unusual time!)

Series
Combinatorics Seminar
Time
Friday, October 20, 2017 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Mike Molloy – University of Toronto
We prove that every triangle-free graph with maximum degree $D$ has list chromatic number at most $(1+o(1))\frac{D}{\ln D}$. This matches the best-known bound for graphs of girth at least 5. We also provide a new proof that for any $r \geq 4$ every $K_r$-free graph has list-chromatic number at most $200r\frac{D\ln\ln D}{\ln D}$.

Branched covers II

Series
Geometry Topology Working Seminar
Time
Friday, October 20, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
John Etnyre – Georgia Tech

Note this talk is only 1 hour (to allow for the GT MAP seminar at 3.

In this series of talks I will introduce branched coverings of manifolds and sketch proofs of most the known results in low dimensions (such as every 3 manifold is a 3-fold branched cover over a knot in the 3-sphere and the existence of universal knots). This week we will continue studying branched covers of surfaces. Among other things we should be able to see how to use branched covers to see some relations in the mapping class group of surfaces.

Modeling and predicting urban crime – How data assimilation helps bridge the gap between stochastic and continuous models

Series
GT-MAP Seminar
Time
Friday, October 20, 2017 - 15:00 for 2 hours
Location
Skiles 006
Speaker
Prof. Martin Short – GT Math
Data assimilation is a powerful tool for combining mathematical models with real-world data to make better predictions and estimate the state and/or parameters of dynamical systems. In this talk I will give an overview of some work on models for predicting urban crime patterns, ranging from stochastic models to differential equations. I will then present some work on data assimilation techniques that have been developed and applied for this problem, so that these models can be joined with real data for purposes of model fitting and crime forecasting.