Seminars and Colloquia by Series

Friday, October 20, 2017 - 11:00 , Location: Skiles 005 , Mike Molloy , University of Toronto , Organizer: Lutz Warnke
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 $200r\frac{D\ln\ln D}{\ln D}$. 
Friday, October 20, 2017 - 10:00 , Location: Skiles 114 , Kisun Lee , Georgia Institute of Technology , Organizer: Timothy Duff
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.
Thursday, October 19, 2017 - 15:05 , Location: Skiles 006 , Yao Xie , ISyE, Georgia Institute of Technology , Organizer: Mayya Zhilova
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.
Wednesday, October 18, 2017 - 13:55 , Location: Skiles 006 , Sudipta Kolay , Georgia Tech , Organizer: Jennifer Hom
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.
Wednesday, October 18, 2017 - 13:55 , Location: Skiles 005 , Alex Yosevich , University of Rochester , Organizer: Michael Lacey
We are going to prove that indicator functions of convex sets with a smooth boundary cannot serve as window functions for orthogonal Gabor bases.
Wednesday, October 18, 2017 - 12:10 , Location: Skiles 006 , Rachel Kuske , Georgia Tech , Organizer:
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.
Monday, October 16, 2017 - 15:00 , Location: Skiles 006 , Larry Rolen , Georgia Tech , , Organizer: Larry Rolen
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.
Monday, October 16, 2017 - 14:00 , Location: Skiles 005 , Dr. Barak Sober , Tel Aviv University , , Organizer: Doron Lubinsky
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.
Monday, October 16, 2017 - 13:55 , Location: Skiles 006 , Kyle Hayden , Boston College , Organizer: John Etnyre
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.
Friday, October 13, 2017 - 15:00 , Location: Skiles 005 , Heather Smith , Georgia Tech , Organizer: Lutz Warnke
The original notion of poset dimension is due to Dushnik and Miller (1941). Last year, Uerckerdt (2016) proposed a variant, called local dimension, which has garnered considerable interest. A local realizer of a poset P is a collection of partial linear extensions of P that cover the comparabilities and incomparabilities of P. The local dimension of P is the minimum frequency of a local realizer where frequency is the maximum multiplicity of an element of P. Hiraguchi (1955) proved that any poset with n points has dimension at most n/2, which is sharp. We prove that the local dimension of a poset with n points is O(n/log n). To show that this bound is best possible, we use probabilistic methods to prove the following stronger result which extends a theorem of Chung, Erdős, and Spencer (1983): There is an n-vertex bipartite graph in which each difference graph cover of the edges will cover one of the vertices Θ(n/log n) times. (This is joint work with Jinha Kim, Ryan R. Martin, Tomáš Masařı́k, Warren Shull, Andrew Uzzell, and Zhiyu Wang)