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Series: Geometry Topology Seminar

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.

Monday, October 16, 2017 - 14:00 ,
Location: Skiles 005 ,
Dr. Barak Sober ,
Tel Aviv University ,
barakino@gmail.com ,
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.

Series: Algebra Seminar

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.

Series: Research Horizons Seminar

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.

Series: Analysis Seminar

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 - 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.

Series: Stochastics Seminar

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.

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.

Series: Combinatorics Seminar

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 - 13:55 ,
Location: Skiles 006 ,
John Etnyre ,
Georgia Tech ,
Organizer: John Etnyre

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.

Series: GT-MAP Seminars

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.