Seminars and Colloquia by Series

Three-isogeny Selmer groups and ranks of abelian varieties in quadratic twist families

Series
Algebra Seminar
Time
Monday, October 23, 2017 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Robert Lemke Oliver – Tufts University –
We determine the average size of the $\phi$-Selmer group in any quadratic twist family of abelian varieties having an isogeny $\phi$ of degree 3 over any number field. This has several applications towards the rank statistics in such families of quadratic twists. For example, it yields the first known quadratic twist families of absolutely simple abelian varieties over $\mathbb{Q}$, of dimension greater than one, for which the average rank is bounded; in fact, we obtain such twist families in arbitrarily large dimension. In the case that $E/F$ is an elliptic curve admitting a 3-isogeny, we prove that the average rank of its quadratic twists is bounded; if $F$ is totally real, we moreover show that a positive proportion of these twists have rank 0 and a positive proportion have $3$-Selmer rank 1. We also obtain consequences for Tate-Shafarevich groups of quadratic twists of a given elliptic curve. This is joint work with Manjul Bhargava, Zev Klagsbrun, and Ari Shnidman.

The immersed cross-cap number of a knot

Series
Geometry Topology Seminar
Time
Monday, October 23, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Mark Hughes – BYU
The immersed Seifert genus of a knot $K$ in $S^3$ can be defined as the minimal genus of an orientable immersed surface $F$ with $\partial F = K$. By a result of Gabai, this value is always equal to the (embedded) Seifert genus of $K$. In this talk I will discuss the embedded and immersed cross-cap numbers of a knot, which are the non-orientable versions of these invariants. Unlike their orientable counterparts these values do not always coincide, and can in fact differ by an arbitrarily large amount. In further contrast to the orientable case, there are families of knots with arbitrarily high embedded 4-ball cross-cap numbers, but which are easily seen to have immersed cross-cap number 1. After describing these examples I will discuss a classification of knots with immersed cross-cap number 1. This is joint work with Seungwon Kim.

Recurrence on abelian cover. Closed geodesics in manifolds of negative curvature

Series
CDSNS Colloquium
Time
Monday, October 23, 2017 - 11:15 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Albert Fathi – Georgia Institute of Technology
If h is a homeomorphism on a compact manifold which is chain-recurrent, we will try to understand when the lift of h to an abelian cover is also chain-recurrent. This has consequences on closed geodesics in manifold of negative curvature.

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.

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

Please Note: 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.

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 $200r\frac{D\ln\ln D}{\ln D}$.

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.

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.

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.

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