Seminars and Colloquia by Series

Symbolic Generic Initial Systems and Matroid Configurations

Series
Algebra Seminar
Time
Monday, February 18, 2019 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Robert Walker – U Michigan
We survey dissertation work of my academic sister Sarah Mayes-Tang (2013 Ph.D.). As time allows, we aim towards two objectives. First, in terms of combinatorial algebraic geometry we weave a narrative from linear star configurations in projective spaces to matroid configurations therein, the latter being a recent development investigated by the quartet of Geramita -- Harbourne -- Migliore -- Nagel. Second, we pitch a prospectus for further work in follow-up to both Sarah's work and the matroid configuration investigation.

Local rigidity of Lyapunov spectrum for toral automorphisms

Series
CDSNS Colloquium
Time
Monday, February 18, 2019 - 11:15 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Boris Kalinin – Penn State

We will discuss the regularity of the conjugacy between an Anosov automorphism L of a torus and its small perturbation. We assume that L has no more than two eigenvalues of the same modulus and that L^4 is irreducible over rationals. We consider a volume-preserving C^1-small perturbation f of L. We show that if the Lyapunov exponents of f with respect to the volume are the same as the Lyapunov exponents of L, then f is C^1+ conjugate to L. Further, we establish a similar result for irreducible partially hyperbolic automorphisms with two-dimensional center bundle. This is joint work with Andrey Gogolev and Victoria Sadovskaya

Periodic approximation of Lyapunov exponents for cocycles over hyperbolic systems.

Series
CDSNS Colloquium
Time
Monday, February 18, 2019 - 10:10 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Victoria Sadovskaya – Penn State
We consider a hyperbolic dynamical system (X,f) and a Holder continuous cocycle A over (X,f) with values in GL(d,R), or more generally in the group of invertible bounded linear operators on a Banach space. We discuss approximation of the Lyapunov exponents of A in terms of its periodic data, i.e. its return values along the periodic orbits of f. For a GL(d,R)-valued cocycle A, its Lyapunov exponents with respect to any ergodic f-invariant measure can be approximated by its Lyapunov exponents at periodic orbits of f. In the infinite-dimensional case, the upper and lower Lyapunov exponents of A can be approximated in terms of the norms of the return values of A at periodic points of f. Similar results are obtained in the non-uniformly hyperbolic setting, i.e. for hyperbolic invariant measures. This is joint work with B. Kalinin.

2019 Georgia Scientific Computing Symposium

Series
Applied and Computational Mathematics Seminar
Time
Saturday, February 16, 2019 - 21:30 for 8 hours (full day)
Location
Skiles 005
Speaker
Various speakers – GT, Emory, UGA and GSU

The Georgia Scientific Computing Symposium is a forum for professors, postdocs, graduate students and other researchers in Georgia to meet in an informal setting, to exchange ideas, and to highlight local scientific computing research. The symposium has been held every year since 2009 and is open to the entire research community.

This year, the symposium will be held on Saturday, February 16, 2019, at Georgia Institute of Technology. Please see

http://gtmap.gatech.edu/events/2019-georgia-scientific-computing-symposium

for more information

Contagion in random graphs and systemic risk

Series
Combinatorics Seminar
Time
Friday, February 15, 2019 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Hamed Amini – Georgia State University
We provide a framework for testing the possibility of large cascades in random networks. Our results extend previous studies on contagion in random graphs to inhomogeneous directed graphs with a given degree sequence and arbitrary distribution of weights. This allows us to study systemic risk in financial networks, where we introduce a criterion for the resilience of a large network to the failure (insolvency) of a small group of institutions and quantify how contagion amplifies small shocks to the network.

The Proof of an Abstract Nash-Moser Implicit Function Theorem

Series
Dynamical Systems Working Seminar
Time
Friday, February 15, 2019 - 03:05 for 1 hour (actually 50 minutes)
Location
Skiles 246
Speaker
Yian Yao – GT Math
I will present a proof of an abstract Nash-Moser Implicit Function Theorem. This theorem can cope with derivatives which are not boundly invertible from one space to itself. The main technique is to combine Newton steps - which loses derivatives with some smoothing that restores them.

A tight net with respect to a random matrix norm and applications to estimating singular values

Series
Stochastics Seminar
Time
Thursday, February 14, 2019 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
G. Livshyts – SOM, GaTech
In this talk we construct a net around the unit sphere with strong properties. We show that with exponentially high probability, the value of |Ax| on the sphere can be approximated well using this net, where A is a random matrix with independent columns. We apply it to study the smallest singular value of random matrices under very mild assumptions, and obtain sharp small ball behavior. As a partial case, we estimate (essentially optimally) the smallest singular value for matrices of arbitrary aspect ratio with i.i.d. mean zero variance one entries. Further, in the square case we show an estimate that holds only under simply the assumptions of independent entries with bounded concentration functions, and with appropriately bounded expected Hilbert-Schmidt norm. A key aspect of our results is the absence of structural requirements such as mean zero and equal variance of the entries.

Polynomial to exponential transition in Ramsey theory

Series
Joint School of Mathematics and ACO Colloquium
Time
Thursday, February 14, 2019 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Dhruv Mubayi – University of Illinois at Chicago
After a brief introduction to classical hypergraph Ramsey numbers, I will focus on the following problem. What is the minimum t such that there exist arbitrarily large k-uniform hypergraphs whose independence number is at most polylogarithmic in the number of vertices and every s vertices span at most t edges? Erdos and Hajnal conjectured (1972) that this minimum can be calculated precisely using a recursive formula and Erdos offered $500 for a proof. For k=3, this has been settled for many values of s, but it was not known for larger k. Here we settle the conjecture for all k at least 4. Our method also answers a question of Bhatt and Rodl about the maximum upper density of quasirandom hypergraphs. This is joint work with Alexander Razborov.

Convex Geometry of the Truncated Moment Problem

Series
High Dimensional Seminar
Time
Wednesday, February 13, 2019 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Greg Blekherman – Georgia Tech

Moment problem is a classical question in real analysis, which asks whether a set of moments can be realized as integration of corresponding monomials with respect to a Borel measure. Truncated moment problem asks the same question given a finite set of moments. I will explain how some of the fundamental results in the truncated moment problem can be proved (in a very general setting) using elementary convex geometry. No familiarity with moment problems will be assumed. This is joint work with Larry Fialkow.

Some results for functionals of Aharanov-Bohm type

Series
Analysis Seminar
Time
Wednesday, February 13, 2019 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Michael Loss – Georgia Tech
In this talk I present some variational problems of Aharanov-Bohm type, i.e., they include a magnetic flux that is entirely concentrated at a point. This is maybe the simplest example of a variational problems for systems, the wave function being necessarily complex. The functional is rotationally invariant and the issue to be discussed is whether the optimizer have this symmetry or whether it is broken.

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