Seminars and Colloquia by Series

Saturday, February 16, 2019 - 21:30 , Location: Skiles 005 , Various speakers , GT, Emory, UGA and GSU , Organizer: Sung Ha Kang

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

for more information

Friday, February 15, 2019 - 15:00 , Location: Skiles 005 , Hamed Amini , Georgia State University , Organizer: Lutz Warnke

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.

Friday, February 15, 2019 - 03:05 , Location: Skiles 246 , Yian Yao , GT Math , Organizer: Jiaqi Yang

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.

Thursday, February 14, 2019 - 15:05 , Location: Skiles 006 , G. Livshyts , SOM, GaTech , Organizer: Christian Houdre

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.

Thursday, February 14, 2019 - 11:00 , Location: Skiles 006 , Dhruv Mubayi , University of Illinois at Chicago , Organizer: Prasad Tetali

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.

Wednesday, February 13, 2019 - 15:00 , Location: Skiles 006 , Greg Blekherman , Georgia Tech , Organizer: Galyna Livshyts

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.

Wednesday, February 13, 2019 - 13:55 , Location: Skiles 005 , Michael Loss , Georgia Tech , Organizer: Shahaf Nitzan

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.

Wednesday, February 13, 2019 - 12:05 , Location: Skiles 006 , Josephine Yu , Georgia Tech , Organizer: Trevor Gunn

For a polytope P, the h-vector is a vector of integers which can be calculated easily from the number of faces of P of each dimension. For simplicial polytopes, it is well known that the h-vector is symmetric (palindromic) and unimodal. However in general the h-numbers may even be negative. In this talk I will introduce the tropical h-vector of a polytope, which coincides with the usual h-vector of the dual polytope, if the polytope is simple. We will discuss how they are related to toric varieties, tropical geometry, and polytope algebra. I will also discuss some open problems.

Series: PDE Seminar
Tuesday, February 12, 2019 - 15:00 , Location: skiles 006 , Ting Zhang , Zhejiang University , , Organizer: Xukai Yan

Abstract: In this talk, we consider the Cauchy problem of the N-dimensional incompressible viscoelastic fluids with N ≥ 2. It is shown that, in the low frequency part, this system possesses some dispersive properties derived from the one parameter group e∓itΛ. Based on this dispersive effect, we construct global solutions with large initial velocity concentrating on the low frequency part. Such kind of solution has never been seen before in the literature even for the classical incompressible Navier-Stokes equations. The proof relies heavily on the dispersive estimates for the system of acoustics, and a careful study of the nonlinear terms. And we also obtain the similar result for the isentropic compressible Navier-Stokes equations. Here, the initial velocity with arbitrary B⋅N 2 −1 2,1 norm of potential part P⊥u0 and large highly oscillating are allowed in our results. (Joint works with Daoyuan Fang and Ruizhao Zi)

Monday, February 11, 2019 - 14:00 , Location: Skiles 006 , Daniel Álvarez-Gavela , IAS , Organizer: John Etnyre

We will present an h-principle for the simplification of singularities of Lagrangian and Legendrian fronts. The h-principle says that if there is no homotopy theoretic obstruction to simplifying the singularities of tangency of a Lagrangian or Legendrian submanifold with respect to an ambient foliation by Lagrangian or Legendrian leaves, then the simplification can be achieved by means of a Hamiltonian isotopy. We will also discuss applications of the h-principle to symplectic and contact topology.