Seminars and Colloquia by Series

Curvature and Isoperimetry in Graphs

Series
Dissertation Defense
Time
Thursday, September 28, 2017 - 09:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Peter Ralli – School of Mathematics, Georgia Tech –
This dissertation concerns isoperimetric and functional inequalities in discrete spaces. The majority of the work concerns discrete notions of curvature. There isalso discussion of volume growth in graphs and of expansion in hypergraphs. [The dissertation committee consists of Profs. J. Romberg (ECE), P. Tetali (chair of the committee), W.T. Trotter, X. Yu and H. Zhou.]

Bounded Fourier multipliers with applications to Balian-Low type theorems

Series
Analysis Seminar
Time
Wednesday, September 27, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Michael Northington – Georgia Tech
The Gabor system of a function is the set of all of its integer translations and modulations. The Balian-Low Theorem states that the Gabor system of a function which is well localized in both time and frequency cannot form an Riesz basis for $L^2(\mathbb{R})$. An important tool in the proof is a characterization of the Riesz basis property in terms of the boundedness of the Zak transform of the function. In this talk, we will discuss results showing that weaker basis-type properties also correspond to boundedness of the Zak transform, but in the sense of Fourier multipliers. We will also discuss using these results to prove generalizations of the Balian-Low theorem for Gabor systems with weaker basis properties, as well as for shift-invariant spaces with multiple generators and in higher dimensions.

Null-Homotopic Embedded Spheres of Codimenion One

Series
Geometry Topology Student Seminar
Time
Wednesday, September 27, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Anubhav Mukherjee – Georgia Tech
Let S be an (n-1)-sphere smoothly embedded in a closed, orientable, smooth n-manifold M, and let the embedding be null-homotopic. We'll prove in the talk that, if S does not bound a ball, then M is a rational homology sphere, the fundamental group of both components of M\S are finite, and at least one of them is trivial. This talk is based on a paper of Daniel Ruberman.

Quolloquium: Spectral geometry of quantum waveguides

Series
Other Talks
Time
Wednesday, September 27, 2017 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
David Krejcirik – Czech Technical University –

Please Note: CORRECTED DATE. NOTE: This is the first in a forthcoming series of colloquia in quantum mathematical physics that will take place this semester. The series is a spin-off of last year's QMath conference, and is intended to be of broad interest to people wanting to know the state of the art of current topics in mathematical physics.

We shall make an overview of the interplay between the geometry of tubular neighbourhoods of Riemannian manifold and the spectrum of the associated Dirichlet Laplacian. An emphasis will be put on the existence of curvature-induced eigenvalues in bent tubes and Hardy-type inequalities in twisted tubes of non-circular cross-section. Consequences of the results for physical systems modelled by the Schroedinger or heat equations will be discussed.

How to stretch taffy most efficiently?

Series
Research Horizons Seminar
Time
Wednesday, September 27, 2017 - 12:10 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Balasz Strenner – Georgia Tech
Taffy pullers are machines designed to stretch taffy. They can modeled by surface homeomorphisms, therefore they can be studied by geometry and topology. I will talk about how efficiency of taffy pullers can be defined mathematically and what some of the open questions are. I will also talk about Macaw, a computer program I am working on, which does related computations and which will hopefully help answer some of the open questions.

How to stretch taffy most efficiently?

Series
Research Horizons Seminar
Time
Wednesday, September 27, 2017 - 12:10 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Balazs Strenner – GA Tech
Taffy pullers are machines designed to stretch taffy. They can modeled by surface homeomorphisms, therefore they can be studied by geometry and topology. I will talk about how efficiency of taffy pullers can be defined mathematically and what some of the open questions are. I will also talk about Macaw, a computer program I am working on, which does related computations and which will hopefully help answer some of the open questions.

Small scale creation in ideal fluid

Series
PDE Seminar
Time
Tuesday, September 26, 2017 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Alexander Kiselev – Duke University –
I will review recent results on small scale creation in solutions of the Euler equation. A numerical simulation due to Hou and Luo suggests a new scenario for finite time blow up in three dimensions. A similar geometry in two dimensions leads to examples with very fast, double exponential in time growth in the gradient of vorticity. Such growth is know to be sharp due to upper bounds going back to 1930s. If I have time, I will also discuss several models that have been proposed to help understand the three-dimensional case.

p-adic metric line bundles and integral points on curves

Series
Algebra Seminar
Time
Monday, September 25, 2017 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Amnon Besser – Georgia Tech –

Please Note: postponed from September 18

In this talk I first wish to review my work with Balakrishnan and Muller, giving an algorithm for finding integral points on curves under certain (strong) assumptions. The main ingredients are the theory of p-adic height pairings and the theory of p-adic metrized line bundles. I will then explain a new proof of the main result using a p-adic version of Zhang's adelic metrics, and a third proof which only uses the metric at one prime p. At the same time I will attempt to explain why I think this last proof is interesting, being an indication that there may be new p-adic methods for finding integral points.

On boundaries of relatively hyperbolic right-angled Coxeter groups

Series
Geometry Topology Seminar
Time
Monday, September 25, 2017 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Hung Tran – Georgia
We give "visual descriptions" of cut points and non-parabolic cut pairs in the Bowditch boundary of a relatively hyperbolic right-angled Coxeter group. We also prove necessary and sufficient conditions for a relatively hyperbolic right-angled Coxeter group whose defining graph has a planar flag complex with minimal peripheral structure to have the Sierpinski carpet or the 2-sphere as its Bowditch boundary. We apply these results to the problem of quasi-isometry classification of right-angled Coxeter groups. Additionally, we study right-angled Coxeter groups with isolated flats whose $\CAT(0)$ boundaries are Menger curve. This is a joint work with Matthew Haulmark and Hoang Thanh Nguyen.

Computational hemodynamics for Computer Aided Clinical Trials: looking at the theory, struggling with the practice

Series
Applied and Computational Mathematics Seminar
Time
Monday, September 25, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Professor Alessandro Veneziani – Emory Department of Mathematics and Computer Science
When we get to the point of including the huge and relevant experience of finite element fluid modeling collected in over 25 years of experience in the treatment of cardiovascular diseases, the risk of getting “lost in translation” is real. The most important issues are the reliability that we need to guarantee to provide a trustworthy decision support to clinicians; the efficiency we need to guarantee to fit into the demand coming from a large volume of patients in Computer Aided Clinical Trials as well as short timelines required by special circumstances (emergency) in Surgical Planning. In this talk, we will report on some recent activities taken at Emory to make this transition possible. Reliability requirements call for an appropriate integration of measurements and numerical models, as well as for uncertainty quantification. In particular, image and data processing are critical to feeding mathematical models. However, there are several challenges still open, e.g. in simulating blood flow in patient-specific arteries after stent deployment; or in assessing the correct boundary data set to be prescribed in complex vascular districts. The gap between theory, in this case, is apparent and good simulation and assimilation practices in finite elements for clinical hemodynamics need to be drawn. The talk will cover these topics. For computational efficiency, we will cover some numerical techniques currently in use for coronary blood flow, like the Hierarchical Model Reduction or efficient methods for coping with turbulence in aortic flows. As Clinical Trials are currently one of the most important sources of information for medical research and practice, we envision that the suitable achievement of reliability and efficiency requirements will make Computer Aided Clinical Trials (specifically with a strong Finite-Elements-in-Fluids component) an important source of information with a significant impact on the quality of healthcare. This is a joint work with the scholars and students of the Emory Center for Mathematics and Computing in Medicine (E(CM)2), the Emory Biomech Core Lab (Don Giddens and Habib Samady), the Beta-Lab at the University of Pavia (F. Auricchio ). This work is supported by the US National Science Foundation, Projects DMS 1419060, 1412963 1620406, Fondazione Cariplo, Abbott Vascular Inc., and the XSEDE Consortium.

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