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Series: Analysis Seminar

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.

Series: Other Talks

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.

Series: Research Horizons Seminar

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.

Series: Research Horizons Seminar

Series: PDE Seminar

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.

Series: Algebra Seminar

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.

Series: Geometry Topology Seminar

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.

Monday, September 25, 2017 - 13:55 ,
Location: Skiles 005 ,
Professor Alessandro Veneziani ,
Emory Department of Mathematics and Computer Science ,
Organizer: Martin Short

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.

Series: CDSNS Colloquium

For the tipping elements in the Earth’s climate system, the most important issue to address is how stable is the desirable state against random perturbations. Extreme biotic and climatic events pose severe hazards to tropical rainforests. Their local effects are extremely stochastic and difficult to measure. Moreover, the direction and intensity of the response of forest trees to such perturbations are unknown, especially given the lack of efficient dynamical vegetation models to evaluate forest tree cover changes over time. In this study, we consider randomness in the mathematical modelling of forest trees by incorporating uncertainty through a stochastic differential equation. According to field-based evidence, the interactions between fires and droughts are a more direct mechanism that may describe sudden forest degradation in the south-eastern Amazon. In modeling the Amazonian vegetation system, we include symmetric α-stable Lévy perturbations. We report results of stability analysis of the metastable fertile forest state. We conclude that even a very slight threat to the forest state stability represents L´evy noise with large jumps of low intensity, that can be interpreted as a fire occurring in a non-drought year. During years of severe drought, high-intensity fires significantly accelerate the transition between a forest and savanna state.

Series: Combinatorics Seminar

Clash with "The IDEaS Seminar Series": the talk of Ravi Kannan at 3pm on "Topic Modeling: Proof to Practice" might of interest (Location: TSRB Auditorium) -- Topic Modeling is used in a variety of contexts. This talk will outline from first principles the problem, and the well-known Latent Dirichlet Al-location (LDA) model before moving to the main focus of the talk: Recent algorithms to solve the model-learning problem with provable worst-case error and time guarantees. We present a new algorithm which enjoys both provable guarantees as well performance to scale on corpora with billions of words on a single box. Besides corpus size, a second challenge is the growth in the number of topics. We address this with a new model in which topics lie on low-dimensional faces of the topic simplex rather than just vertices.