Seminars and Colloquia by Series

The phase diagram of the Caffarelli-Kohn-Nirenberg inequalities

Series
School of Mathematics Colloquium
Time
Monday, February 22, 2016 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Michael Loss – School of Mathematics, Georgia Tech
The Caffarelli-Kohn-Nirenberg inequalities form a two parameter family of inequalities that interpolate between Sobolev's inequality and Hardy's inequality. The functional whose minimization yields the sharp constant is invariant under rotations. It has been known for some time that there is a region in parameter space where the optimizers for the sharp constant are {\it not} radial. In this talk I explain this and related problems andindicate a proof that, in the remaining parameter region, the optimizers are in fact radial. The novelty is the use of a flow that decreases the functional unless the function is a radial optimizer. This is joint work with Jean Dolbeault and Maria Esteban.

Toric compactifications of semi-algebraic sets

Series
Algebra Seminar
Time
Monday, February 22, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Daniel Plaumann – Universität Konstanz –
We study compactifications of real semi-algebraic sets that arise from embeddings into complete toric varieties. This makes it possible to describe the asymptotic growth of polynomial functions on such sets in terms of combinatorial data. We discuss the phenomena that arise in examples along with some applications to positive polynomials. (Joint work with Claus Scheiderer)

Asymptotic zero distribution of some multiple orthogonal polynomials

Series
Analysis Seminar
Time
Monday, February 22, 2016 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Walter Van Assche – University of Leuven, Belgium
The asymptotic distribution of the zeros of two families of multiple orthogonal polynomials will be given, namely the Jacobi-Pineiro polynomials (which are an extension of the Jacobi polynomials) and the multiple Laguerre polynomials of the first kind (which are an extension of the Laguerre polynomials). We use the nearest neighbor recurrence relations for these polynomials and a recent result on the ratio asymptotics of multiple orthogonal polynomials. We show how these asymptotic zero distributions are related to the Fuss-Catalan distribution.

Georgia Scientific Computing Symposium

Series
Other Talks
Time
Saturday, February 20, 2016 - 09:00 for 8 hours (full day)
Location
Mathematics and Science Center, Emory University
Speaker
various – various
The Georgia Scientific Computing Symposium (GSCS) 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 at Emory University. The format of the day-long symposium is a set of invited presentations, poster sessions and a poster blitz, and plenty of time to network with other attendees. Invited speakers include: Michele Benzi, Mathematics and Computer Science, Emory University; Steven Hamilton, Radiation Transport Group, Oak Ridge National Laboratory; Alexandra Smirnova, Mathematics and Statistics, Georgia State University; Phanish Suryanarayana, School of Civil & Environmental Engineering, Georgia Institute of Technology; Molei Tao, Mathematics, Georgia Institute of Technology; Qing Zhang, Mathematics, University of Georgia. Poster sessions will be held during the lunch and afternoon breaks.

The Peierls barrier in one-dimensional models II

Series
Dynamical Systems Working Seminar
Time
Friday, February 19, 2016 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 170
Speaker
Lei Zhang – Georgia Inst. of Technology
The Peierls barrier is an observable which characterizes whether the the set minimizers with a prescribed frequency of a periodic variational problem form a continuum or have gaps. In solid state physics Peierls barrier characterizes whether ground states with a fixed density are pinned or are able to slide. The Peierls barrier is a microscopic explanation of static friction. Remarkably, in dynamical systems, Peierls barrier appears also as characterizing whether KAM circles break down into Cantor sets. Hence, the Peierls barrier has been investigated both by physicists and by mathematicians using a variety of methods. We plan to cover the basic definitions of the variational models and some of the basic results obtainedfrom the 80's. Continuation of last week's seminar

On the infinitesimal versions of Log Brunn Minkowski and Gaussian Brunn Minkowski conjectures

Series
Stochastics Seminar
Time
Thursday, February 18, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Galyna Livshyts – School of Mathematics, Georgia Tech
Log Brunn-Minkowski conjecture was proposed by Boroczky, Lutwak, Yang and Zhang in 2013. It states that in the case of symmetric convex sets the classical Brunn-MInkowski inequality may be improved. The Gaussian Brunn-MInkowski inequality was proposed by Gardner and Zvavitch in 2007. It states that for the standard Gaussian measure an inequality analogous to the additive form of Brunn_minkowski inequality holds true for symmetric convex sets. In this talk we shall discuss a derivation of an equivalent infinitesimal versions of these inequalities for rotation invariant measures and a few partial results related to both of them as well as to the classical Alexander-Fenchel inequality.

The Driverless Car Revolution

Series
Other Talks
Time
Thursday, February 18, 2016 - 13:30 for 1.5 hours (actually 80 minutes)
Location
John and Joyce Caddell Building Flex Space
Speaker
S. Rutt Bridges – Georgia Tech, Geosciences, Alumni

The role of VC-dimension in the one-bit restricted isometry property

Series
Analysis Seminar
Time
Wednesday, February 17, 2016 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Scott Spencer – Georgia Tech –
Compressed sensing illustrates the possibility of acquiring and reconstructing sparse signals via underdetermined (linear) systems. It is believed that iid Gaussian measurement vectors give near optimal results, with the necessary number of measurements on the order of $s \log(n/s)$ - $n$ is ambient dimension and $s$ is the sparsity threshold. The recovery algorithm used above relies on a certain quasi-isometry property of the measurement matrix. A surprising result is that the same order of measurements gives an analogous quasi-isometry in the extreme quantization of one-bit sensing. Bylik and Lacey deliver this result as a consequence of a certain stochastic process on the sphere. We will discuss an alternative method that relies heavily on the VC-dimension of a class of subsets on the sphere.

Convergence of gradient flows and scaling limit for particle systems

Series
Other Talks
Time
Wednesday, February 17, 2016 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Max Fathi – Department of Mathematics, UC Berkeley
In this talk, I will explain how the gradient flow structure of reversible Markov chains (that was discovered by Maas and Mielke independently in 2011) and the Sandier-Serfaty approach to convergence of gradient flows can be combined to study scaling limits for interacting particle systems on lattices. The exposition will be focused on the case of the simple exclusion process on the discrete torus. Joint work with Marielle Simon (INRIA Lille).

Population biology of Schistosoma, its control and elimination: insights from mathematics and computations

Series
Mathematical Biology Seminar
Time
Wednesday, February 17, 2016 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Professor David Gurarie – CWRU –
Schistosoma is a parasitic worm that circulates between human and snail hosts. Multiple biological and ecological factors contribute to its spread and persistence in host populations. The infection is widespread in many tropical countries, and WHO has made control of schistosomiasis a priority among neglected tropical diseases.Mathematical modeling is widely used for prediction and control analysis of infectious agents. But host-parasite systems with complex life-cycles like Schistosoma, pose many challenges. The talk will outline the basic biology of Schistosoma, and the principles employed in mathematical modeling of macro parasites. We shall review conventional approaches to Schistosomiasis starting with the classical work of MacDonald, and discuss their validity and implications. Then we shall outline more detailed “stratified worm burden approach”, and show how combining mathematical and computer tools one can explore real-world systems and make reliable predictions for long term control outcomes and the problem of elimination.

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