## Seminars and Colloquia by Series

Thursday, November 3, 2011 - 23:05 , Location: Skiles 006 , Alexei Poltoratski , Texas A&M , Organizer: Michael Lacey
One of the basic problems of Harmonic analysis is to determine ifa given collection of functions is complete in a given Hilbert space. Aclassical theorem by Beurling and Malliavin solved such a problem in thecase when the space is $L^2$ on an interval and the collection consists ofcomplex exponentials. Two closely related problems, the so-called Gap andType Problems, studied by Beurling, Krein, Kolmogorov, Levinson, Wiener andmany others, remained open until recently.In my talk I will  present solutions to the Gap and Type problems anddiscuss their connectionswith adjacent fields.
Monday, October 24, 2011 - 16:00 , Location: Skiles 006 , , MIT , , Organizer: Greg Blekherman
Optimization problems involving sparse vectors or low-rank matrices are of great importance in applied mathematics and engineering. They provide a rich and fruitful interaction between algebraic-geometric concepts and convex optimization, with strong synergies with popular techniques like L1 and nuclear norm minimization. In this lecture we will provide a gentle introduction to this exciting research area, highlighting key algebraic-geometric ideas as well as a survey of recent developments, including extensions to very general families of parsimonious models such as sums of a few permutations matrices, low-rank tensors, orthogonal matrices, and atomic measures, as well as the corresponding structure-inducing norms.Based on joint work with Venkat Chandrasekaran, Maryam Fazel, Ben Recht, Sujay Sanghavi, and Alan Willsky.
Thursday, September 29, 2011 - 11:05 , Location: Skiles 006 , Ernie Croot , Georgia Tech , Organizer:
In many integer factoring algorithms, one produces a sequence of integers (created in a pseudo-random way), and wishes to rapidly determine a subsequence whose product is a square (which we call a `square product').  In his lecture at the 1994 International Congress of Mathematicians, Pomerance observed that the following problem encapsulates all of the key issues:  Select integers a1, a2, ..., at random from the interval [1,x], until some (non-empty) subsequence has product equal to a square.  Find good esimates for the expected stopping time of this process.  A good solution to this problem should help one to determine the optimal choice of parameters for one's factoring algorithm, and therefore this is a central question. In this talk I will discuss the history of this problem, and its somewhat recent solution due to myself, Andrew Granville, Robin Pemantle, and Prasad Tetali.
Thursday, September 15, 2011 - 11:05 , Location: Skiles 006 , Robin Pemantle , Math, University of Pennsylvania , , Organizer: Prasad Tetali
Problem: describe the asymptotic behavior of the coefficients  a_{ij} of the Taylor series for 1/Q(x,y) where Q is a polynomial. This problem is the simplest of a number  of such problems arising in analytic combinatorics  whose answer was not until recently known.  In joint  work with J. van der Hoeven and T. DeVries, we  give a solution that is completely effective and requires only assumptions that are met in the generic  case.  Symbolic algebraic computation and homotopy continuation tools are required for implementation.
Thursday, April 21, 2011 - 11:01 , Location: Skiles 269 , Richard Wentworth , University of Maryland , , Organizer:
This will be a survey talk on some aspects of the geometry and topology of moduli spaces of representations of surface groups into Lie groups. I will discuss recent generalizations of the techniques of Atiyah and Bott on equivariant Morse theory. These extend results on stable bundles to Higgs bundles and associated moduli spaces, which correspond to representation varieties into noncompact Lie groups
Thursday, April 14, 2011 - 11:00 , Location: Skiles 005 , Jeff Wu , ISyE GATech , Organizer:
Motivated by a problem in the synthesis of nanowires, a sequential space filling design, called Sequential Minimum Energy Design (SMED), is proposed for exploring and searching for the optimal conditions in complex black-box functions. The SMED is a novel approach to generate designs that are model independent, can quickly carve out regions with no observable nanostructure morphology, allow for the exploration of complex response surfaces, and can be used for sequential experimentation. It can be viewed as a sequential design procedure for stochastic functions and a global optimization procedure for deterministic functions. The basic idea has been developed into an implementable algorithm, and guidelines for choosing the parameters of SMED have been proposed. Convergence of the algorithm has been established under certain regularity conditions. Performance of the algorithm has been studied using experimental data on nanowire synthesis as well as standard test functions.(Joint work with V. R. Joseph, Georgia Tech and T. Dasgupta, Harvard U.)
Thursday, March 17, 2011 - 11:05 , Location: Skiles 005 , , Vanderbilt University , , Organizer: Mohammad Ghomi
In this talk, I will introduce a notion of geometric complexity  to study topological rigidity of manifolds. This is joint work with Erik Guentner and Romain Tessera. I will try to make this talk accessible to graduate students and non experts.
Thursday, February 24, 2011 - 11:05 , Location: Skiles 269 , , Georgia Institute of Technology , Organizer:
Consider any dynamical system with the phase space (set of all states) M. One gets an open dynamical system if M has a subset H (hole) such that any orbit escapes ("disappears") after hitting H. The question in the title naturally appears in dealing with some experiments in physics, in some problems in bioinformatics, in coding theory, etc. However this question  was essentially ignored in the dynamical systems theory. It occurred that it has a simple and counter intuitive answer. It also brings about a new characterization of periodic orbits in chaotic dynamical systems. Besides, a duality with Dynamical Networks allows to introduce dynamical characterization of the nodes (or edges) of Networks, which complements such static characterizations as centrality, betweenness, etc. Surprisingly this approach allows to obtain new results about such classical objects as Markov chains and introduce a hierarchy in the set of their states in regard of their ability to absorb or transmit an "information". Most of the results come from a finding that one can make finite (rather than traditional large) time predictions on behavior of dynamical systems even if they do not contain any small parameter. It looks plausible that a variety of problems in dynamical systems, probability, coding, imaging ... could be attacked now. No preliminary knowledge is required. The talk will be accessible to students.
Thursday, January 27, 2011 - 11:00 , Location: Skiles 006 , Igor Rodnianski , Princeton University , Organizer:
The talk will introduce basic mathematical concepts of General Relativity and review the progress, main challenges and open problems, viewed through the prism of the evolution problem. I will illustrate interaction of Geometry and PDE methods in the context of General Relativity on examples ranging from incompleteness theorems and formation of trapped surfaces to geometric properties of black holes and their stability.
Thursday, January 20, 2011 - 11:00 , Location: Skiles 005 , , University of Minnesota (Minneapolis) , Organizer:
Information encoded in a bar code can be read using a laser scanner or a camera-based scanner. For one-dimensional bar codes, which are in most prevalent use, the information that needs to be extracted are the widths of the black and white bars. The collection of black and white bars may be viewed as a binary one-dimensional image. The signal measured at the scanner amounts to the convolution of the binary image with a smoothing kernel. The challenge is that the smoothing kernel, in addition to the binary image, is also unknown. This presentation will review the technology behind bar code scanning and present several approaches to the decoding problem.