Seminars and Colloquia by Series

Complex Geometry and Operator Theory

Series
School of Mathematics Colloquium
Time
Tuesday, February 14, 2012 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Ron Douglas – Texas A&M University
An intesting class of bounded operators or algebras of bounded operators on Hilbert spaces, particularly on Hilbert spaces of holomorphic functions, have a natural interpretation in terms of concepts from complex geometry. In particular, there is an intrinsic hermitian holomorphic vector bundle and many questions can be answered in terms of the Chern connection and the associated curvature. In this talk we describe this setup and some of the results obtained in recent years using this approach. The emphasis will be on concrete examples, particularly in the case of Hilbert spaces of holomorphic functions such as the Hardy and Bergman spaces on the unit sphere in C^n.

CANCELLED!

Series
School of Mathematics Colloquium
Time
Wednesday, February 8, 2012 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jeff Kahn – Mathematics, Rutgers University
Pardon the inconvenience. We plan to reschedule later...

Permutations and polynomiality in algebra and topology

Series
School of Mathematics Colloquium
Time
Friday, December 9, 2011 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Benson Farb – University of Chicago

Please Note: There will be a tea 30 minutes before the colloquium.

Tom Church, Jordan Ellenberg and I recently discovered that the i-th Betti number of the space of configurations of n points on any manifold is given by a polynomial in n. Similarly for the moduli space of n-pointed genus g curves. Similarly for the dimensions of various spaces of homogeneous polynomials arising in algebraic combinatorics. Why? What do these disparate examples have in common? The goal of this talk will be to answer this question by explaining a simple underlying structure shared by these (and many other) examples in algebra and topology.

Celebration of Mind: Connecting Mathematics, Magic and Mystery

Series
School of Mathematics Colloquium
Time
Thursday, December 1, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Klaus 1116W
Speaker
Colm Mulcahy – Spelman College

Please Note: Hosts are Ernie Croot and Dan Margalit.

We survey some new and classic recreations in the fields of mathematics, magic and mystery in the style of Martin Gardner, Prince of Recreational Mathematics, whose publishing career recently ended after an astonishing 80 years. From card tricks and counter-intuitive probability results to new optical illusions, there will be plenty of reasons to celebrate the ingenuity of the human mind.

The power and weakness of randomness (when you are short on time)

Series
School of Mathematics Colloquium
Time
Thursday, November 10, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Avi Wigderson – School of Mathematics, Institute for Advanced Study

Please Note: This is a joint ARC-SoM colloquium, and is in conjunction with the ARC Theory Day on November 11, 2011

Man has grappled with the meaning and utility of randomness for centuries. Research in the Theory of Computation in the last thirty years has enriched this study considerably. I'll describe two main aspects of this research on randomness, demonstrating respectively its power and weakness for making algorithms faster. I will address the role of randomness in other computational settings, such as space bounded computation and probabilistic and zero-knowledge proofs.

Spectral gaps and completeness of complex exponentials

Series
School of Mathematics Colloquium
Time
Thursday, November 3, 2011 - 23:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Alexei Poltoratski – Texas A&M
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.

From Sparsity to Rank, and Beyond: algebra, geometry, and convexity

Series
School of Mathematics Colloquium
Time
Monday, October 24, 2011 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Pablo Parrilo – MIT –
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.

On the Square Dependence Problem

Series
School of Mathematics Colloquium
Time
Thursday, September 29, 2011 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ernie Croot – Georgia Tech
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.

On the coefficients of a bivariate rational function

Series
School of Mathematics Colloquium
Time
Thursday, September 15, 2011 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Robin Pemantle – Math, University of Pennsylvania –
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.

Topology of representation varieties of surface groups

Series
School of Mathematics Colloquium
Time
Thursday, April 21, 2011 - 11:01 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Richard Wentworth – University of Maryland –
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

Pages