Seminars and Colloquia by Series

Tuesday, March 13, 2012 - 11:05 , Location: Skiles 006 , Jeff Kahn , Mathematics, Rutgers University , , Organizer: Prasad Tetali
Thresholds for increasing properties are a central concern in probabilistic combinatorics and elsewhere. (An increasing property, say F, is a superset-closed family of subsets of some (here finite) set X; the threshold question for such an F asks, roughly, about how many random elements of X should one choose to make it likely that the resulting set lies in F? For example: about how many random edges from the complete graph K_n are typically required to produce a Hamiltonian cycle?) We'll discuss recent progress and lack thereof on a few threshold-type questions, and try to say something about a ludicrously general conjecture of G. Kalai and the speaker to the effect that there is always a pretty good naive explanation for a threshold being what it is.
Thursday, March 8, 2012 - 11:05 , Location: Skiles 006 , F. Alberto Grünbaum , University of California, Berkeley , Organizer: Plamen Iliev
I will review the well known method (pushed mainly by Karlin and McGregor) to study birth-and-death processes with the help of orthogonal polynomials. I will then look at several extensions of this idea, including ¨poker dice¨ (polynomials in several variables) and quantum walks (polynomials in the unit circle).
Thursday, February 23, 2012 - 11:05 , Location: Skiles 006 , Alexander Shapiro , ISyE, Georgia Tech , Organizer: Anton Leykin
In many practical situations one has to make  decisions sequentially  based on data available at  the  time of the decision and facing uncertainty of the future. This leads to optimization problems which can be formulated in a framework of multistage stochastic programming. In this talk  we consider risk neutral and risk averse approaches to multistage stochastic programming. We discuss conceptual and computational issues involved in formulation and solving such problems. As an example we give numerical results based on  the Stochastic Dual Dynamic Programming method applied to planning of the Brazilian interconnected power system.
Tuesday, February 14, 2012 - 11:00 , Location: Skiles 005 , Ron Douglas , Texas A&M University , Organizer:
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.
Wednesday, February 8, 2012 - 11:05 , Location: Skiles 005 , Jeff Kahn , Mathematics, Rutgers University , Organizer: Prasad Tetali
Pardon the inconvenience. We plan to reschedule later...
Friday, December 9, 2011 - 16:00 , Location: Skiles 006 , Benson Farb , University of Chicago , Organizer: John Etnyre

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.
Thursday, December 1, 2011 - 11:00 , Location: Klaus 1116W , Colm Mulcahy , Spelman College , Organizer: Dan Margalit

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.
Thursday, November 10, 2011 - 11:00 , Location: Skiles 006 , Avi Wigderson , School of Mathematics, Institute for Advanced Study , Organizer: Prasad Tetali

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.
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 , Pablo Parrilo , 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.