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Chalmers University of Technology
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Wed 10 Apr 2013, 3:00pm
Probability Seminar / Symbolic Dynamics and Ergodic Theory Seminar
ESB 2012
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The many faces of the T T-inverse process
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ESB 2012
Wed 10 Apr 2013, 3:00pm-4:00pm
Abstract
The T T-inverse process or equivalently "random walk in random scenery" is a family of stationary processes that exhibits an amazing amount of behavior. Each random walk yields such a process and as you vary the random walk, you obtain essentially all possible ergodic theoretic behaviors. There is also a phase transition that arises which we can only partially prove. I will give an overview of this area which contains work both old and (somewhat) new.
This work is done jointly with a number of people including Frank den Hollander, Mike Keane and Sebastien Blachere.
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Thu 11 Apr 2013, 9:00am
SPECIAL
One Time Event
Graduate Student Center, Room 203
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Doctoral Exam
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Graduate Student Center, Room 203
Thu 11 Apr 2013, 9:00am-11:30am
Details
Let E and f be an Eisenstein series and a cusp form, respectively, of the same weight k 2 and of the same level N, both eigenfunctions of the Hecke operators, and both normalized so that a1 = 1. The main result we seek is
that when E and f are congruent mod a prime p (which may be a prime ideal lying over a rational prime p > 2), the algebraic parts of the special values L(E; ; j) and L(f; ; j) satisfy congruences mod the same prime. On the way to proving the congruence result, we construct the modular symbol attached to an Eisenstein series.
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UBC
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Thu 11 Apr 2013, 3:30pm
Number Theory Seminar
room MATH 126
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Forms in many variables over the primes
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room MATH 126
Thu 11 Apr 2013, 3:30pm-4:30pm
Abstract
We study the number of solutions of diophantine equations f(x1,...,xn)=v when the variables xi are restricted to primes. It has been established by Birch and Schmidt that one has the expected number of integer solutions if f is a homogeneous integral polymomial of sufficiently large rank with respect to its degree. We show that the same phenomenon holds when the variables are restricted to primes, extending the results of Hua for diagonal forms. We illustrate some of the ideas on quadratic forms and discuss some elements of the proof of the general case.
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UIUC
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Mon 15 Apr 2013, 3:10pm
Algebraic Geometry Seminar
ESB 4133
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Varieties in flag manifolds and their patch ideals
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ESB 4133
Mon 15 Apr 2013, 3:10pm-4:10pm
Abstract
This talk addresses the problem of how to analyze and discuss singularities of a variety X that "naturally'' sits inside a flag manifold. Our three main examples are Schubert varieties, Richardson varieties and Peterson varieties. The overarching theme is to use combinatorics and commutative algebra to study the "patch ideals", which encode local coordinates and equations of X. Thereby, we obtain formulas and conjectures about X's invariants. We will report on projects with (subsets of) Erik Insko (Florida Gulf Coast U.), Allen Knutson (Cornell), Li Li (Oakland University) and Alexander Woo (U. Idaho).
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INRIA Grenoble, France
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Tue 16 Apr 2013, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133
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Exploiting uncontrolled information in nonsmooth optimization methods
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ESB 4133
Tue 16 Apr 2013, 12:30pm-1:30pm
Abstract
We consider convex nonsmooth optimization problems whose objective function is known through some expensive procedure. For example, this is the case in several problems that arise in electricity production management, where the objective function is itself the result of an optimization subproblem.
In this context, it often exists extra information - cheap but with unknown accuracy - that is not used by the algorithms. In this talk, we present a way to incorporate this coarse information into two classical nonsmooth optimization algorithms: Kelley method and level bundle method. We prove that the resulting methods are convergent and we present numerical illustrations showing that they speed up resolution.
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UIUC
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Tue 16 Apr 2013, 2:00pm
Discrete Math Seminar
MATH 126
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Jeu de taquin, increasing tableaux, and longest increasing subsequences of words
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MATH 126
Tue 16 Apr 2013, 2:00pm-3:30pm
Abstract
I will describe a theory of jeu de taquin for increasing tableaux, extending Schutzenberger's work on standard Young tableaux. Our original motivation came from Schubert calculus. However, I'll also describe a specific connection to the study of longest increasing sequences (LIS) of words. This is joint work with Hugh Thomas (U. New Brunswick) and Ofer Zeitouni (U. Minnesota).
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