Department of

Mathematics


Seminar Calendar
for events the day of Friday, February 21, 2014.

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Questions regarding events or the calendar should be directed to Tori Corkery.
     January 2014          February 2014            March 2014     
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Friday, February 21, 2014

3:00 pm in 343 Altgeld Hall,Friday, February 21, 2014

Combinatorial positivity in the Schubert calculus via dual equivalence graphs

Frank Sottile (Texas A&M)

Abstract: Algebraic geometry poses many positivity challenges to enumerative combinatorics. Two notable such challenges are Macdonald's positivity conjecture, and structure constants in the Schubert Calculus. This talk will explain how Assaf's solution to the first, through her new method for showing symmetry and Schur-positivity of quasi-symmetric generating functions, may be applied to resolve a (by now old) problem of the positivity of some of the structure constants in the Schubert calculus of the flag manifold. This is joint with with Nantel Bergeron and Sami Assaf.

4:00 pm in 345 Altgeld Hall,Friday, February 21, 2014

A general van der Corput lemma and underlying Ramsey theory (Part II)

Anush Tserunyan (UIUC Math)

Abstract: Consider a measure-preserving action of a countable group G on a standard probability space and suppose that this action is mixing along a given filter F on G; e.g. mild mixing corresponds to F=IP*, while letting F be the filter of sets of upper density 1 gives weak mixing for amenable G. These notions of mixing imply double recurrence for such systems, and it is a major theme in ergodic Ramsey theory to amplify this to multiple recurrence. This is often done using a so-called van der Corput difference (ratio) lemma, which "drops" the degree of the recurrence, thus enabling proofs by induction. Analogues of this lemma had been proven for various filters, but the existing proofs were different in each case. We prove a van der Corput lemma for a general class of filters, which includes those mentioned above, as well as idempotent ultrafilters. This is based on a new Ramsey theorem for semigroups related to labeling edges between the semigroup elements with their ratios. --- This is a continuation of the talk given in the Logic seminar on Tuesday February 11th.

4:00 pm in 241 Altgeld Hall,Friday, February 21, 2014

The Schubert problem

Dominic Searles (UIUC Math)

Abstract: The problem of finding a nonnegative integral formula for the Schubert structure constants of the cohomology ring of a generalized flag variety is longstanding. We will explore some of the geometric motivation for this problem, and some recent progress. There will be examples and computations.