Department of

Mathematics


Seminar Calendar
for events the day of Friday, February 14, 2014.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, February 14, 2014

3:00 pm in 343 Altgeld Hall,Friday, February 14, 2014

Combinatorial Ergodicity

Oliver Pechenik (UIUC)

Abstract: Let G be a group acting with finite orbits on a set X, f any complex-valued function on X, and g the function on G-orbits given by averaging f. Surprisingly often, the function g turns out to be constant. In such cases, Propp and Roby say that the triple (X,G,f) exhibits combinatorial ergodicity (or homomesy). For rectangular semistandard tableaux under promotion, ergodicity was conjectured by Propp and Roby and proved by the speaker in joint work with J. Bloom and D. Saracino. We will discuss this result in the context of various other combinatorial examples of ergodicity.

4:00 pm in 345 Altgeld Hall,Friday, February 14, 2014

A class of strange expansions of dense linear orders by open sets

Chris Miller (Ohio State)

Abstract: There are expansions of dense linear orders by open sets (of arbitrary arities) such that all of the following hold: 1) Every definable set is a boolean combination of existentially definable sets. 2) Some definable sets are not existentially definable. 3) Some coordinate projections of closed bounded definable sets are somewhere both dense and codense. 4) There is a unique maximal reduct having the property that every unary definable set either has interior or is nowhere dense. It properly expands the underlying order, yet is still rather trivial. At least some of these structures arise naturally in model theory. For example, if G is a generic predicate for the real field, then the expansion of (G,<) by the G-traces of all semialgebraic open sets is such a structure; moreover, it is interdefinable with the structure induced on G in (R,+,x,G). (Joint work with Dolich and Steinhorn.)

4:00 pm in 241 Altgeld Hall,Friday, February 14, 2014

Formal group laws, or who put algebraic geometry in my topology?

Nima Rasekh (UIUC Math)

Abstract: Cohomology theories give valuable insight into the properties of topological spaces. Over time, more and more cohomology theories have been discovered and therefore mathematicians realized the need for a classification. In this talk, we mention how we can use formal group laws to classify cohomology theories and, in particular, go over the correspondence between their universal objects. If time permits, we will also look at the algebro-geometric picture.