Department of

Mathematics


Seminar Calendar
for events the day of Friday, September 19, 2014.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, September 19, 2014

4:00 pm in 243 Altgeld Hall,Friday, September 19, 2014

Flat Geometries and Representations of the Fundamental Group

Brian Collier (UIUC Math)

Abstract: Back in the day, Klein gave a famous talk where he addressed the question: what is a geometry? His proposed answer to this question was his Erlanger program. In this talk we will give a modern treatment of Klein's ideas with the notion of a $(G,X)$ structure. After developing some general theory, we will focus on flat geometries. Our main examples will be hyperbolic geometry and Lorentzian geometry. Flatness of $(G,X)$ structures on a topological space $M$ can also be packaged in the language of $G$-bundles on $M$ with flat connections; and so, is intimately related with representations $\pi_1(M)\rightarrow G$. This perspective gives some very nice tools to study things like moduli spaces of certain $(G,X)$ structures.

4:00 pm in 345 Altgeld Hall,Friday, September 19, 2014

Model theory of transseries

Lou van den Dries (UIUC Math)

Abstract: Last spring, Matthias Aschenbrenner, Joris van der Hoeven, and LvdD finished a twenty year quest by finding and proving the key model-theoretic and algebraic facts about the differential field of transseries (in the spirit of Tarski's classical results about the logical properties of the field of real numbers). In two seminar talks on this work, I will sketch our results, and discuss some problems about the differential algebra and model theory of transseries that are still open. - This talk will be continued on Tuesday September 23rd in the Logic seminar.