Department of

# Mathematics

Seminar Calendar
for events the day of Friday, November 20, 2015.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, November 20, 2015

4:00 pm in 243 Altgeld Hall,Friday, November 20, 2015

#### Fuchsian representations and geodesic flows with an eye towards Anosov structures.

###### Brian Collier (UIUC Math)

Abstract: Fuchsian representations are discrete faithful representations of the fundamental group of a closed surface into PSL(2,R) (the isometry group of the hyperbolic plane), and are in bijection with the Teichmüller space of hyperbolic structures on the surface. Using Higgs bundle techniques, Nigel Hitchin showed that there is a natural generalization of Fuchsian representations into the group PSL(n,R), however the geometry associated these representations remained mysterious until Labourie's work on Anosov representations. The aim of this talk is to motivate (especially to the speaker) why one should work to understand Anosov structures. After setting the scene, most of the time will be spent talking about Fuchsian representations and the geodesic flow on hyperbolic surfaces.

4:00 pm in 345 Altgeld Hall,Friday, November 20, 2015

#### Surreal numbers as a differential field

###### Lou van den Dries   [email] (UIUC Math)

Abstract: I will talk about a (pre-)preprint by Aschenbrenner, van der Hoeven, and myself, where we answer some questions raised by the Bararducci-Mantova paper. For example, the natural embedding of the differential field of transseries into the differential field No is elementary, and any Hardy field can be embedded into the differential field No.