Department of

# Mathematics

Seminar Calendar
for events the day of Friday, November 1, 2013.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, November 1, 2013

4:00 pm in 314 Altgeld Hall,Friday, November 1, 2013

#### Beyond renormalization in parabolic dynamics

###### Giovanni Forni (University of Maryland)

Abstract: We will describe a geometric point of view on renormalization for two examples of parabolic dynamical systems, linear skew shifts over rotations on the two-dimensional torus and billiards in rational polygons. We will discuss an extension of the renormalization approach to the case of higher dimensional skew-shifts and to billiards in arbitrary polygons.

This plenary lecture is the the start of the Midwest Dynamical Systems Conference, being held on Nov 2 and 3 in 314 Altgeld Hall and 239 Altgeld Hall.

4:00 pm in 241 Altgeld Hall,Friday, November 1, 2013

#### Riemann-Roch: From Riemann to Grothendieck.

###### Matej Penciak (UIUC Math)

Abstract: Riemann was interested in solving the Mittag-Leffler problem of finding meromorphic functions on a Riemann surface with prescribed simple poles. In 1857 Riemann gave an inequality relating topological properties and the number of points that guaranteed the existence of such functions. This launched a century's worth of generalizations and reinterpretations. In this talk we will look at Riemann's original argument and follow a path through this century of development looking at the contributions of Roch, Noether, Hirzebruch, and Grothendieck.

4:00 pm in 345 Altgeld Hall,Friday, November 1, 2013

#### Buechi, Cantor and Diophantus of Alexandria

###### Philipp Hieronymi (UIUC)

Abstract: I will give a progress report on the following two problems I have been working on for a while now: 1) finding a Cantor set C such that the expansion of the real field by C is model theoretically tame, 2) understanding the expansion of the ordered additve group of real numbers by two predicates, one for $\mathbf{Z}$ and one for $a\mathbf{Z}$, where $\mathbf{Z}$ is the set of integers and $a$ is an irrational number. In particular, their connection to Buechi's theorem on the monadic second order theory of one successor will be discussed.