Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, January 21, 2016.

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events for the
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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
    December 2015           January 2016          February 2016
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4  5                   1  2       1  2  3  4  5  6
6  7  8  9 10 11 12    3  4  5  6  7  8  9    7  8  9 10 11 12 13
13 14 15 16 17 18 19   10 11 12 13 14 15 16   14 15 16 17 18 19 20
20 21 22 23 24 25 26   17 18 19 20 21 22 23   21 22 23 24 25 26 27
27 28 29 30 31         24 25 26 27 28 29 30   28 29
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Thursday, January 21, 2016

11:00 am in 241 Altgeld Hall,Thursday, January 21, 2016

#### Gap Distribution in Circle Packings

###### Xin Zhang (UIUC Math)

Abstract: Given a configuration of finitely many tangent circles, one can form a packing of infinitely many circles by Möbius inversions. Fixing one circle from such a packing, we study the distribution of tangencies on this circle via the spectral theory of automorphic forms. Specifically, we will use Anton Good's theorem to show that these tangencies are uniformly distributed when naturally ordered by a growing parameter, and the limiting gap distribution exists, which is conformally invariant. This is a joint work with Zeev Rudnick.

12:00 pm in 243 Altgeld Hall,Thursday, January 21, 2016

#### Limits of Teichmüller geodesics

###### Chris Leininger (UIUC Math)

Abstract: I will discuss joint work with Brock, Modami, and Rafi in which we describe local combinatorial constructions for quasi-geodesics in the curve complex which limit to non-uniquely ergodic laminations. We have good control on the intersection numbers for these sequences, and in particular, we are able to analyze the limiting behavior in the Thurston boundary of Teichmüller space of Teichmüller rays defined by these laminations. These limits exhibit new and unexpected phenomena.