Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, February 24, 2005.

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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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Thursday, February 24, 2005

12:00 pm in 464 Loomis,Thursday, February 24, 2005

#### Higgs bundles and Calabi-Yau threefolds

###### Tony Pantev (U Penn, Math)

1:00 pm in Altgeld Hall 347,Thursday, February 24, 2005

#### The intersection form and geodesic currents on free groups (continued)

###### Ilya Kapovich   [email] (UIUC)

Abstract: The notion of a geometric intersection number between free homotopy classes of closed curves on surfaces plays a pivital role in Thurston's treatment of the Teichmuller space and of the dynamics of surface homeomorphisms. In particular, Bonahon proved that this notion extends to a symmetric and bilinear notion of intersection number between two geodesic currents on a hyperbolic surface. We investigate to what extend these ideas are applicable in the free group context. Thus we define and study an Out(F_n)-equivariant "intersection form" on the product of the (non-projectivized) Culler-Vogtmann outer space and the space of geodesic currents on a free group. We also find an obstruction, arising from non-symmetric behaviour of generic stretching factors of free group automorphisms, to the existence of a symmetric notion of an intersection number between two geodesic currents on a free group. Time permitting, we will discuss an embedding of the Culler-Vogtmann outer space into the projectivized space of geodesic currents, based on the use of Patterson-Sullivan conformal densities.

1:00 pm in 241 Altgeld Hall,Thursday, February 24, 2005

#### Digital expansions, exponential sums and central limit theorems.

###### Michael Drmota (Technical University, Wien)

Abstract: The purpose of this talk is to present recent results on the distribution of the values of the ($q$-ary) sum of digits function $s_q(n)$, where we mainly focus on two problems, the joint distribution $(s_{q_1}(n),s_{q_2}(n))$ of two different expansions and on the distribution of the sum-of-digits function of squares: $s_q(n^2)$.