# Math Calendar

### Upcoming Events

## Subnormal subgroups in free groups, their growth and co-growth

Alexander Olshanskii, Vanderbilt University

Location: Stevenson 1310

We (1) compare subnormal closures of finite sets in a free group $F$; (2) obtain the limit for the series of subnormal closures of a single element in $F$; (3) prove that the exponential growth rate (e.g.r.) $\lim_{n\to \infty}\sqrt[n]{g_H(n)}$, where $g_H(n)$ is the growth function of a subgroup $H$ with respect to a finite free basis of $F$, exists for any subgroup $H$ of the free group $F$; (4) give sharp estimates from below for the e.g.r. of subnormal subgroups in free groups; and (5) find the co-growth of the subnormal closures of free generators.

## Departmental Welcome Event

Location: Stevenson 5211

Department Chair Dietmar Bisch will introduce newcomers to the department. Refreshments will follow in Stevenson 1425.

## Connes’ character rigidity conjecture for lattices in higher rank groups

Jesse Peterson, Vanderbilt University

Location: Stevenson 1310

We show that lattices in higher rank center-free simple Lie groups are operator algebraic superrigid, i.e., any unitary representation of the lattice which generates a II_1 factor extends to a representation of its group von Neumann algebra. This generalizes results of Margulis and Stuck-Zimmer, and answers in the affirmative a conjecture of Connes.

## Talk Title TBA

Koichi Shimada, University of Tokyo

Location: Stevenson 1432

## Formal conjugacy growth and hyperbolicity

Yago Antolin Pichel, Vanderbilt University

Location: Stevenson 1310

Rivin conjectured that the formal conjugacy growth series of an hyperbolic group is rational if and only if the group is virtually cyclic. In this talk, I will present a proof of Rivin’s conjecture and supporting evidence for the analogous statement for acylindrically hyperbolic groups. This is a joint work with Laura Ciobanu.

## Talk Title TBA

Boris Lishak, Toronto

Location: Stevenson 1310

## Talk Title TBA

Matthew Kennedy, University of Waterloo

Location: Stevenson 1432

## Talk Title TBA

Rolando de Santiago, University of Iowa

Location: Stevenson 1432

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