# Math Calendar

### Upcoming Events

## Bases formed by translates of one function in the space of p-integrable functions

Thomas Schlumprecht, Texas A&M

Location: Stevenson 5211

We consider subspaces of the space of p-integrable functions on the real number line, which are generated by a sequence of functions which is obtained by shifting in a uniform discrete manner the same function f. In particular we are interested in the question whether or not this space could be the whole space of p-integrable functions, assuming the sequence enjoys some basic properties. This is, in different combinations, joint work with Freeman, Odell, Sari, Zhang and Zsak. Tea at 3:30 pm in SC 1425. (Contact Person: Alex Powell)

## Talk Title TBA

Christoph Walker, Leibniz Unversität Hannover (Germany)

Location: Stevenson 1307

## Unique Prime Factorization for ${\rm II}_1$ Factors with Cartan Subalgebras

Daniel Hoff, UC San Diego

Location: Stevenson 1432

A tracial von Neumann algebra $M$ is called prime if it cannot be decomposed as the tensor product of two nontrivial (not type ${\rm I}$) subalgebras. Naturally, if $M$ is not prime, one asks if $M$ can be uniquely factored as a tensor product of prime subalgebras. The first result in this direction is due to Ozawa and Popa in 2003, who gave a large class of groups $\mathcal{C}$ such that for any $\Gamma_1, \dots, \Gamma_n \in \mathcal{C}$, the associated von Neumann algebra $L(\Gamma_1) \,\overline{\otimes}\, \cdots \,\overline{\otimes}\, L(\Gamma_n)$ is uniquely factored. This talk will focus on unique prime factorization in the setting of von Neumann algebras which contain Cartan subalgebras. Here we encounter an interesting general obstruction to unique prime factorization in the sense of Ozawa and Popa. We will describe this obstruction and how their techniques can be adapted to avoid it.

## Bi-exact groups, strongly ergodic actions and group measure space type III factors with no central sequence

Yusuke Isono, RIMS

Location: Stevenson 1310

We investigate the asymptotic structure of (possibly type III) crossed product von Neumann algebras arising from arbitrary actions of bi-exact discrete groups (e.g. free groups) on amenable von Neumann algebras. We particularly prove a spectral gap rigidity result for the crossed products and, using recent results of Boutonnet-Ioana-Salehi Golsefidy, we provide the first example of group measure space type III factors with no central sequences. This is joint work with C. Houdayer.

## Visual Transduction: A Signaling Paradigm Across Orders of Scale

Colin Klaus, Vanderbilt University

Location: Stevenson 1307

Visual Transduction in Rod and Cone photoreceptor cells is one of the best quantified G-protein signaling cascades known to biologists. Here photons of light are converted by biochemical processes into a system’s response by diffusion of the 2nd messengers cGMP and Ca2+. The morphology of these photoreceptor cells is striking and both highly regulated, highly ordered. In this talk, I will present on how the partial differential equations’ techniques of Homogenization and Concentrating Capacity may be used at once to capture the effects of this geometry and especially its disparate physical scales.

## Talk Title TBA

Alex Iosevich, University of Rochester

Location: Stevenson 5211

Tea at 3:30 pm in SC 1425. (Contact Person: Akram Aldroubi)

## Talk Title TBA

Jeff Cheeger, NYU

Location: Stevenson 5211

Tea at 3:30 pm in SC 1425. (Contact Person: Marcelo Disconzi)

## Talk Title TBA

Peter May, University of Chicago

Location: Stevenson 5211

Tea at 3:30 pm in SC 1425. (Contact Person: Anna Marie Bohmann)

## Talk Title TBA

Alex Eskin, University of Chicago

Location: Stevenson 5211

Tea at 3:30 pm in SC 1425. (Contact Person: Mark Sapir)

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