# Math Calendar

### Upcoming Events

## Square percolation with applications to random right-angled Coxeter groups

Victor Falgas-Ravry, Vanderbilt University

Location: Stevenson 1432

Motivated by applications to group theory, we study two global properties of random graphs. We determine the thresholds for G(n,p) being an `augmented suspension’ (AS) and being `constructible from squares’ (CFS). As a consequence of our work, we determine the threshold at which random right-angled Coxeter groups become thick of order one. Thickness is an inductively defined property of groups, which may be thought of as a geometric obstruction to Gromov’s notion of relative hyperbolicity, and has a number of applications in geometric group theory. For example, thickness of order one implies quadratic divergence for right-angled Coxeter groups. Our work also ties in with some intriguing probabilistic questions about subgraph percolation, most of which are poorly understood. Joint work with Jason Behrstock, Mark Hagen and Tim Susse.

## Talk Title TBA

Volodymyr Nekrashevych, Texas A&M

Location: Stevenson 1310

## Around hyperbolic Coxeter polyhedra II

Matthieu Jacquemet, Vanderbilt University

Location: Stevenson 1310

In this second talk, we shall discuss recent results related to two natural classes of hyperbolic polyhedra : simplices, and Coxeter cubes. It time permits, we shall outline a couple of open problems which could be attacked by using these new results.

## 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

Yunxiang Ren, Vanderbilt University

Location: Stevenson 1432

## Regularity of manifolds with bounded Ricci curvature and the codimension 4 conjecture

Jeff Cheeger, NYU

Location: Stevenson 5211

Let X^n denote the Gromov-Hausdorff limit of a noncollapsing sequence of Riemannian manifolds with uniformly bounded Ricci curvature. Around 1990, early workers, in particular, Mike Anderson, conjectured that apart from a (possibly empty) closed subset S of (Hausdorff) codimension greater or equal to 4, X^n is a smooth riemannian manifold. The example of limits of scaled down 4-dimensional complete noncompact Ricci flat spaces showed that such a result would be sharp. We will try to explain the statement of the conjecture and some of the ideas in the proof. This is joint work with Aaron Naber. Tea at 3:30 pm in SC 1425. (Contact Person: Marcelo Disconzi)

## Talk Title TBA

Noah Snyder, Indiana University Bloomington

Location: Stevenson 1432

## Talk Title TBA

Nem Kosovalic, University of South Alabama

Location: Stevenson 1307

## Talk Title TBA

Robert L. Parker, UC San Diego

Location: Stevenson 5211

Tea at 3:30 pm in SC 1425. (Contact Person: Doug Hardin)

## Shanks Workshop on Geometric Analysis, March 11 – 12, 2016

Location: Stevenson 1432

## 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

Thomas Sinclair, Purdue University

Location: Stevenson 1432

## Talk Title TBA

Tilak Bhattacharya, Western Kentucky University

Location: Stevenson 1307

## Talk Title TBA

David Penneys, University of California, Los Angeles

Location: Stevenson 1432

## Talk Title TBA

Alex Eskin, University of Chicago

Location: Stevenson 5211

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

## Talk Title TBA

Robert Bryant, Duke

Location: Stevenson 5211

Tea at 3:30 pm in SC 1425. (Contact Person: Bruce Hughes)

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