# Math Calendar

### Upcoming Events

## Geodesic growth of right angled Coxeter groups

Yago Antolin-Pichel, Vanderbilt University

Location: Stevenson 1432

In this talk I will recall the definition of a Cayley graph, motivate the interest of understanding the growth of the Cayley graph and the geodesic growth. I will talk about a joint work with L.Ciobanu answering a question of Loeffler, Meier and Worthington. If time permits, I will also present a work of Ciobanu and Kolpakov, who recently constructed a family right angled coxeter groups with the same geodesic growth.

## Around hyperbolic Coxeter polyhedra I

Matthieu Jacquemet, Vanderbilt University

Location: Stevenson 1310

Unlike their spherical and Euclidean cousins, hyperbolic Coxeter polyhedra do not exist any more in higher dimensions, and are far from being classified. In this first talk, we intend to give a survey on their existence and classification. No particular background will be assumed.

## PRESTRAINED ELASTICITY: FROM SHAPE FORMATION TO MONGE-AMPERE ANOMALIES

Marta Lewicka, University of Pittsburgh

Location: Stevenson 5211

This lecture is concerned with the analysis of thin elastic films exhibiting residual stress at free equilibria. Examples of such structures and their actuations include: plastically strained sheets; specifically engineered swelling or shrinking gels; growing tissues; atomically thin graphene layers, etc. These and other phenomena can be studied through a variational model, pertaining to the non-Euclidean version of nonlinear elasticity, which postulates formation of a target Riemannian metric, resulting in the morphogenesis of the tissue which attains an orientation-preserving configuration closest to being the metric’s isometric immersion. In this context, analysis of scaling of the energy minimizers in terms of the film’s thickness leads to the rigorous derivation of a hierarchy of limiting theories, differentiated by the embeddability properties of the target metrics and, a-posteriori, by the emergence of isometry constraints with low regularity. This leads to questions of rigidity and flexibility of solutions to the weak formulations of the related PDEs, including the Monge-Ampere equation. In particular, we observe that the set of $C^{1,\alpha}$ solutions to the Monge-Ampere equation is dense in $C^0$ provided that $\alpha<1/7$, whereas rigidity holds when $\alpha>2/3$. Tea at 3:30 pm in SC 1425. (Contact Person: Gieri Simonett)

## 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.

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Noah Snyder, Indiana University Bloomington

Location: Stevenson 1432

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Jeff Cheeger, NYU

Location: Stevenson 5211

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

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Nem Kosovalic, University of South Alabama

Location: Stevenson 1307

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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)

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Thomas Sinclair, Purdue University

Location: Stevenson 1432

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Tilak Bhattacharya, Western Kentucky University

Location: Stevenson 1307

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David Penneys, University of California, Los Angeles

Location: Stevenson 1432

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Alex Eskin, University of Chicago

Location: Stevenson 5211

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

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Robert Bryant, Duke

Location: Stevenson 5211

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

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