# Calendar

## Yesterday

### Automorphic Forms and Representation Theory Seminar, Professor Carl Wang Erickson, Brandeis University, REC 316

Thursday, Apr 28 1:30 pm - 2:30 pm

## Harder-Narasimhan Theory for Kisin Modules

Abstract: We begin by introducing Kisin varieties in the context of Galois deformation rings. We will then describe a generalization of Farguesâ€™ Harder-Narasimhan theory for finite flat group schemes to the larger category of Kisin modules, including the result that a tensor product of semi-stable Kisin modules is semi-stable. This theory gives rise to stratifications of Kisin varieties. This is joint work with Brandon Levin.### PDE Seminar, Professor John Lewis, University of Kentucky, REC 117

Thursday, Apr 28 3:30 pm - 4:30 pm

## Regularity of p-Harmonic Functions

Abstract: In this talk, given a bounded domain $\Omega\subset R^n=$ Euclidean n space, we discuss what is known about the interior regularity of a $p$ harmonic function $u$ in $\Omega$, when $1 < p < \infty$; $p\neq 2$. That is, $u\colon \Omega\to R$ is a weak solution to the $p$ Laplace equation: $$ \nabla\cdot (|\nabla u|^{p-2}\nabla u)=0\text{ in }\Omega,\text{ when }1 < p < \infty, p\neq 2. $$ Included in this discussion will be recent work of Vogel and the author on polynomial solutions to the $p$ Laplace equation.## Today

## Mathematics in Medical Imaging

Abstract: Medical Imaging has had a profound impact on our lives, and there are few fields the role of mathematics is more appreciated than medical imaging. In this talk, we will review how mathematics made the state-of-art medical imaging technologies possible and will discuss the role of mathematicians in the future development of medical imaging.### Commutative Algebra Seminar, Dr. Youngsu Kim, University of California Riverside, UNIV 017

Friday, Apr 29 1:30 pm - 2:30 pm

## Defining Ideals of Special Fiber Rings and Birational Morphisms of Projective Varieties

Abstract: Suppose that a rational map between two projective spaces over a field is defined by a set of homogeneous polynomials of the same degree. It is interesting and important to study if such a map is birational onto its image. In this talk, we present an algebraic characterization under some assumptions on the ideal generated by the polynomials. Our result is obtained by analyzing the defining ideal of the special fiber ring. This is joint work with Vivek Mukundan.## Dedekind zetas of real quadratic fields as periods of eisenstein series

Abstract: The real analytic eisenstein series E_s are a concrete family of smooth functions on the complex upper half plane, where are designed to be invariant under the action of SL(2,Z) by linear fractional transformations. The Dedekind zeta function of a number field describes the arithmetic of number fields, much in the way that Euler-Riemann's zeta function describes that of Z. In this talk I show that, for a particular family of number fields, the latter can be obtained from the form; thus allowing for the geometry of the complex upper half plane to be brought to bear on the study of arithmetic.For those interested, reference material can be found on Paul Garrett's website.

## Next Week

### CCAM Seminar, Professor Ching-Shan Chou, Ohio State University, REC 225

Monday, May 2 3:30 pm - 4:30 pm

## Computer Simulations of Yeast Mating Reveal Robustness Strategies for Cell-Cell Interactions

Cell-to-cell communication is fundamental to biological processes which require cells to coordinate their functions. In this talk, we will present the first computer simulations of the yeast mating process, which is a model system for investigating proper cell-to-cell communication. Computer simulations revealed important robustness strategies for mating in the presence of noise. These strategies included the polarized secretion of pheromone, the presence of the alpha-factor protease Bar1, and the regulation of sensing sensitivity.Mathematical Models of Ebola Virus Disease and Vaccine Preventable Diseases

Committee: Z. Feng (chair), G. Buzzard, N.K. Yip, J. Glasser

## May

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