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Thu Sep 05

Colloquium

3:35pm - Vincent Hall 16
Colloquium - Canceled
Alina Chertock, NSCU

Chemotaxis is a movement of micro-organisms or cells towards the areas of high concentration of a certain chemical, which attracts the cells and may be either produced or consumed by them. In its simplest form, the chemotaxis model is described by a system of nonlinear PDEs: a convection-diffusion equation for the cell density coupled with a reaction- diffusion equation for the chemoattractant concentration. It is well-known that solutions of such systems may develop spiky structures or even blow up in finite time provided the total number of cells exceeds a certain threshold. This makes development of numerical methods for chemotaxis systems extremely delicate and challenging task.

In this talk, I will present a family of high-order numerical methods for the Keller-Segel chemotaxis system and several related models. Applications of the proposed methods to to multi-scale and coupled chemotaxis–fluid system and will also be discussed.

Thu Sep 19

Colloquium

3:35pm - Vincent Hall 16
The Langlands Program: An Introduction and Recent Progress
Solomon Friedberg,, Boston College

The Langlands Program, connecting algebra, analysis and geometry in diverse ways, is foundational to modern number theory. I will introduce this program and indicate some recent progress. As we shall see, a great deal still remains to be done.

Thu Oct 17

Colloquium

3:35pm - Vincent Hall 16
Hopf monoids relative to a hyperplane arrangement
Marcelo Aguiar, Cornell University

The talk is based on recent and ongoing work with Swapneel
Mahajan. We will introduce a notion of Hopf monoid relative to a real
hyperplane arrangement. When the latter is the braid arrangement, the
notion is closely related to that of a Hopf monoid in Joyal's category
of species, and to the classical notion of connected graded Hopf
algebra. We are able to extend many concepts and results from the
classical theory of connected Hopf algebras to this level. The
extended theory connects to the representation theory of a certain
finite dimensional algebra, the Tits algebra of the arrangement. This
perspective on Hopf theory is novel even when applied to the classical
case. We will outline our approach to generalizations of the classical
Leray-Samelson, Borel-Hopf, and Cartier-Milnor-Moore theorems to this
setting. Background on hyperplane arrangements will be reviewed.

Thu Oct 31

Colloquium

3:35pm - Vincent Hall 16
Differential operators on invariant rings
Anurag Singh, University of Utah

Work of Levasseur and Stafford describes the rings of differential operators on various classical invariant rings of characteristic zero; in each of these cases, the differential operators form a simple ring. Towards an attack on the simplicity of rings of differential operators on invariant rings of reductive groups over the complex numbers, Smith and Van den Bergh asked if reduction modulo p works for differential operators in this context. In joint work with Jack Jeffries, we establish that this is not the case for various classical groups.

Thu Nov 14

Colloquium

3:35pm - Vincent Hall 16
Colloquium
Joe Kramer-Miller, UC Irvine
Thu Mar 19

Colloquium

3:35pm - Vincent Hall 16
Colloquium
Mauro Maggioni, Ordway Visitor, Johns Hopkins University
Thu Apr 23

Colloquium

3:35pm - Vincent Hall 16
Colloquium
Dionisios Margetis - Ordway Visitor, University of Maryland, College Park