ColoState Math Department Colloquium

Fall 2017:

Mon. 09/25, 4-5pm, Weber 223

Jason Cantarella, University of Georgia

Host Clayton Shonkwiler

manifold of space polygons. Applications include the study of random walks

and polymers, linkages, and protein shapes. We'll start with the geometry of

the space of open polygons in R^3, as this naturally models protein shapes.

We identify this space with quaternionic projective space, and use the metric

on HP^n to cluster some protein shapes. We will then turn to closed polygons,

where we use the natural symplectic structure of closed polygon space to

understand the distribution of point-to-point distances in the polygon and

construct a sampling algorithm. To end the talk, we'll discuss some work

in progress on making the metric structure of closed polygon space more

easily visible by writing closed polygons as a quotient space (instead of

a subspace) of the open polygons.

Mon. 10/16, 4-5pm, Weber 223

Martina Bukac, University of Notre Dame

Host James Liu

Applications to Blood Flow"

plays a fundamental role in many biomedical applications. An example of such

application is the interaction between blood, arterial wall, and blood clot. This

multi-physics problem features three different types of coupling: fluid-elastic structure

coupling, fluid-poroelastic material coupling, and elastic structure-poroelastic material

coupling, resulting in a fully coupled, non-linear, moving boundary problem. As a

consequence, numerical algorithms that split the fluid dynamics, structure mechanics,

and poroelastic material dynamics are a natural choice. We propose stable, partitioned

methods for the coupled problem. We present numerical tests where we investigate

the effects of the material properties of the poroelastic medium on the fluid flow. Our

findings indicate that the flow patterns highly depend on the storativity of the poroelastic

material.

Mon. 11/13, 3-4pm, Weber 237

Joceline Lega, University of Arizona

Host: Patrick Shipman

Hoon Hong, North Carolina State University

Host: Dan Bates

(1) It is bigger (hence better) than the previous bounds.

(2) It is covariant under the scaling of the roots, unlike the previous bounds.

If time allows, we will also describe a generalization to multivariate polynomials systems. This is a joint work with Aaron Herman and Elias Tsigaridas.

Mon. 02/12, 4-5pm, Weber 223

David Zureick-Brown, Emory University

Host: Rachel Pries

Last modified by James Liu, Mon. 10/30/2017