ColoState Math Department Colloquium

Barbara Fantechi, Scuola Internazionale Superiore di Studi Avanzati (Italy)

Host: Renzo Cavalieri

Abstract:

manifold; in fact it is a symplectic manifold with a compatible complex

structure. Gromov Witten invariants are defined both for smooth projective

varieties over an arbitrary algebraically closed field, and for compact

symplectic manifolds with a compatible almost complex structure. We outline

differences and similarities in the definitions, and sketch ongoing attempts

to find a common language.

Mon. 04/16, 4-5pm, Weber 223

Leah Edelstein-Keshet, University of British Columbia

Host: Yongcheng Zhou

Abstract:

of proteins. Among these are central regulators (GTPases) that control

the polarity, the contraction or the spreading of a cell. In my talk, I

will describe efforts at understanding the emergent behaviour using

mathematical modeling at the level of a cell and of a tissue made up of

many cells. The models lead to interesting mathematics, as well as

insights into behaviour observed in experimental cell biology. I will

review both partial and ordinary differential equation versions of our

models, and illustrate some new methods devised to analyse these. I will

conclude with recent work on waves of contraction observed in a tissue

composed of many "model cells".

Gideon Simpson, Drexel University

Host: David Aristoff

Abstract:

simulations of materials is how to reach physically meaningful time

scales. While the fundamental time scale of the atomistic models

is that of the femtosecond, physically meaningful phenomenon may

take microseconds or longer to occur. This precludes a direct

numerical simulation with, for instance, a Langevin model of the

material from reaching physical time scales. The time scale

separation challenge has motivated the development of a variety

of multiscale methods, including accelerated molecular dynamics,

kinetic Monte Carlo, phase field models, and diffusive molecular

dynamics. In this talk, I will survey some of these approaches

and discuss common mathematical assumptions that underlie them

while also highlighting where approximations have been made.

Rigorous results will be presented, where available, along with

outstanding mathematical challenges.

Thu. 03/22, 1-2pm, TILT Auditorium

Catherine Good

Host: Jess Ellis

(Postponed to Fall 2018, due to weather conditions in Northeast)

Title:

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

David Zureick-Brown, Emory University

Host: Rachel Pries

Fall 2017:

Mon., 11/13, 4-5pm, Weber 237

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

Joceline Lega, University of Arizona

Host: Patrick Shipman

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.

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.

Last modified by James Liu, Mon. 03/05/2018