ColoState Math Department Colloquium

Confirmed Speakers

Fall 2017: 

Mon. 09/25, 4-5pm, Weber 223 
Jason Cantarella, University of Georgia
Host Clayton Shonkwiler

Title: "The Differential Geometry of Spaces of Polygons and Polymers"

Abstract: We are interested in understanding the geometry of the Riemannian
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

Title: "Interaction between a Fluid and Elastic and Poroelastic Materials with
Applications to Blood Flow"

Abstract: The interaction between a fluid, elastic structure, and poroelastic material
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

Mon. 11/13, 3-4pm, Weber 237
Joceline Lega, University of Arizona
Host: Patrick Shipman

Title: "A Three-pronged Approach to Predicting the Spread of Mosquito-borne Diseases"

Abstract:  Aedes aegypti is a mosquito that can transmit diseases like dengue, chikungunya, and Zika.  This talk will present a three-pronged approach to the modeling of Aedes aegypti-borne diseases, resulting from a collaboration with colleagues in the College of Public Health and in the School of Geography and Development at the University of Arizona.  Specifically, I will first discuss a mosquito abundance model that takes into account how meteorological data (temperature, precipitation, relative humidity) affect mosquito development and survival, and will describe its calibration against surveillance data in Puerto Rico.  Then, I will present a simple nonlinear growth model that is able to capture trends in disease incidence reports at the level of a country, and illustrate its efficacy in predicting the 2014-15 chikungunya epidemic in the Caribbean and the Americas.  Finally, I will show how a network-based approach that includes population flow between cities allows for a unified description of the spread of chikungunya and Zika in the small island nation of Dominica.  This talk will be accessible to a broad audience of scientists interested in the mathematical modeling of mosquito-borne diseases.

Mon., 11/13, 4-5pm, Weber 237
Hoon Hong, North Carolina State University
Host: Dan Bates

Title: "Root Separation Bound"

Abstract:  Let f be a square-free polynomial.  The root separation of f is the minimum of the pair-wise distance between the complex roots of f.  Finding a lower bound on the root separation is a fundamental problem, arising in numerous disciplines.  Due to its importance, there has been extensive research on this problem, resulting in various bounds.  In this talk, we present another bound, which is "nicer" than the previous bounds in that
(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.

Spring 2018:

Mon. 02/12, 4-5pm, Weber 223
David Zureick-Brown, Emory University
Host: Rachel Pries

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