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Graduate Colloquia
Spring 2003
Tuesdays, 4:30 - 5:30pm in JWB 335
Math 6960-001 (1 - 3 credit hours)

The goal of this Colloquium is to encourage interaction among graduate students, specifically between graduate students who are actively researching a problem and those who have not yet started their research. Speakers will discuss their research or a related introductory topic on a level which should be accessible to nonspecialists. The discussions will be geared toward graduate students in the beginning of their program, but all are invited to attend. This invitation explicitly includes undergraduate students.

Talks will be held on Tuesdays at 4:30pm in JWB 335, unless otherwise noted.

Jan 14  (24)

Speaker:  Ken Golden
Title:  Mathematical models of composite materials undergoing phase transitions
Abstract: We will give an overview of mathematical modeling of the effective electromagnetic, thermal, and fluid transport properties of composite materials, particularly those which exhibit a sharp transition in behavior as some parameter is varied near a critical value. In particular, we focus on sea ice, a composite of pure ice with random brine and air inclusions, and electrorheological (ER) fluids, composites of a viscous fluid such as oil containing glass or metal spheres. Sea ice is distinguished from other porous media such as bones or rocks in that its microstructure and bulk properties depend strongly on temperature. Above a critical value of around -5 degrees C, the brine phase is connected and the sea ice is permeable, allowing transport of brine, nutrients, biomass, and heat through the ice. These processes play an important role in air-sea-ice interactions, in sea ice production and decay, in the life cycles of sea ice algae, and in remote sensing of the pack. For ER fluids, if an electric field is applied to the system with an initially random configuration of spheres, and if its strength exceeds a critical value, then the glass spheres coagulate into chains parallel to the field, and further into columns with a crystalline-like arrangement for the spheres. The fluid composite then behaves as a solid. For metal spheres, fractal net-like structures form. Some mathematical areas which will be discussed include percolation theory, homogenization for partial differential equations, forward and inverse scattering, bounds on effective transport coefficients via functional analytic and complex variable methods, diffusion processes, and statistical mechanics. At the conclusion, we will show a short video on a recent winter expedition into the Antarctic sea ice pack.
Jan 21 (24)
Speaker:  Renzo Cavalieri
Title:  Frobenius Algebras and T.Q.F.T.'s: a passionate kiss between algebra and geometry
Abstract:  Frobenius Algebras are extremely elementary and common algebraic structures. Namely, algebras with the extra structure of an inner product "compatible" with multiplication. Topological Quantum Field Theories are cute, extremely topological constructions, that, in the 2-dimensional case, turn out to be surprisingly equivalent to Frobenius Algebras. Goal of the talk is to introduce the characters and witness "the kiss". Time and energies permitting, I'll try to also give some ideas of one somewhat deep application these simple tools seem to have, i.e. how to use them to count coverings of a Riemann Surface.

Jan 28  (27)
Speaker: Fred Adler
Title:  Gender Bias in a Virus
Abstract:  Hantavirus recently emerged as a deadly disease of humans in the Four Corners area. The virus is carried by deer mice, and is generally more prevalent in male than in female mice. In collaboration with biologists here at the University of Utah, I have been developing models of disease dynamics that take into account how mouse behavior depends on gender (males bite each other more) and on climate (wet conditions lead to crowding that might induce mice to bite more). Viral abundance depends quite sensitively on how mice respond to crowding, and we can predict whether the entire human population of Utah will be at risk if the drought ever ends.

Feb 4  (27)
Speaker:  Robert Hanson
Title:  Minimizing Integral Functionals with Euler
Abstract: This is an introduction to the method of Euler-Lagrange to transform the problem of minimizing a functional into the problem of solving a differential equation. We will derive the method look at three examples where we can apply it.

Feb 11  (26)
Speaker:  Greg Piepmeyer
Title:  Some Discussion of Topics Related to Cancelation
Abstract: TBA

Feb 18  (21)
Speaker:  Fumi Sato
Title:  Symmetries of Equations
Abstract: I will explain how to obtain new solutions of a given equation from one very simple solution using symmetries methods. The primary applications of these methods are the solutions of nonlinear differential equations.

Feb 25   (21)
Speaker:  Tom Robbins
Title:  Damn, I can't get rid of these things!
Abstract: Two questions that often arise in plant invasion biology is whether an invasive plant species will become established in a particular habitat and if so, will it begin to spread and at what speed. For a homogeneous habitat this question is well understood. For this talk we will consider the infinite, heterogeneous case. We will first derive a PDE model for seed dispersal coupled to an Integrodifference model for the community dynamics. We will then derive a set of conditions under which a plant species can be established in a new habitat.

Mar 4   (19)
Speaker:  Evan Haskell
Title:  TBA
Abstract:   TBA

Mar 11  (17)
Speaker: Peter Alfeld
Title:  Multivariate Splines and the Four Color Map Theorem
Abstract: The Four Color Map Theorem states that every planar map can be colored with only four colors so that no two neighboring countries are of the same color.

Multivariate Splines are smooth piecewise polynomial functions of two variables defined on a triangulation. Many basic questions, such as the dimension of some spline spaces, are unanswered to date. They are trivial for functions of one variable, but they are difficult for bivariate splines for two reasons: The answer depends on the geometry of the triangulation (and not just the combinatorics, as one might expect), and it is difficult to localize arguments. In the latter aspect multivariate spline problems resemble the four color map problem. Indeed some of the techniques used for the solution of the four color map problem, including the heavy use of computers, may eventually bear fruit for the solution of multivariate spline problems.

In this talk I will sketch the techniques used for the solution of the four color map problem, show how they can be used for the solution of multivariate spline problems, and describe some open problems in multivariate spline research.


Mar 18  (Spring Break)
Speaker:  N/A
Title:  N/A
Abstract: N/A

Mar 25   (17)
Speaker:  Inbo Sim
Title:  Regularity for Elliptic Equations with General Growth Conditions
Abstract: In this talk, I shall introduce the concept of regularity for weak solutions and show the regularity of solutions for elliptic equations of divergence form with non-standard growth conditions.

Monday, March 31   (Special Recruitment Colloquium)
Speaker: Matt Clay, Brynja Kohler, An Le
Title:  TBA
Abstract: TBA

Speaker:  David Hartenstine
Title:  Job Search Seminar
Abstract: N/A

April 15  
Speaker: Frank Lynch
Title:  Apples, Oranges and \epsilon
Abstract: When modeling a physical system, facts about that system may lead to small parameters. We can often take advantage of these small parameters to make new discoveries about the physical system. In this talk, I will motivate the existence of small parameters including "how to know" when something is small. I will discuss several techniques for dealing with small parameters and close with an example from my research.

April 22  

GSAC Organizational Meeting for 2003/2004

Past Graduate Colloquia

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Department of Mathematics
University of Utah
155 South 1400 East, JWB 233 
Salt Lake City, Utah 84112-0090 
Tel: 801 581 6851, Fax: 801 581 4148