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Graduate Colloquia
Spring 2003
Tuesdays, 4:30  5:30pm in JWB 335
Math 6960001 (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 airseaice 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 crystallinelike
arrangement for the spheres. The fluid composite then behaves as a solid.
For metal spheres, fractal netlike 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 2dimensional 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 EulerLagrange 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
nonstandard growth conditions.
Monday, March 31 (Special Recruitment Colloquium)
Speaker: Matt Clay, Brynja Kohler, An Le
Title: TBA
Abstract: TBA
April 8 CANCELLED
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 841120090
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