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Address: Mathematics | University of Alabama
at Birmingham
1300 University Blvd | Birmingham,
AL 35294-1170
Phone: 943 2154 | Fax: 934 9025 ;
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Friday, August 29, 2008
Hassan Fatallah
University of Alabama at Birmingham
"New Mathematical Model Reveals Positive and Negative Loops Causing the Paradoxical Effects of Clockwork Orange Mutations
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2:00 pm / CH-301
Abstract.
Clockwork Orange (CWO) is a key negative regulator of central elements of the molecular network of the Drosophila circadian clock; it
represses the transcription of per, tim, vri, pdpd1, and cwo. Paradoxically, cwo-mutant flies exhibit lower levels of per, tim, pdp1,
and vri and higher levels of cwo mRNAs as compared to wild type. We introduce a new system of ordinary differential equations
to model the dynamics of this molecular network. Simulations generate 24-hour rhythmic oscillations and entrainment in response to
time shifts. In silico targeted deletions reveal that the paradoxical effects of cwo mutations are caused by a positive loop containing
vri and the negative cwo autoregulatory loop.
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Friday, September 5, 2008
Vladimir Oliker.
Emory University
"The Aleksandrov problem and Monge-Kantorovich optimal transport of curvature on S^n"
2:00 pm / CH-301
Postponed to October 31, 2008, 2pm CH-301
Abstract.
In this talk I will describe a variational solution to a problem of A.D. Aleksandrov concerning existence and
uniqueness of a closed convex hypersurface in Euclidean space with prescribed
integral Gauss curvature.
Remarkably, in variational formulation this
problem turned out to be closely connected with the Monge-Kantorovich
theory of optimal mass transport on S^n.
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Friday, September 12, 2008
Shihshu Walter Wei.
University of Oklahoma.
"p-Harmonic maps and 1-forms, generalized 1-harmonic equations, topology and algebra""
2:00 pm / CH-301
Abstract.
P-Harmonic maps are natural generalizations of
linear transformations, analytic functions, solutions of (systems of
partial differential) Cauchy-Riemann equations, conformal mappings,
geodesics, minimal surfaces, harmonic maps (in which p=2) and
many more. In fact, p-harmonic geometry is a birthplace of many other
branches of mathematics. There are numerous relations among p-harmonic
maps, geometric flows, Lie groups and other areas of mathematics and
sciences. We will explore some of them. In particular, we wish to discuss
some recent progress in generalized 1-harmonic equations, p-harmonic
1-forms, the inverse mean curvature flows, Finsler
geometry, topology and algebra.
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Friday, September 19, 2008
Maxim Zinchenko.
California Institute of Technology.
"Szego-type Theorems in Spectral Theory of Finite Gap Jacobi Matrices"
2:00 pm / CH-301
Abstract.
In spectral theory for Jacobi matrices or approximation
theory for orthogonal polynomials, the goal is to relate information
about the recurrence coefficients (aka Jacobi parameters) to
information about the measure of orthogonality (aka spectral
measure). The most studied case is the case of Jacobi matrices with
the essential spectra consisting of a single interval on the real
line. An interesting question that we would like to address is what
happens when gaps occur in the essential spectrum? In particular, in
this talk we will discuss variants of Szeg\H{o}-type theorem and
Szeg\H{o}-type asymptotics for Jacobi matrices with essential spectra
given by finite unions of closed intervals. These results can be
viewed as perturbation results for Jacobi matrices with periodic and
almost periodic Jacobi parameters.
The talk is based on joint work with Jacob Christiansen and Barry
Simon. Our results rely on potential theory and analytic function
theory, with an important link to Riemann surfaces and Fuchsian
groups..
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Friday, September 26, 2008
Christian Remling.
University of Oklahoma.
"The absolutely continuous spectrum of Jacobi matrices "
2:00 pm / CH-301
Abstract.
We are interested in general properties of
Jacobi matrices (of Schr"odinger operators, if you prefer)
with some absolutely continuous spectrum. It turns out that
there are special building blocks with rather peculiar
properties that must be used to produce any kind of
absolutely continuous spectrum.
I'll discuss this result and some of its ramifications.
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Friday, October 10, 2008
W. D. Evans.
Cardiff University
"Representation of compact linear operators in Banach spaces and nonlinear eigenvalue problems"
2:00 pm / CH-301
Abstract.
Let X and Y be
Banach spaces with strictly convex duals, and let
T be a compact linear map from X to Y. I shall talk about recent work with
David Edmunds and Desmond Harris in which we show that a certain nonlinear
equation, involving T and its adjoint,, has a normalised solution (an "eigenvector")
corresponding to an "eigenvalue", and
that the same is true for each member of a countable family of similar
equations involving the restrictions of T to certain subspaces of X. The
action of T can be described in terms of these "eigenvectors",
the resulting expansion reducing to the familiar spectral representation of
the modulus of T when X and Y are Hilbert spaces. There are applications to
the p-Laplacian, the p-biharmonic
operator and integral operators of Hardy type.
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Friday, October 31, 2008
Vladimir Oliker.
Emory University
"The Aleksandrov problem and Monge-Kantorovich optimal transport of curvature
on S^n"
2:00 pm / CH-301
Abstract.
In this talk I will describe a variational
solution to a problem
of A.D. Aleksandrov concerning existence and
uniqueness of a closed convex
hypersurface in Euclidean space with prescribed
integral Gauss curvature.
Remarkably, in variational formulation this
problem turned out to be closely connected with the Monge-Kantorovich
theory of optimal mass transport on S^n.
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Friday, November 7, 2008
Dhruba Adhikari.
Mississippi University for Women
"Some Topological Degree Theories and Applications"
2:00 pm / CH-301
Abstract.
First, a brief introduction to the development of
various topo- logical degree theories and their generalizations will be
presented. Then as an application of the Browder and Skrypnik degrees, a
result concerning the existence of nonzero solutions of operator equations
of the form Tx + Cx = 0 in reexive Banach spaces will be given. Here, T and
C are certain operators of monotone type. Lastly, applications to
invariance of domain and eigenval- ues of recently developed degree theory,
which generalizes the Berkovits-Mustonen degree theory, will also be given.
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Friday, November 21, 2008
Peter Bates.
Michigan State University
"Some Mathematical Problems Arising in Materials Science"
2:00 pm / CH-301
Abstract.
Equations for a material that can exist stably in one of two homogeneous states are
derived from a microscopic or lattice viewpoint with the
assumption that the evolution follows a gradient flow of the free energy with respect to some metric.
Alternatively, Newtonian dynamics can be considered.
The resulting lattice dynamical systems are analyzed, as are equations on the continuum where the
lattice interaction energy is viewed as an approximation to a Riemann integral. These equations are
lattice or nonlocal versions of the Allen-Cahn, Cahn-Hilliard, Phase-Field, or Klein-Gordon equations.
Some results presented here provide for the well-posedness of the equations, while others give asymptotics
or quantitative behavior of special solutions, such as traveling waves or pulses.
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