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Upcoming Seminars
MONDAY, February 25, 2008
GRADUATE STUDENT RESEARCH SEMINAR PSA 103 12:00 p.m.
Steven Spiriti, Department of Mathematics and Statistics
"Free-knot Splines, Penalties, and Optimization Algorithms for
Nonparametric Regression"
ABSTRACT: Free-knot splines are a well-known technique in
nonparametric regression. However, it can be difficult to find
the best positions of the knots. Three random-search algorithms
will be proposed to accomplish this task. In addition, a newer
technique, P-splines, will be investigated and compared to free-
knot splines.
Bagels and juice will be served in PSA 103 at 11:50 a.m.
TUESDAY, February 26, 2008
APPLIED ANALYSIS AND PDE READING SEMINAR PSA 546 3:00 p.m.
For more information, contact Svetlana Roudenko.
COLLOQUIUM (SCHOOL DIRECTOR CANDIDATE) PSF 101 3:00 p.m.
William Trotter, Georgia Institute of Technology
"Combinatorics: Mathematics That Starts Close to the Origin...
But Doesn't Stay There"
ABSTRACT: We discuss three challenging open problems in
combinatorial mathematics. Each is easily understood by an
undergraduate. However, two of the problems have a long
history, with a number of well-known researchers contributing
partial results. These two problems are respectively: (a) the
existence of order-respecting hamiltonian paths in the subset
lattice; and (b) the analysis of First Fit in coloring interval
graphs. The third problem is relatively new and asks whether
two natural classes of segment orders are distinct.
Refreshments will be served in PSA 206 at 2:30 p.m.
WEDNESDAY, February 27, 2008
NUMBER THEORY SEMINAR PSA 308 1:40 p.m.
Helene Nehrebecki, Department of Mathematics and Statistics
"Waring's problem"
ABSTRACT: Waring's problem states that every positive integer
is the sum of 9 cubes, 19 fourth powers, and so on. In this
talk, we will discuss results leading to the solution of
Waring's problem. Finally, we will explore recent advancements
in this area.
"VISION FOR NEW SCHOOL" PRESENTATION PSF 101 5:30 p.m.
William Trotter, Georgia Institute of Technology
Dr. William (Tom) Trotter, a candidate for director of the
new school, will address his vision for the new school our
department will become in an open session to a general audience
of faculty staff and students.
THURSDAY, February 28, 2008
COMPUTATIONAL AND APPLIED MATHEMATICS PROSEMINAR
PSA 206 12:15 p.m.
Weizhu Bao, National University of Singapore
"Mathematical Analysis and Numerical Simulation of
Bose-Einstein Condensation"
ABSTRACT: In this talk, I review the mathematical results of
the dynamics of Bose-Einstein condensate (BEC) and present some
efficient and stable numerical methods to compute ground states
and dynamics of BEC. As preparatory steps, we take the 3D Gross-
Pitaevskii equation (GPE) with an angular momentum rotation,
scale it to obtain a four-parameter model and show how to
reduce it to 2D GPE in certain limiting regimes.
Then we study numerically and asymptotically the ground
states, excited states and quantized vortex states as well as
their energy and chemical potential diagram in rotating BEC.
Some very interesting numerical results are observed. Finally,
we study numerically stability and interaction of quantized
vortices in rotating BEC. Some interesting interaction patterns
will be reported.
COLLOQUIUM (FYM DIRECTOR CANDIDATE) PSA 206 2:00 p.m.
Paul Abraham, Kent State University - Stark Campus
"How Scholarship in Mathematics Education, Teaching and
Mathematics Have (at times) Interacted For Me"
ABSTRACT: In this presentation I would like to describe some of
my scholarship in mathematics education, teaching, and
mathematics, and ways they have influenced each other. In
particular I would like to trace my current interests in large-
scale assessment to my earlier scholarly efforts in teaching,
in particular uses of programming as a teaching tool, and in
mathematics.
DISTINGUISHED LECTURE SERIES LSE 104 4:00 p.m.
Chris Byrnes, Washington University
"Vector Fields, Angular One-Forms and Periodic Orbits"
ABSTRACT: Periodic phenomena are pervasive in nature and in
engineered systems. They are exhibited, for example, in
idealized models of the solar system and in observed circadian
rhythms by which basic biological functions are believed to be
regulated. The GPS system has 27 satellites rotating about the
earth in precise stable orbits, each orbit being provided in an
almanac in every GPS receiver. As another class of examples,
electronic devices producing stable periodic signals underlie
the electrification of the world and wireless communications.
We will begin this talk with an historical review of classica
existence ciriteria for periodic orbits on a smooth surface,
with or without boundary. As an example, we will analyze a
stable oscillating circuit that is in widespread commercial use
today. In fact, every cell-phone has two, one used for
transmitting 0's and the other for transmitting 1's at stable
radio frequencies. In this example, the vector field has an
"angular" one-form, a concept with roots in earlier work of
G. D. Birkhoff. Roughly speaking, an angular one-form is a
closed nonsingular one-form which is a generalized form of
angular velocity analogous to the interpretation of a Lyapunov
function as a generalized form of energy.
Forty years ago Smale asked whether every nonvanishing smooth
vector field on the solid torus had a periodic orbit. In 1996,
G. and K. Kuperberg answered this in the negative. Nonetheless,
in this talk we present a series of positive results on the
existence of periodic orbits for any vector field X on
n-dimensional solid tori having an angular one-form. Moreover,
using the validity of the Poincare Conjecture in all dimensions
we prove a converse theorem in the spirit of Lyapunov theory:
If a vector field X on has an asymptotically stable periodic
orbit, then there exists a neighborhood M of the orbit which is
homeomorphic to a solid torus, on which X has an angular
one-form.
These are corollaries of a Main Theorem, which is valid for a
broad class of n-dimensional compact manifolds (with or without
boundary). In closing, we illustrate the Main Theorem in the
case of 3-dimensional manifolds, using Thurston's
Geometrization Program.
Refreshments will be served in PSA 206 at 3:15 p.m.
FRIDAY, February 29, 2008
DISTINGUISHED LECTURE SERIES EVENT PSA 206 1:30 p.m.
Chris Byrnes, Washington University
Distinguished lecturer Chris Byrnes will hold an informal
discussion with students.
Coffee, tea and snacks will be provided.
"VISION FOR FIRST YEAR MATHEMATICS" PRESENTATION
PSA 203 1:40 p.m.
Paul Abraham, Kent State University - Stark Campus
"Some Potential First Steps with First Year Mathematics at
Arizona State University"
ABSTRACT: In this presentation I would like to describe some
preliminary ideas for what my first steps as the first year
director of mathematics at ASU might be. I will also summarize
my experiences and accomplishments as coordinator of
mathematics at Kent State Stark, in particular relating
potential ideas for ASU to analogous efforts at Kent State.
Refreshments will be served in PSA 108 at 1:25 p.m.
C*-ALGEBRA SEMINAR PSA 307 2:40 p.m.
Kamran Reihani, Department of Mathematics and Statistics
"Spectral Triples for Trees"
(Joint work with Matilde Marcolli)
DISTINGUISHED LECTURE SERIES EVENT
SEMINAR PSA 206 2:40 p.m.
(Jointly sponsored by SenSIP and
Department of Mathematics and Statistics)
Chris Byrnes, Washington University
"Important Moments in Systems and Control"
ABSTRACT: In this talk we progress from a historical review of
the applications of mathematical methods in systems and control
to our recent work on the generalized moment problem using
methods from topology and nonlinear analysis. We discuss
applications to a class of moment problems arising in controls
and signal processing applications such as robust controls and
spectral estimation.
Coffee, tea and snacks will be provided.
MATH BIOLOGY SEMINAR ECG 237 3:40 p.m.
Ulrike Feudel, Institute for Chemistry and Biology
of the Marine Environment
Carl von Ossietyky University Oldenburg, Germany
"Spatio-Temporal Patterns in Simple Models of Marine Systems"
ABSTRACT: Spatio-temporal patterns in marine systems are a
result of the interaction of population dynamics with physical
transport processes. These physical transport processes can be
either diffusion processes in marine sediments or advection of
biological species in the water column. We study in a
simplified model the dynamics of one population of bacteria and
its nutrient in sediments, taking into account that the
considered bacteria possess an active as well as an inactive
state, where activation is processed by signal molecules.
Furthermore the nutrients are transported actively by
bioirrigation and passively by diffusion. It is shown that
under certain conditions Turing patterns can occur which yield
heterogeneous spatial patterns of species. The influence of
bioirrigation on Turing patterns leads to the emergence of "hot
spots", i.e. localized regions of enhanced bacterial activity.
In the water column advection is the dominant physical process.
We study the influence of mesoscale hydrodynamic structures on
biological growth processes in the wake of an island. Using a
stream function approach for the velocity field we show how the
upwelling of nutrients away from the island affects the
evolution of plankton close to it. In particular we show that
mesoscale vortices act as incubators for plankton growth
leading to localized plankton blooms within vortices.
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