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Upcoming Seminars
MONDAY, March 24, 2008
GRADUATE STUDENT RESEARCH SEMINAR PSA 103 12:00 p.m.
Jacob Shotwell, Department of Mathematics and Statistics
"Higher-Rank Graph C*-Algebras"
ABSTRACT: Directed graph algebras and their higher-dimension
generalizations have been studied extensively in recent years.
They have been a highly useful tool in the study of C*-algebras.
Many deep properties of a graph algebra can be characterized in
terms of relatively simple graph-theoretic properties. This
makes for a rich source of user-friendly constructions of some
slightly abstruse topics from the theory of C*-algebras, such as
crossed products or the K-theory of a C*-algebra.
In this talk, we will define k-graphs and associate a
C*-algebra to each k-graph. Many of the problems in this field
are graph-theoretic in nature. We will survey these graph-
theoretic questions and see how they have interesting
implications for the associated C*-algebra.
Bagels and juice will be served in PSA 103 at 11:50 a.m.
COLLOQUIUM (SCHOOL DIRECTOR CANDIDATE) PSA 206 3:00 p.m.
Krishnaswami Alladi, University of Florida
"New Perspectives in the Theory of Partitions and Q-Series"
ABSTRACT: The theory of partitions and q-series was founded by
Euler in the mid-eighteenth century and underwent a glorious
transformation under the magic touch of the Indian genius
Srinivasa Ramanujan. The subject is now at the cross-roads of
number theory, combinatorics, analysis, and the theory of
modular forms and has connections with Lie algebras, computer
science and physics. After briefly tracing some of the landmark
results in the subject, I will describe some new perspectives
in the study of Rogers-Ramanujan (R-R) type identities, namely
q-hypergeometric identities that connect partitions defined by
difference conditions with partitions defined by congruence
conditions. I will show how the combinatorics of words leads to
significant generalizations and refinements of certain R-R type
partition theorems, yielding new weighted partition identities,
new infinite and finite q-hypergeometric identities, as well as
insights into the structure of classical results like the
Jacobi triple product identity for theta functions. The talk
will be accessible to non-experts.
Refreshments will be served in PSA 206 at 2:40 p.m.
TUESDAY, March 25, 2008
MATHEMATICS AND COGNITION SEMINAR PSA 206 12:15 p.m.
Bruce Rogers, Department of Mathematics and Statistics
"Consensus and Contention: Elections and Social Decisions"
ABSTRACT: How well does the outcome of an election reflect the
actual wishes of a society? We'll outline the some basic
results in the theory of social choice--the theorems of Arrow,
Sen and Gibbard-Satterwait. The most famous result, Arrow's
Theorem, states there is no "fair" way to decide an election
with 3 or more candidates. But is the notion of fairness as
formalized in the theorems applicable to real elections and
everyday decisions? We will outline a proof of Arrow's theorem
and then discuss wider applications of social choice theorems.
That is, do Arrow-like results come into play every time we
make decisions?
Cookies and coffee will be served at 12:00 p.m.
SCHOOL VISION PRESENTATION PSA 206 1:40 p.m.
Krishnaswami Alladi, University of Florida
APPLIED ANALYSIS AND PDE READING SEMINAR PSA 546 3:00 p.m.
For more information, contact Svetlana Roudenko.
WEDNESDAY, March 26, 2008
COLLOQUIUM (FACULTY CANDIDATE) PSA 206 11:00 a.m.
Carla van de Sande, University of Pittsburgh
"Online Tutoring in the Calculus:
Looking at What's in Front of Us"
ABSTRACT: Free, open (to the public), online homework forums
allow students to voice ideas, receive help on assignments, and
get answers to questions in mathematics, especially in the
calculus. These national and international forums, staffed by
volunteer tutors who have the time, ability, and interest to
help others, routinely get thousands of visitors each day. The
forums provide a rich source of authentic mathematical
conversations, insight into common student difficulties, and
examples of vibrant online learning communities. To date,
little research has been conducted on the nature, quality, and
value of these sites. I will present a series of investigations
of tutoring exchanges in calculus forums looking at student
problem-solving activity, the complexity and quality of
mathematical and pedagogical content, and the ways in which
participating tutors interact as a virtual community. I will
conclude with a discussion of how this research can be applied
to improving calculus instruction and learning.
Refreshments will be served in PSA 206 at 10:45 a.m.
NUMBER THEORY SEMINAR PSA 308 1:40 p.m.
Daniel Corral, Department of Mathematics and Statistics
"A Connected Topology for the Integers"
ABSTRACT: We discuss a paper of Solomon W. Golomb, where
arithmetic progressions are used to define a basis of open
sets, yielding a topology on Z. We show how this topology can
be used to prove the infinitude of primes.
COMPUTATIONAL AND APPLIED MATHEMATICS PROSEMINAR
GWC 487 2:00 p.m.
Russ Park, Department of Mathematics and Statistics
"Optimal Compression and Numerical Stability of Gegenbauer
Reconstructions"
ABSTRACT: Image reconstruction methods are characterized by the
source data space on which they operate, the range space and
the degree to which objectives such as artifact suppression,
compression and numerical stability are optimized. The
Gegenbauer reconstruction method operates on Fourier source
data, projecting it onto a finite set of Gegenbauer polynomials.
Gegenbauer data is then expanded on sub-domains of physical
space segmented by presumed jump discontinuities in the source
data. The absence of jump discontinuities within each sub-
domain assures spectral convergence as long as reconstruction
parameters lambda and m linearly track the resolution N as it
approaches infinity. The implicit benefit of Gegenbauer
reconstruction is source data compression, unfortunately the
process is also limited by numerical instability as either
lambda or m, or both, increase.
Early studies on this issue assumed lambda and m to be
linearly tied to N and then characterized the bounds of
instability as well as recommended safe reconstruction
parameter combinations. Subsequent work demonstrated how to
automatically predict the source data smoothness parameters,
of which apriori knowledge is required for accurate
reconstruction. This study performs asymptotic analyses on the
predicted error bounds as N goes to infinity while fixing
either m or lambda, leading to the discovery of reconstruction
parameters optimized for an objective of either compression or
numerical stability. Finally, the effectiveness of this new
approach is illustrated by extensive numerical experiments.
THURSDAY, March 27, 2008
COMPUTATIONAL AND APPLIED MATHEMATICS PROSEMINAR
PSA 206 12:15 p.m.
Alexandra Smirnova, Georgia State University
"Iteratively Regularized Gauss-Newton Method with Parameter
Decomposition for 2D Inverse Problem in Optical Tomography"
ABSTRACT: A new convergence result for an Iteratively
Regularized Gauss Newton (IRGN) algorithm with a Tikhonov
regularization term using a seminorm generated by a linear
operator is established [SRK07]. The convergence theorem uses
an a posteriori stopping rule and a modified source condition,
without any restriction on the nonlinearity of the operator.
The theoretical results are illustrated by simulations for a
2D version of the exponentially ill-posed optical tomography
inverse problem for the diffusion and absorption coefficient
spatial distributions. The modified Tikhonov regularization
performs the mapping of the minimization variables, which are
the coefficients of the spline expansions for the diffusion and
absorption, to physical space. This incorporates the inherently
differing scales of these variables in the minimization, and
also suggests relative weighting of the regularization terms
with respect to each parameter space. The presented
modification of the IRGN allows greater flexibility for
implementations of IRGN solutions of ill-posed inverse problems
in which differing scales in physical space hinder standard
IRGN inversions.
FRIDAY, March 28, 2008
MATH BIOLOGY SEMINAR ECG 237 3:40 p.m.
Yi Li, University of Iowa
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