Metroplex Algebraic Geometry, Algebra and
Number Theory (AGANT) Seminar,
a joint venture of
UNT,
UTA and
TCU
Date/Time/Room:
Friday (4/17/2009) at 4:00 pm in 304 Pickard Hall
Speaker:
Dr.
Martin Malandro, Assistant Professor,
Department of Mathematics &
Statistics, Sam Houston State
University.
"Fast Fourier Transforms for Inverse
Semigroups"
Abstract:
The classical fast discrete Fourier transform has found a wealth of
applications ranging from seismic analysis to the fast multiplication of
large numbers. There is a general theory of Fourier transforms for finite
groups, in which the Fourier transform on the cyclic group of order n is
the classical Fourier transform. In this talk we will generalize the notion
of the Fourier transform to finite inverse semigroups (which are group-like
objects that capture local symmetries) and provide a general framework for
constructing fast Fourier transforms on these objects. We will also discuss
fast Fourier transforms for specific inverse semigroups of interest and potential
applications. We will proceed from a representation-theoretic point of view
and emphasize the algebra involved in the construction of these algorithms.
This talk should be accessible to graduate students with an interest in algebra
(I will begin by defining the classical discrete Fourier transform, inverse
semigroups, representations, etc.)
A map of UTA may be found at
http://www.uta.edu/maps/,
and directions to UTA are on that website.
Note that PKH is the triangular building in the central-campus region of
the map. Select Pickard Hall from the building selector. PKH is next to
the ``garage'' & is on Nedderman Dr between Planatarium Place (aka College
St) & West St. West St is one-way northbound between W Mitchell St and
3rd St. Parking is available in the nearby (East and SE of PKH) parking lots
with a UTA permit (but many people park there late on Fridays with no permit
and are not caught). There are a few metered parking spots on the East side
of Pickard Hall on West St. Visitor (free), & metered, parking is available
by Davis Hall (marked DH in SW part of the submap). A parking garage
(expensive) is nextdoor to PKH (use West St to get to it). Note that if
heading south on Cooper, then no left turn is allowed to Nedderman Dr.
Note that PKH 304 is on the 3rd floor of PKH; turn right out of elevator
on 3rd floor.
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