UTA Department of Mathematics

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.