UIUC Dept. of Mathematics Seminar Calendar

    September 2009          October 2009          November 2009    
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Friday, October 23, 2009

Women in Mathematics Seminar
1:00 pm in 141 Altgeld Hall, Friday, October 23, 2009

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Submitted by akwiatk2.

Inmi Kim (UIUC Math)
Constructions of Gabor dual windows
Abstract: I'll give you a brief explanation about the Short Time Fourier Transform and some related theorems. Then we'll see the window conditions for being dual windows in Gabor system. If we have some restrictions on our windows, we can get very simplified window condition which is used for my Gabor dual windows constructions in 1-dimension. Also, if time is okay, I'll give you further topics such as higher dimensional constructions and directionally sensitive Gabor elements.

Algebra, Geometry and Combinatorics Seminar
3:00 pm in 445 Altgeld Hall, Friday, October 23, 2009

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Submitted by llpku.

Mahir Bilen Can (Tulane University)
Cross section lattices
Abstract: The cross section lattice of an algebraic monoid (Zariski closure of an algebraic group) is defined and investigated by Mohan Putcha in 80's. It is a finite lattice of idempotents parametrizing the two sided orbits of the group of invertible elements acting on the monoid.
In this talk after reviewing some of the background we are going to look into the combinatorial properties of the cross section lattices. In particular we are going to determine which cross section lattices are supersolvable, and we are going to study their quasi-symmetric functions.
In a recent paper Lex Renner shows that if the algebraic monoid comes from an irreducible representation of a semisimple group then the minimal element of the cross section lattice provides information about the singularity of the associated affine toric variety (Zariski closure of a maximal torus in the monoid). If time permits, we are going to talk about our conjecture on the shape of a cross section lattice when the toric variety is rationally smooth. (No prior knowledge of algebraic monoids is required.)