UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

February 05, 2008

939 Evans Hall

12:15AM: The Shape of Minimal Free Resolutions I

David Eisenbud

I'll describe a group of conjectures on free resolutions by Mats Boij and Jonas Soederberg that Frank Schreyer and I recently proved. This talk will be introductory in character.

5:00PM: The geometric Weil representation with applications to radar and

Ronny Hadani

I will describe a special class of complex valued functions on the finite line f_p, which we call the \textit{oscillator class}. Functions in this class satisfy many interesting properties which make them ideal for applications in digital signal processing, including radar and communication. In my lecture, i will introduce the weil representation of the finite symplectic group sl_2(f_p), which will be used to define the oscillator class. I will proceed to describe an algebra-geometric counterpart (see: arxiv:math/0610818) of the weil representation, which will be used to prove a specific property of functions in this class. In the course, i will give a brief exposition to the theory of L-adic cohomology and to grothendieck's sheaf-to-function correspondence, a procedure which forms the bridge between the algebra-geometric and the function settings.

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