University of Georgia
Department of Mathematics

Seminar Schedule
August 18 - August 22, 2003

All Seminars are held in BOYD Graduate Studies Bldg. unless otherwise noted.

MONDAY, August 18, 2003

VIGRE Algebra Seminar
2:30-3:30pm, Room 410
Speaker: Daniel Nakano, University of Georgia
Title of talk: Nilpotent matrices (aka Everything you wanted to know about Jordan Canonical Forms, but were afraid to ask)
Abstract: In this introductory talk I will present the basic background material concerning the orbit theory for the general linear group. The orbit theory has a deep and rich structure with connections to both cohomology and representation theory. The main goal of this VIGRE seminar will be to study the structures of certain varieties of nilpotent matrices called restricted nullcones. There are many open questions about the structures of these varieties. It is hoped that progress by the VIGRE group can be made in determining these varieties when the prime of the underlying field has small characteristic.

Faculty and Graduate Social
3:00pm, Room 409
Coffee, Cookies, Tea

Fall Introductory Faculty Meeting
3:30p.m., Room 328
This will be a meeting of Faculty and graduate students and will serve as the Fall introductory faculty meeting.

TUESDAY, August 19, 2003

VIGRE
2:00-3:15pm, Room 304
Speaker: Mukel Patel, University of Georgia
Title of talk: The Conceptual Structure of Mathematics
Abstract: An extremely brief introduction to large scale structure of mathematics as a unified organic ever evolving entity. Furthermore, the *need* to consider such a viewpoint, its ramifications in the education of future mathematicians, and on the *integration* of research in mathematics education---vertical, horizontal, and other uncountably many directions. And of course, the intended audiance includes both accomplished working mathematicians, as well as those aspiring to become one. I will hand out a sort of semi-outline of a book I would like to write on this theme, and which has the same title as this talk.

WEDNESDAY, August 20, 2003

Faculty and Graduate Social
3:00pm, Room 409
Coffee, Cookies, Tea

Group Representation & Cohomology
2:30p.m., Room 410
Speaker: Dave Benson, University of Georgia
Title of talk: Stable categories and derived categories
Abstract: This seminar will be an introduction to the stable category and the derived category of modules over the group algebra of a finite group (or more generally of a finite dimensional Frobenius algebra), and the relationships between them. It will be a mixture of introductory material and some very recent progress, so there should be something for everyone.

Algebraic Geometry
2:30pm, Room 303
Organizational Meeting: All students interested in algebraic geometry are encouraged to attend the organizational meeting (the first 15 min).
Speaker: Valery Alexeev, University of Georgia
Title: "Mirror symmetry for toric varieties, flag varieties and reductive varieties"
Abstract: Mirror symmetry conjecture, invented by physicists working on the "theory of everything", states that families of Calabi-Yau manifolds (giving the missing 6 dimensions of our 10-dimensional space) come in mirror-dual pairs whose properties are oddly interchanged. After reviewing a classical (mathematical) construction of Batyrev for mirror symmetry of CYs in toric varieties and a more recent construction of Batyrev-Ciocan-Fontanine-Kim-van Straten for flag manifolds, I will
discuss a generalization to the case of reductive varieties (joint with Brion).

Number Theory
3:30pm, Room 304
Speaker: Matt Baker, University of Georgia
Title of talk: Adeles and Ideles
Abstract: After a 15-minute organizational discussion, in which we map out a plan for this semester's Number Theory Seminar, I will give a brief introduction to adeles and ideles, and state some important elementary facts about them. An excellent online reference for details which will inevitably be left out of the talk is Tom Weston's expository paper "The Idelic Approach to Number Theory", which can be found at http://www.math.amherst.edu/~taweston/

FRIDAY, August 22, 2003

Geometry
2:30p.m., Room 322
Organizational Meeting