Seminar Schedule
April 24-28, 2006
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.
MONDAY April 24, 2006
Geometry-Topology Seminar
2:30pm, Room 222
No meeting this week
Algebra
2:30pm, Room 410
Speaker: Nadia Mazza, University of Georgia
Title: Endotrivial modules for symmetric and alternating
groups
Abstract: Endotrivial modules are known to play an important
role in the modular representation theory of finite groups. Three years ago,
we (i.e. Jon Carlson, Nadia Mazza and Daniel Nakano) started a project to classify
the endotrival modules over families of finite simple groups and related groups.
In this talk, we will give an account of the endotrivial modules and report
on the status of our advances in the classification in the case of the symmetric
and alternating groups.
Faculty and Graduate Student Social
3:00pm, Room 409
Coffee, Cookies, Tea
VIGRE-Algebraic Geometry
3:30pm, Room 304
TUESDAY, April 25, 2006
VIGRE-Graduate
Student Seminar
2:00p.m., Room 304
Speaker: Adrian Jenkins, Purdue University
Title of talk: Local classification problems in complex
analysis
Abstract: We will look at germs of holomorphic functions $f$
which fix the origin (and in fact, most of our interest will be in those functions
so that $f'(0)=1$), and consider the question of local classification under
certain changes of variable. The goal here will be to understand the local dynamics
of such functions by relating them to certain "good" model functions
(e.g. linear functions, Mobius transforms, and in general, functions which are
easy to iterate). This talk will serve as an introduction to the analysis seminar
to be given later in the day. All definitions will be given, and the talk should
be of an introductory nature (really, the only prerequisite is a good first
course in complex analysis).
WEDNESDAY, April 26, 2006
Geometry in the Curriculum Seminar
1:25pm, Aderhold, Room 111
Speaker: Tom Banchoff, University of Georgia
Title of talk: Seminar wrap-up and plans for the future
Algebraic Geometry
2:30pm, Room 410
Speaker: Gavril Farkas (University of Texas, Austin)
Title of talk: Effective divisors on moduli spaces.
Abstract: One of the fundamental invariants of any variety
is its cone of effective divisors. In the case of the moduli space of curves
the shape of the cone was predicted by the Slope Conjecture of Harris and Morrison
which singled out the classical Brill-Noether divisors as being extremal. I
will present a general method of constructing "exceptional" divisors
on a large class of moduli spaces using the syzygies of the parametrized objects.
This construction provides among other things a doubly infinite sequence of
counterexamples to the Slope Conjecture and shows that the moduli space of Prym
varieties of dimension g is of general type for g>12.
Analysis
2:30pm, Room 302
Speaker: Adrian Jenkins (Perdue)
Title of talk: Smooth Conjugacies of Holomorphic Germs
in {\mathbf{C}}
Abstract: We consider holomrphic functions $f$, defined in
a small neighborhood of the origin, of the form $f(z)=z+az^{2}+\cdots $, where
$a$ is not zero. Such functions are always locally conjugated via a homeomorphism
to the time-one map $f_{0}$ of the vector field $V(z)=z^{2}$. However, if one
requires that the homeomorphism $H$ be
$C^{1}$ in a neighborhood of the origin, then immediately, one can show that
in
fact $H$ is necessarily holomorphic or antiholomorphic, and thus such a classification
is very restrictive.
VIGRE- Algebra
2:30pm, Room 303
Speaker: Brian Boe, University of Georgia
Title of talk: Existence of extra cohomology in degree
p+r
Faculty and Graduate Student Social
3:00pm, Room 409
Coffee, Cookies, Tea
Arithmetic Geometry/Number Theory
3:30pm, Room 304
Speaker: Steve Winburn, University of Georgia
Title of talk: Newman's short proof of the prime number
theorem
THURSDAY, April 27, 2006
VIGRE – Feynman Diagrams
2:00pm, Room 326
VIGRE – Cardiac Physiology
2:00pm, Room 640
VIGRE- Zeta Functions
2:15pm, Room 303
VIGRE-Algebraic Geometry
2:00pm, Room 304
Faculty and Graduate Social
3:00pm. Room 409
Coffee, Tea, Cookies
Colloquium
3:30pm, Room 304
Speaker: Gavril Farkas (University of Texas, Austin)
Title of talk: The global geometry of the moduli space
of curves.
Abstract: The moduli space of curves M_g is the universal parameter
space for Riemann surfaces of given genus. Its study has been initiated by Riemann
in 1857 and it has been a long-standing problem to describe the nature of the
moduli space as an algebraic variety. I will survey the history of the problem
starting with Severi's conjecture from 1915 predicting that M_g is always unirational,
continuing with the work of Harris and Mumford spectacularly disproving Severi's
conjecture and finally discussing a recent result which settles this problem
in one of the most interesting remaining cases, that of genus 22.