Seminar Schedule
August 21 - 25, 2006
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.
MONDAY, August 21, 2006
Topology
2:30pm, Room 222
Organizational Meeting
Algebra
2:30pm, Room 410
Speaker: Jon Carlson, University of Georgia
Title of talk: "The poset of elementary abelian p-subgroups
of rank at least two."
Abstract: The poset of elementary abelian subgroups plays a
large role in the representation theory of a group. For one thing it determines
the rank of the group of endotrival modules. We show that if we restrict to
elementary abelian subgroups having rank at least 2, then the poset has at most
five connected components.
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Tea, Cookies
TUESDAY, August 22, 2006
VIGRE
Graduate Student Seminar
There will be 2 30-min. talks, introducing the VIGRE groups.
2:00pm, Room 302
Speaker: Dino Lorenzini, University of Georgia
Title of talk: Algebraic Graph Theory
2:30pm, Room 302
Speaker: Dan Nakano, University of Georgia
Title of talk: Lie Algebras
Analysis
3:30pm, Room 222
No Meeting this week
WEDNESDAY, August 23, 2006
Algebraic Geometry
2:30pm, Room 410
Speaker: G. Michael Guy, University of Georgia
Title of talk: Moduli of weighted stable maps and their
gravitational descendants
Abstract: We study the intersection theory on the moduli spaces
of maps of $n$-pointed curves $f:(C,s_1,... s_n)\to V$ which are stable with
respect to a weight data $(a_1,..., a_n)$, $0\le a_i\le 1$. After describing
the structure of these moduli spaces, we prove a formula describing the way
each descendant changes under a wall crossing. As a corollary, we compute the
weighted descendants in terms of the usual ones, i.e. for the weight data $(1,...,1)$,
and vice versa. (Based on a joint work with V. Alexeev.)
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Tea, Cookies
Arithmetic Geometry/Number Theory
3:30pm, Room 304
Speaker: Pete Clark, University of Georgia
Title of talk: Selections from the Arithmetic Geometry
of Shimura Curves, Part I
Abstract: The elliptic modular curves X_0(N) -- as well
as their modular coverings and quotients -- are of guaranteed importance in
modern number theory, by virtue of the fact that they parameterize all elliptic
curves over Q. They are also extremely interesting in their own right, as a
family of curves whose extra structure gives a foothold into their Diophantine
properties. We will review definition of the modular curves as (i) compact Riemann
surfaces, and (ii) coarse solutions to a moduli problem involving elliptic curves,
and explain how the latter leads -- at least when N is squarefree -- to a particularly
simple description of the minimal regular Z-model. This canonical integral model
plays a key role in so many places, e.g. in Mazur's spectacular classification
of rational points on X_1(N) and X_0(N) (which we will state but not, of course,
prove).
In particular, in studying the characteristic p fibers of X_0(N) it comes to pass that there is a finite locus of points which exerts an eerie control on the arithmetic of everything in sight: the supersingular locus. This locus can in turn be described in terms of ideal theory of a maximal order in the definite quaternion algebra of prime discriminant p; conversely, we will see how our knowledge of the intregral model allows us (following Igusa) to compute the "class number" of this maximal order.
In the second talk, we will begin by wondering what geometric object
THURSDAY, August 24, 2006
VIGRE
Graduate Student Seminar
There will be 2 30-min. talks, introducing the VIGRE groups.
2:00pm, Room 302
Speaker: Elham Izadi, University of Georgia
Title of talk: Algebraic Geometry
2:30pm, Room 302
Speaker: Malcolm Adams, University of Georgia
Title of talk: Applied Dynamical Systems
Wavelets and Splines
2:30pm, Room 524
No Meeting this week
FRIDAY, August 25, 2006
Probability Theory
2:30pm, Room 323
Speaker: Q. Zhang, University of Georgia
Title of talk: Control Theory: An introduction
Geometry
2:30pm, Room 326
Organizational Meeting
We will get organized with suggestions for internal talks and for outside speakers.
We encourage graduate students with an interest in the subject (even in their
first year!) to attend and to give talks. This year's seminar will have a reading
component, so bring suggestions for interesting papers.