Seminar Schedule
October 4 - 8, 2004

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

MONDAY, October 4, 2004

Algebra
2:30-3:30p.m., Room 410
Speaker: Jon Kujawa, University of Georgia
Title: Representation Theory of the Symmetric Group, II
Abstract: This is the second in a series of talks in the VIGRE algebra seminar.

Probability Theory
2:45-4:00pm, Room 302
Speaker: M. Pemy, University of Georgia
Title of talk: Numerical Methods for European Options

Faculty and Graduate Social
3:00 p.m., Room 409
Coffee, Cookies, Tea

VIGRE Algebraic Geometry Group
3:30-4:30 p.m., Room 304

Topology
3:30-4:30pm, Room 326
Speaker: TBA
Title of talk: TBA

Lie Theory
3:30p.m., Room 303
No Meeting this week

TUESDAY, October 5, 2004

VIGRE Graduate Student Seminar
2:00p.m., Room 304
Speaker: G. Michael Guy, University of Georgia
Title of talk: Eliminating Envy
Abstract: What do the following situations have in common: Pirates returning from a night of raiding townsfolk, Victorious countries following a war of conquest, Your 5th birthday party? Give up? In each situation there are things which must be divided amongst a group of "deserving" parties. Who gets what? The process by which this is decided is often called "Cake Division". We will discuss several aspects of "Cake Division" and explain why naive solutions create a (possibly dangerous) situation of envy. We will discuss complete solutions to this problem which avoid envy for the case when there are only 2 or 3 "deserving" parties and indicate the complexity which arises when we consider more than 3.

This will be a very elementary talk which I hope everyone will find as interesting as I do. Feel free to invite undergrads and bring your friends and anyone else you find loitering in the halls.

Dynamics on Berkovich Space
3:30-5:30p.m., Room 326
No Meeting this week

WEDNESDAY, October 6, 2004

Algebraic Geometry
2:30-3:45 p.m., Room 410
Speaker: Valery Alexeev, University of Georgia
Title of talk: "The ubiquity of Coxeter-Dynkin graphs"
Abstract: In 1934, Patrick Du Val discovered that 1) there is a class of surface
singularities which is in bijection with reflection groups (and root systems) of types A-D-E; 2)
the possible configurations of degenerate surfaces "of del Pezzo series" X_d, d=1,2...8 are in
bijection with reflection subgroups of the root systems E_8,E_7...A_1, with four exceptions.
The proof was by comparing two long lists, one of which was obtained by Coxeter, also in 1934.

I will introduce A-D-E root systems, Coxeter's reflection groups, Du Val singularities, del Pezzo
surfaces, Kodaira's elliptic fibers, and connections between these apriori very different theories. Time
permitting, I will give a complete classification of a class of singular del Pezzo surfaces which is strictly
larger than Du Val's case. That will include an "ideological" proof of Du Val's discovery, without
comparing two long lists.

The talk is aimed at 1st year graduate students and above.

VIGRE – Cardiac Physiology
2:30p.m., Room 323

VIGRE – Clifford Algebras
2:30p.m., Room 322

Faculty and Graduate Social
3:00 p.m., Room 409
Coffee, Cookies, Tea

Number Theory
3:45-5:15pm, Room 304
Speaker: Su-ion Ih, University of Georgia
Title of talk: The arithmetic of varieties I.

THURSDAY, October 7, 2004

VIGRE - Rational points on curves
2:00p.m., Room 304

FRIDAY, October 8, 2004

Student Arithmetic/Algebraic Geometry Seminar
12:00p.m. - Room 410
Speaker: Zubeyir Cinkir, University of Georgia
Title of talk: Tate Curve, Part III
Abstract: This is the 3rd of the series of the talks on "uniformization theorems of
elliptic curves over a complete field k". The 1st talk was about motivations and
background knowledge when the field k is R or C. The 2nd talk was about
k^(*)/t^(Z) being isomorhic to E_t(k) whenever k is nonarchimedean and
with a condition on the j-invariant of E_t. In this talk, we will discuss some
applications of this result and talk about further directions exploiting
these ideas.

VIGRE-Algebra
2:30p.m., Room 410
Speaker: TBA
Title of talk: TBA

Spline Analysis
2:30-3:30p.m., Room 303
Speaker: Taytana Sorokina, University of Georgia
Title of talk: Trivariate Spline Macro-Elements, continued

Geometry
2:30 p.m., Room 326
Speaker: John McCuan, Georgia Tech/U. of Georgia
Title of talk: Geometric expansion of curves and surfaces, part II

Wavelet Analysis
3:30-4:30 p.m., Room 303
No meeting this week