Rutgers University at Newark
Algebra & Number Theory Seminar
Academic year 2010-2011

The seminar is meeting in Smith Hall, Room 204 (mathematics seminar room).
The seminar is organized by Zhengyu Mao and Yiannis Sakellaridis.

Format: This is mostly a learning seminar, with occasional invited talks.

Click on the name of the speaker or scroll down for the abstract (if available).

Spring Semester

Tuesday 25 January, 3:30-5:15pm
Geometric Satake isomorphism and the result of Gaitsgory-Nadler.
Jonathan Sparling
Wednesday 2 February, 2:30-3:45pm
Cancelled
 
Tuesday 15 February, 4:00-5:15pm
Geometric Satake isomorphism and the result of Gaitsgory-Nadler.
Jonathan Sparling
Wednesday 23 February, 2:30-3:45pm
Special values of zeta functions associated to number fields and the geometry of cusp divisors on related modular varieties.
Robert Sczech
Tuesday 1 March, 4:00-5:15pm
Special values of zeta functions associated to number fields and the geometry of cusp divisors on related modular varieties.
Robert Sczech
Friday 18 March, 11:00am-12:15pm
Special values of zeta functions associated to number fields and the geometry of cusp divisors on related modular varieties.
Robert Sczech
Wednesday 30 March, 4:00-5:15pm
Geometric Satake isomorphism and the result of Gaitsgory-Nadler.
Jonathan Sparling
Thursday 14 April, 4:00-5:15pm
The Local Langlands Conjecture.
Cesar Valverde
Wednesday 20 April, 2:30-3:45pm
The Local Langlands Conjecture.
Cesar Valverde
Thursday 28 April, 4:00-5:15pm
The Local Langlands Conjecture.
Cesar Valverde
Tuesday 17 May, 11:00am-12:30pm
The Local Langlands Conjecture.
Cesar Valverde
Tuesday 17 May, 1:30-3:00pm
Restriction problems in the representation theory of classical groups (after Gan, Gross, Prasad).
Yiannis Sakellaridis
Tuesday 24 May, 1:00-2:30pm
Restriction problems in the representation theory of classical groups (after Gan, Gross, Prasad).
Yiannis Sakellaridis

Fall Semester

Tuesday 14 September
Overview of spherical varieties.
Yiannis Sakellaridis
Tuesday 21 September
Invariants and compactifications of spherical varieties, I.
Cesar Valverde
Tuesday 28 September
Invariants and compactifications of spherical varieties, II.
Zhengyu Mao
Tuesday 5 October
Invariants and compactifications of spherical varieties, III.
Tuesday 12 October
Moment map and the associated root system, I.
Bart Van Steirteghem
Tuesday 19 October
  Moment map and the associated root system, II.
Bart Van Steirteghem
Tuesday 26 October
Cancelled.
 
Tuesday 2 November
Moment map and the associated root system, III.
Bart Van Steirteghem
Tuesday 9 November
Moment map and the associated root system, IV.
Yiannis Sakellaridis
Tueday 16 November
Cancelled.

Tuesday 23 November Moment map and the associated root system, V.
Bart - Yiannis
Tuesday 30 November
Moment map and the associated root system, VI.
Yiannis Sakellaridis  
Tuesday 7 December
Moment map and the associated root system, VII.
Wednesday 15 December
The geometric Satake isomorphism and the result of Gaitsgory-Nadler. 
Jonathan Sparling

Back to the Department of Mathematics & Computer Science.

Abstracts

Sept. 14
Title: Overview of spherical varieties.
Speaker: Yiannis Sakellaridis
Abstract: I will give an overview of selected topics in the theory of spherical varieties, including their compactification theory and the root system associated to them. I will mention basic references, propose a schedule of talks and we will decide on the distribution of talks.

Sept. 21
Title: Invariants and compactifications of spherical varieties, I.
Speaker: Cesar Valverde
Abstract: An overview of actions of groups on algebraic varieties, their invariants, and a discussion of highest weight modules in the coordinate rings of G and of U\G. Basic reference:  M, Brion: Introduction to actions of algebraic groups.

Sept. 28
Title: Invariants and compactifications of spherical varieties, II.
Speaker: Zhengyu Mao
Abstract: The basic invariants of spherical varieties (cone of invariant valuations, colors, ...) and the classification of spherical embeddings in terms of these invariants. Basic reference:  F. Knop: The Luna-Vust theory of spherical embeddings.

Oct. 5
Title: Invariants and compactifications of spherical varieties, III.
Speakers: Zhengyu Mao and Yiannis Sakellaridis
Abstract: Continuation of the theory of spherical embeddings. Various examples. Basic reference:  F. Knop: The Luna-Vust theory of spherical embeddings.

Oct. 12, 19 and Nov. 2
Title: Moment map and the associated root system, I, II, III.
Speakers: Bart van Steirteghem
Abstract: We'll begin by reviewing the basics of finite reflection groups and their relationship to root systems. Following Knop's "Some Remarks on Multiplicity Free Spaces" (1998) we'll show how one can associate a finite reflection group to a spherical module.

Feb. 2 and 23
Title: Special values of zeta functions associated to number fields and the geometry of cusp divisors on related modular varieties.
Speakers: Robert Sczech
Abstract: According to a classical result of Klingen-Siegel, the special values of partial zeta functions associated to ideal classes in number fields (at integral values of the complex variables) are all rational numbers. In fact, these numbers are always zero except for the case where the underlying number field is a totally real extension of the rational number field. In my talk I will explain how to calculate these rational numbers. It turns out that the problem of calculating these rational numbers is essentially equivalent to the problem of constructing cusp divisors on a smooth compactification of Hilbert modular varieties. Roughly speaking, one can say that the special values in question are in essence selfintersection numbers of the associated cusp divisors. The talk will be elementary and therefore accessible to interested graduate students.