Rutgers University at Newark


Format: This is mostly a learning seminar, with occasional invited talks. 
Tuesday 25 January, 3:305:15pm 


Wednesday 2 February, 2:303:45pm 


Tuesday 15 February, 4:005:15pm 


Wednesday 23 February, 2:303:45pm 


Tuesday 1 March, 4:005:15pm 


Friday 18 March, 11:00am12:15pm 


Wednesday 30 March, 4:005:15pm 


Thursday 14 April, 4:005:15pm 


Wednesday 20 April, 2:303:45pm 


Thursday 28 April, 4:005:15pm 


Tuesday 17 May, 11:00am12:30pm 


Tuesday 17 May, 1:303:00pm 


Tuesday 24 May, 1:002:30pm 


Tuesday 14 September 


Tuesday 21 September 


Tuesday 28 September 


Tuesday 5 October 


Tuesday 12 October 


Tuesday 19 October 


Tuesday 26 October 


Tuesday 2 November 
Moment map and the associated root system, III.


Tuesday 9 November 


Tueday 16 November 


Tuesday 23 November  Moment map and the associated root system, V.  
Tuesday 30 November 


Tuesday 7 December 
Moment map and the associated root system, VII.


Wednesday 15 December  The geometric Satake isomorphism and the result of
GaitsgoryNadler. 
Back to the Department of Mathematics & Computer Science. 
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
LunaVust 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
LunaVust 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 KlingenSiegel,
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.