Previous Special Year Seminar
Modular symbols and arithmetic
In these lectures, we will explore what insight can be gained
into the arithmetic of Galois representations in a given dimension
through the geometry of a higher-dimensional locally symmetric
space near a boundary component. The starting point for...
Working group on microlocal analysis and automorphic forms
10:00am|Physics Library, Bloomberg Hall 201
This will be an informal working group on aspects of microlocal
analysis that are relevant to automorphic forms. We will try to
study Archimedean zeta integrals (which are related to local
L-functions) using tools from the geometric theory of...
Transfer operators between relative trace formulas in rank one II
I will introduce a new paradigm for comparing relative trace
formulas, in order to prove instances of (relative) functoriality
and relations between periods of automorphic forms.More precisely,
for a spherical variety $X=H\backslash G$ of rank one...
Transfer operators between relative trace formulas in rank one
I will introduce a new paradigm for comparing relative trace
formulas, in order to prove instances of (relative) functoriality
and relations between periods of automorphic forms.More precisely,
for a spherical variety $X=H\backslash G$ of rank one...
Derived deformation rings for group representations
Søren Galatius
10:00am|Physics Library, Bloomberg Hall 201
It is well known that an irreducible representation of a group
$G$ over a field $k$ admits a universal deformation to a
representation over a complete Noetherian local ring, provided that
it is absolutely irreducible, i.e. remains irreducible after...
Motivic correlators and locally symmetric spaces IV
According to Langlands, pure motives are related to a certain
class of automorphic representations.Can one see mixed motives in
the automorphic set-up? For examples, can one see periods of mixed
motives in entirely automorphic terms? The goal of...
Automorphic forms and motivic cohomology III
In the lectures I will formulate a conjecture asserting that
there is a hidden action of certain motivic cohomology groups on
the cohomology of arithmetic groups. One can construct this action,
tensored with $\mathbb C$, using differential forms...
Automorphic forms and motivic cohomology II
In the lectures I will formulate a conjecture asserting that
there is a hidden action of certain motivic cohomology groups on
the cohomology of arithmetic groups. One can construct this action,
tensored with $\mathbb C$, using differential forms...
Automorphic forms and motivic cohomology I
In the lectures I will formulate a conjecture asserting that
there is a hidden action of certain motivic cohomology groups on
the cohomology of arithmetic groups. One can construct this action,
tensored with $\mathbb C$, using differential forms...
A remark on cohomology of locally symmetric spaces
Let $H = G/K$ be a symmetric space and $X = \Gamma \backslash H$
its locally symmetric quotient. An important problem is to
understand the cohomology of the space $X$ (or, more or less
equivalent, cohomology of the group $\Gamma$). The idea is
that...