Abstract: The goal of this talk will be to explain what are algebraic stacks and why they naturally appear.
If time permits, we will start discussing our main example of moduli spaces of vector bundles on a smooth projective curve.
Key words: groupoids, Grothendieck topologies, etale and smooth morphisms of schemes, algebraic stacks.
Title: Local (L-, \epsilon- and \gamma-) factors, and converse theorems.
Abstract: Our first goal will be to define local (L-,\epsilon- and \gamma-) factors and to study their properties. These factors are needed to formulate the local Langlands correspondence for GL(n), which was outlined two weeks ago. We will do it first for supercuspidal representations of GL(n) and then for local Galois representations, that is, for representations of Gal(\bar{F}/F), where F is a local field.
Probabilistic limit theorems for (distance expanding and hyperbolic) dynamical systems is a well studied
topic. In this talk I will present conditions guaranteeing that a local central limit theorem holds true for certain families of distance
expanding random dynamical systems. If time permits, I will also discuss a version of the Berry-Esseen theorem.
Joint work with Yuri Kifer.
Randomisations, coheir sequences and NSOP1
[Joint with A Chernikov and N Ramsey]
Recall that if T is a theory, then its Keisler randomisation, T^R, is the theory of spaces of random variables which take values in a model of T .
It was show some time ago that if T has IP (e.g., simple unstable), then T^R has TP2, and in particular not simple.
In Eilat I announced the following result [with Chernikov and Ramsey] :
A. If T is NSOP1, then its randomisation T^R is NSOP1
Speaker: Zlil Sela Title: Basic conjectures and preliminary results in non-commutative algebraic geometry
Abstract: Algebraic geometry studies the structure of varieties over fields and commutative rings. Starting in the 1960's ring theorists (Cohn, Bergman and others) have tried to study the structure of varieties over some non-commutative rings (notably free associative algebras).
The lack of unique factorization that they tackled and studied in detail, and the pathologies that they were aware of, prevented any attempt
Speaker: Zlil Sela Title: Basic conjectures and preliminary results in non-commutative algebraic geometry
Abstract: Algebraic geometry studies the structure of varieties over fields and commutative rings. Starting in the 1960's ring theorists (Cohn, Bergman and others) have tried to study the structure of varieties over some non-commutative rings (notably free associative algebras).
The lack of unique factorization that they tackled and studied in detail,
Title: The polynomial method in combinaotrics
(I) Let q be a prime and n an integer. How small can a subset of the vector space (F_q)^n be if it contains a line in every direction?
(II) Let n be a large integer. How large can a subset of (F_3)^n be if it contains no solution to the equation x+y+z=0?
Several important problems in extermal combinaotrics were solved in recent years by introducing polynomials into the problem in a clever way. In many cases, this approach produces incredibly simple and elegant proofs that rely on no more than standard linear algebra.
