Future seminars

February 24th   – February 28th, 2013

 

Colloquium

 

Time and Place: Thursday, February 28th, 14:30-15:30, Mathematics Building, Lecture Hall 2

Speaker:  Antoine Ducros (Paris 6)

Title:  Geometry over p-adic fields: Berkovich's approach

 

Abstract:

p-adic fields have been introduced by number theorists for arithmetic purposes. Such a field is complete with respect to an absolute value with some strange behaviour: for example, every closed ball with positive radius is open, and every point of such a ball is a center. Because of those properties, to develop a relevant geometric theory over p-adic fields is non-trivial: one can not naively mimic what is done in real or complex geometry, and one has to use a more subtle approach.

In this talk we will present that of Berkovich. His main idea is to 'add a lot of points to naive p-adic spaces' in order to get good topological properties, like local compactness or local path-connectedness. After having given the basic definitions, we will focus on some significant examples, especially the Berkovich projective line (which is a real tree) and more generally the Berkovich curves; I will explain how the homotopy type of such a curve is related to the reduction mod p of its equations.

 

Light refreshments will be served after the colloquium in the faculty lounge at 15:30.

YOU ARE CORDIALLY INVITED

 

      

Dynamics Seminar I  


Time and Place: Tuesday, February 26th, 14:00, Mathematics Building, Room 209

Speaker: Weixiao Shen (National University of Singapore)

Title: On stochastic stability of the Manneville-Pomeau map

 

Abstract:

We discuss the stochastic stability of the Manneville-Pomeau map x\mapsto x+x^{1+\alpha} \mod 1. This is a joint work with Sebastian van Strien.

 

 

Dynamics Seminar II  


Time and Place: Tuesday, February 26th, 15:30, Mathematics Building, Room 207

Speaker: Yakov Pesin (Penn State)

Title: A general approach for constructing SRB-measures for chaotic attractors

 

Abstract:

I will survey recent results on existence of SRB measures for hyperbolic and partially hyperbolic attractors and I will discuss a general approach to establishing existence of SRB measures for general chaotic attractors. The approach is based on a certain recurrence condition on the iterates of Lebesgue measure called “effective hyperbolicity”. It is a version of the Lyapunov–Perron regularity in the dissipative case. I will show that if the asymptotic rate of effective hyperbolicity is non-zero on a set of positive Lebesgue measure, then the system has an SRB measure. Some examples will be discussed. This is a joint work with V. Climenhaga and D. Dolgopyat.

Jerusalem Number Theory Seminar  (NOTE UNUSUAL DAY!)


Time and Place: TUESDAY, 26 February 2013, 16:00, Room 209.  
Speaker: Ivan Loseu (Northeastern) 
Title:  Classification of Procesi bundles

Abstract:

Procesi bundle is a vector bundle on the Hilbert scheme of n points on the plane. It was first constructed by Haiman who used it to prove the Schur positivity for Macdonald polynomials. 

This bundle also provides a derived McKay equivalence for the Hilbert scheme. I will basically take the latter for an axiomatic description of a Procesi bundle. I will show that there are exactly two bundles with these properties: Haiman's and its dual. 

Time permitting I will also discuss an extension of this results to other symplectic resolution and a relation between the Procesi bundles and the tautological bundle conjectured by Haiman. 
The proofs are based on the study of Symplectic reflection algebras.

 

Basic Notions Seminar

 

Time and Place: Thursday, February 28th, 16:00, Math., Lecture Hall 2 

Speaker: Emmanuel Farjoun (HUJI)

Title:   The beauty of simplicial sets.



Abstract:

Simplicial sets originated in the 1950s in the work of Eilenberg-Steenrod- MacLane.
Each s.set  is,  by definition, a series of sets  (X_n)_n  connected by   acertain  collection  of maps of sets  X_n---->X_m.
This captures and generalizes the set  of simplices in a simplicial complex.  From this point of view a simplical sets are a sort of  'higher dimensional'  sets.

We will try to explain  this  choice of these collection of set-maps.
In the last 50 years simplicial sets became essential for  nice models and generalizations of  various mathematical concepts
such as  topological spaces, chain complexes, categories, derived functors etc...helping to formulate and prove many results.

Thus we can talk about "simplicial  ring" "simplicial  group" or  "simplicial vector space"  etc as as higher dimensional counterparts of the same, all being  special cases of the same basic idea.