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.
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.