Math
Colloquium
Spring
2009
Math colloquium
meets on Mondays at 12:15 in Schreiber 006,
Previous talks: 2002-2003 , 2003-2004 , 2004-2005 , 2005-2006 , 2006-fall, 2007-spring, 2008-fall, 2008-spring
09.03.2009, 12:15 ****SPECIAL ROOM: MELAMED HALL****
Avi Wigderson, IAS.
The art of
reduction (or, depth through breadth)
ABSTRACT: NP-completeness ties together seemingly unrelated
computational problems across all sciences and mathematics. The key to showing
such connections are reductions (efficient translations between pairs of
problems).
The last couple of decades have seen an incredible growth and sophistication in
utilizing reductions and completeness. These connect seemingly unrelated
computational notions, models and even whole sub-areas of computer science.
Taking a guided tour of the ingredients leading to the celebrated PCP theorem,
I will survey such new reductions, and their general and diverse consequences.
16.03.2009, 12:15
Dmitry Belyaev, Princeton University
Schramm-Loewner Evolution.
ABSTRACT: Oded Schramm was one of the most
extraordinary mathematicians of our time who made valuable contributions to
many areas of mathematics. His revolutionary work transformed our understanding
of critical processes in two dimensions through his introduction of the
Stochastic Loewner evolution.
Ten years ago, while working on the loop-erased random work, Schramm introduced
a family of models that are the only possible conformally invariant scaling
limits of interfaces in statistical physics. Since than, SLE has been
successfully used to resolve many old problems and became an interesting
subject in themselves. It this talk we will discuss the ideas which led to the
introduction of SLE and connections between SLE and statistical physics..
23.03.2009, 12:15
Alexander Its,
Riemann-Hilbert Method.
ABSTRACT: In this talk a general overview of the Riemann-Hilbert method,
which was originated in 1970s-1980s in the theory of integrable
nonlinear PDEs of the KdV
type, will be given. The most recent applications of the Riemann-Hilbert
approach to asymptotic problems arising in the theory of matrix models, combinatorics and integrable
statistical mechanics will be outlined.
30.03.2009, 12:15
Elon Lindenstrauss, The
Hebrew University
On x2,x3 and xAxB.
ABSTRACT: I will discuss Furstenberg's theorem for the action of
multiplicative subgroups of the integers on R/Z (e.g. the semigroup
generated by 2 and 3), generalizations regarding actions of semigroups
of toral automorphisms on R^d/Z^d (e.g. Berend's theorem),
and their quantitative aspects.
I will also explain how these results relate to recent advances in arithmetic combinatorics.
PASSOVER VACATION
20.04.2009,
12:15
David Harari, University de
Paris-Sud
Reciprocity laws and quadratic equations.
ABSTRACT: I will discuss rational and integral solutions of polynomial
equations. Special attention will be paid to integral solutions of quadratic
equations Q(x_1,...,x_n)=a,
where Q is a quadratic form and a is a constant. In particular I will explain
the role played by classical reciprocity laws in number theory.
No colloquium due to Yom Hazikaron
Ceremony.
04.05.2009, 12:15
Eli Glasner, Tel Aviv University
Dynamical
systems, enveloping semigroups, and Banach representations
ABSTRACT: One of the important questions in Banach
space theory until the mid 70's was how to construct a separable Rosenthal
space (i.e. a Banach space not containing `1) which
is not Asplund. The first counterexamples were given
independently by James and Lindenstrauss. I will
review some recent results concerning the trinity mentioned in the title and
show, among other corollaries of these works, how counterexamples to the Banach space problem can be easily obtained from simple
dynamical systems.
This is a joint work with Misha Megrelishvili.
11.05.2009,
12:15
Francois Lalonde, Universite de Montreal.
On the group of transformations of real and Lagrangian
symplectic topology.
ABSTRACT: In projective complex geometry, the real part is
a Lagrangian submanifold.
There is therefore an increasing sequence of sets: real parts of complex
projective manifolds, Lagrangian submanifolds
in symplectic manifolds and totally real submanifolds. Following works of several people, starting
with Gromov, Floer, then
Seidel, Fukaya and his collaborators, and more
recently Biran and Cornea, one may assign quantum
invariants to Lagrangian submanifolds
and extend most cohomology operations to the quantum
level. It turns out that some of these invariants give, for the first time, an
idea to as much a Lagrangian submanifold
sees the global ambient topology and the transformation group of the ambient
space. This applies in particular to the relation between the mapping class
group of the real part of a complex projective manifold and the global Kahler transformation group.
18.05.2009, 12:15
Michael Hochman, Princeton University
Local entropy and projections of Cantor sets.
ABSTRACT: Given a compact set X in the plane, the image of X under
orthogonal projection to almost every line has the maximal possible Hausdorff dimension, i.e. min{1,dim(X)}. An old conjecture
of Furstenberg's predicts that when X=AªB, and A,B
are ª2 and ª3 invariant sets in [0,1], respectively, then this should
hold for every line except the axes (where it fails trivially). I will describe
a proof of this and its measure equivalent, and its relation to some other
conjectures in dynamics and fractal geometry. This is joint work with Pablo Shmerkin.
1.06.2009, 12:15
Ron Peled, NYU
Allocation of Measure to Point Processes.
ABSTRACT: One way to quantify how uniformly spread a point process is, is
to allocate cells of equal volume to each of its points and measure the
regularity of the resulting partition of space. Such allocations, with an
additional equivariance constraint, have been the
subject of many investigations in recent years. I will survey results in the
field, with special focus on the Gradient Flow Allocation, a natural allocation
rule suggested by Sodin and Tsirelson,
and its variant - the Gravitational Allocation.
8.06.2009, 12:15
Mikhail Katz, Bar Ilan
Bi-Lipschitz approximation by
finite-dimensional imbeddings.
ABSTRACT: Gromov's celebrated systolic
inequality from '83 is a universal volume lower bound for M in terms of the
least length of a
noncontractible loop in M. His proof passes via
a strongly isometric imbedding called the Kuratowski
imbedding, into the Banach space of
bounded functions on M. We show that the imbedding admits an approximation
by a (1+C)-bi-Lipschitz (onto its image), finite-dimensional
imbedding for every C>0. Our key tool is the first variation formula
thought of as a real statement in first-order logic,
in the context of non-standard analysis.