Andrei Rapinchuk and I have introduced a new notion of
``weak-commensurability’’ of subgroups of two semi-simple groups.
We have shown that existence of weakly-commensurable Zariski-dense
subgroups in semi-simple groups G_1 and G_2 lead to strong...
This talk will review some theorems and conjectures about phase
transitions of interacting spin systems in statistical mechanics. A
phase transition may be thought of as a change in a typical spin
configuration from ordered state at low temperature...
A classical theorem of Dirichlet establishes the existence of
infinitely many primes in arithmetic progressions, so long as there
are no local obstructions. In 2006 Green and Tao set up a program
for proving a vast generalization of this theorem...
Enumerative geometry is a classical subject often concerned with
enumeration of complex curves of various types in projective
manifolds under suitable regularity conditions. However, these
conditions rarely hold. On the other hand, Gromov-Witten...
The modern theory of dynamical systems, as well as symplectic
geometry, have their origin with Poincare as one field with
integrated Ideas. Since then these fields developed quite
independently. Given the progress in these fields one can make a
good...
It is becoming more and more clear that many of the most
exciting structures of our world can be described as large
networks. The internet is perhaps the foremost example, modeled by
different networks (the physical internet, a network of
devices...
A Lagrangian correspondence is a Lagrangian submanifold in the
product of two symplectic manifolds. This generalizes the notion of
a symplectomorphism and was introduced by Weinstein in an attempt
to build a symplectic category. In joint work with...
I will describe the notions of strong and weak epsilon nets in
range spaces, and explain briefly some of their many applications
in Discrete Geometry and Combinatorics, focusing on several recent
results in the investigation of the extremal...
I will start with a review the basic notions of
Hamiltonian/symplectic vector field and of Hamiltonian/symplectic
group action, and the classical structure theorems of Kostant,
Atiyah, Guillemin-Sternberg and Delzant on Hamiltonian torus
actions...