A classical branching theorem of Weyl describes how an
irreducible representation of
compact U(n+1)U(n+1) decomposes when restricted
to U(n)U(n). The local Gan-Gross-Prasad conjecture provides a
conjectural extension to the setting of...
The goal of this talk is two-fold. We state a parabolic version
of the two realizations theorem and sketch a proof. This version
relates Iwahori-constructible sheaves on parabolic affine flag
variety to coherent sheaves on a parabolic version of the...
In [MIP*=RE by JNVWY] the authors construct a non-local game
that resolves Tsirelson's problem to the negative and by that
refute Connes' embedding conjecture (CEC). The game *-algebra (see
e.g. [KPS]) enables one to construct a finitely presented *...
Some of the central questions in complexity theory address the
amortized complexity of computation (also sometimes known as direct
sum problems). While these questions appear in many contexts, they
are all variants of the following:
String topology, as introduced by Chas and Sullivan 20 years
ago, is a product structure on the free loop space of a manifold
that lifts the classical intersection product from the manifold to
its loop space. I’ll explain how both a product and a...
What edge density of a graph guarantees that that it will
contain a particular subgraph? Or one of a given
family F of subgraphs? The celebrated
Erdős--Stone--Simonovits Theorem characterizes the maximum edge
density in F-free graphs, in terms of...
We are surrounded by functional networks, from fluid transport
in plants and animals to macroscopic elastic scaffoldings and
microscopic crystals and materials, and engineered power grids.
Often, such networks can be seen as optimized for their...
We study configurations of disjoint Lagrangian submanifolds in
certain low-dimensional symplectic manifolds from the perspective
of the geometry of Hamiltonian maps. We detect infinite-dimensional
flats in the Hamiltonian group of the two-sphere...
