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...
Faltings proved the statement, previously conjectured by
Shafarevich, that there are finitely many abelian varieties of
dimension nn, defined over a fixed number field, with good
reduction outside a fixed finite set of primes, up to isomorphism.
In...
I will start with a few comments on the proof of the equivalence
presented in the previous talks. Then I will focus on the
description of the abelian category of perverse sheaves
on the affine flag variety on the coherent side, where the answer
is...
