We define a quantum product on the cohomology of a symplectic
manifold relative to a Lagrangian submanifold, with coefficients in
a Novikov ring. The associativity of this product is equivalent to
an open version of the WDVV equations for an...
Sums of Dirichlet
characters ?n?x?(n)?n?x?(n) (where ?? is a
character modulo some prime rr, say) are one of the best
studied objects in analytic number theory. Their size is the
subject of numerous results and conjectures, such as the
Pólya...
Perverse sheaves and intersection cohomology are central objects
in geometric representation theory. This talk is about their
long-lost K-theoretic cousins, called K-motives. We will discuss
definitions and basic properties of K-motives and explore...
We discuss various (still open) questions on approximations of
finitely generated groups, focusing on finite-dimensional
approximations such as residual finiteness and soficity. We survey
our results on the existence, stability and quantification
of...
The Satisfiability problem is perhaps the most famous problem in
theoretical computer science, and significant effort has been
devoted to understanding randomly generated SAT instances. The
random k-SAT model (where a random k-CNF formula is chosen...
The study of hyperkaehler manifolds of lowest dimension (and of
gauge theory on them) leads to a chain of generalizations of the
notion of a quiver: quivers, bows, slings, and monowalls. This talk
focuses on bows, their representations, and...
Earlier this semester we heard a fascinating talk by James Stone
describing how the equations of compressible magnetohydrodynamics
(MHD) can help us understand the Cosmos. Today we will return to
Earth and describe a mathematical model, derived from...
In the Pandora's Box problem, the algorithm is provided with a
number of boxes with unknown (stochastic) rewards contained inside
them. The algorithm can open any box at some cost, discover the
reward inside, and based on these observations can...
Let g be a semisimple Lie algebra. The affine W-algebra
associated to g is a topological algebra which quantizes the
algebraic loop space of the Kostant slice. It is constructed as a
quantum Hamiltonian (alias quantum Drinfeld--Sokolov) reduction
of...
