One of the major insights of the ``fixed-parameter
tractability’’ (FPT) approach to algorithm design is that, for many
NP-hard problems, it is possible to efficiently *shrink* instances
which have some underlying simplicity. This preprocessing
can...
We prove a strong limitation on the ability of entangled provers
to collude in a multiplayer game. Our main result is the first
nontrivial lower bound on the class MIP* of languages having
multi-prover interactive proofs with entangled provers...
Quillen's higher K-groups, defined in 1971, paved the way for
motivic cohomology of algebraic varieties. Their definition as
homotopy groups of combinatorially constructed topological spaces
initially seems abstract and inaccessible. In...
I will report on recent joint work with L. Lanzani on three
basic projection operators, each associated to an appropriate
domain in C^n. These are: variants of Cauchy-Fantappie integrals;
the Cauchy-Szego projection: and the Bergman projection...
We establish a derived equivalence of the Fukaya category of the
2-torus, relative to a basepoint, with the category of perfect
complexes on the Tate curve over Z[q]. It specializes to an
equivalence, over Z, of the Fukaya category of the...
Welschinger invariants, real analogs of genus 0 Gromov-Witten
invariants, provide non-trivial lower bounds in real algebraic
geometry. In this talk I will explain how to get some wall-crossing
formulas relating Welschinger invariants of the same...
I present some of the very fundamental notions in game theory,
with emphasis on their role in the theory of mechanism design and
implementation. Examples include (1) normal-form games: Nash
equilibrium and full implementation, dominant strategy...
