Computing the volume of a convex body in n-dimensional space is an
ancient, basic and difficult problem (#P-hard for explicit
polytopes and exponential lower bounds for deterministic algorithms
in the oracle model). We present a new algorithm, whose...
What are the possible Hodge numbers of a smooth complex projective
variety? We construct enough varieties to show that many of the
Hodge numbers can take all possible values satisfying the
constraints given by Hodge theory. For example, there are...
Infrared observations from Spitzer Space Telescope and Herschel
Space Observatory are used to study the interstellar dust in M31. A
physical dust model is used to map the dust surface density,
dust/gas ratio, starlight heating intensity, and the...
I will explain how infinite sequences of flops give rise to some
interesting phenomena: first, an infinite set of smooth projective
varieties that have equivalent derived categories but are not
isomorphic; second, a pseudoeffective divisor for which...
Beauville and Voisin proved that decomposable cycles (intersections
of divisors) on a projective K3 surface span a 1-dimensional
subspace of the (infinite-dimensional) group of 0-cycles modulo
rational equivalence. I will address the following...
Monotone submodular maximization over a matroid (MSMM) is a
fundamental optimization problem generalizing Maximum Coverage and
MAX-SAT. Maximum Coverage is NP-hard to approximate better than
\(1-1/e\), an approximation ratio obtained by the greedy...
My talk will be a broad introduction to what is the (mostly
conjectural) higher dimensional generalization of Abel's theorem on
divisors on Riemann surfaces, namely, the relationship between the
structure of the group of algebraic cycles on a...
