One of the primary goals of the mathematical analysis of
algorithms is to provide guidance about which algorithm is the
“best” for solving a given computational problem. Worst-case
analysis summarizes the performance profile of an algorithm by
its...
Over 40 years ago, Karp, Upfal, and Wigderson posed a central
open question in parallel computation: how many adaptive rounds are
needed to find a basis of a matroid using only independence
queries? Their pioneering work gave an upper bound of O(n‾√...
A compact hyperkahler manifold is a higher-dimensional analog of
a K3 surface; Lagrangian fibrations of hyperkahler manifolds are
higher-dimensional versions of elliptic fibrations of K3 surfaces.
A result of Voisin shows that these fibrations yield...
On a projective variety, Simpson showed that there is a
homeomorphism between the moduli space of semisimple flat bundles
and that of polystable Higgs bundles with vanishing Chern classes.
Recently, Bakker, Brunebarbe and Tsimerman proved a version...
The symplectic area of a Lagrangian submanifold L in a
symplectic manifold is defined as the minimal positive symplectic
area of a smooth 2-disk with boundary on L. A Lagrangian torus is
called extremal if it maximizes the symplectic area among
all...
We give a lower bound on the codimension of a component of the
non-abelian Hodge locus within a leaf of the isomonodromy foliation
on the relative de Rham moduli space of flat vector bundles on an
algebraic curve. The bound follows from a more...
A Hodge structure is a certain linear algebraic datum.
Importantly, the cohomology groups of any smooth projective
algebraic variety come equipped with Hodge structures which encode
the integrals of algebraic differential forms over
topological...
