ECH (embedded contact homology) capacities give obstructions to
symplectically embedding one four-dimensional symplectic manifold
with boundary into another. These obstructions are known to be
sharp when the domain is a "concave toric domain" and...
Embedded contact homology gives a sequence of obstructions to
four-dimensional symplectic embeddings, called ECH capacities.
These obstructions are known to be sharp in several interesting
cases, for example for symplectic embeddings of one...
We give a geometric theory of vector-valued modular forms attached
to Weil representations of rank 1 lattices. More specifically, we
construct vector bundles over the moduli stack of elliptic curves,
whose sections over the complex numbers...
The Lipman-Zariski conjecture states that if the tangent sheaf of a
complex variety is locally free then the variety is smooth. In
joint work with Patrick Graf we prove that this holds whenever an
extension theorem for differential 1-forms holds, in...
In many examples of moduli stacks which come equipped with a notion
of stable points, one tests stability by considering "iso-trivial
one parameter degenerations" of a point in the stack. To such a
degeneration one can often associate a real number...
It is classical to study the geometry of projective varieties over
algebraically closed fields through the properties of various
positive cones of divisors or curves. Several counterexamples have
shifted attention from the higher (co)dimensional...
Localization is a topological technique that allows us to make
global equivariant computations in terms of local data at the fixed
points. For example, we may compute a global integral by summing
integrals at each of the fixed points. Or, if we know...
The acclaimed chorus The Crossing performed David Lang's
Pulitzer Prize-winning work, The Little Match Girl
Passion, which combines the haunting Hans Christian Andersen
story with additional texts to create a rich, enthralling,
multi-layered...
