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...
Robbert Dijkgraaf, Director and Leon Levy Professor
How did the universe begin? Robbert Dijkgraaf, Director and Leon
Levy Professor, explains what we know about the Big Bang and
explores the mysteries of our universe. This talk is geared for
children ages 10 and up.
Coffee is the most widely consumed social beverage in Japan.
Looking at coffee as a Japanese "food" allows us some observations
on culinary work in Japan in more general terms, and some
approaches to ideas of domestic, artisanal and industrial food...
