I will discuss some recent work showing that a generic
area-preserving diffeomorphism of a closed surface has an
equidistributed sequence of periodic orbits. The proof uses several
properties of spectral invariants from periodic Floer
homology...
Lagrangian cobordism induces a preorder on the set of Legendrian
links in any contact 3-manifold. We show that any finite collection
of null-homologous Legendrian links in a tight contact 3-manifold
with a common rotation number has an upper bound...
I will start by explaining the construction of a formal scheme
starting with an integral affine manifold Q equipped with a
decomposition into Delzant polytopes. This is a weaker and more
elementary version of degenerations of abelian varieties...
Wiles’s proof of the modularity of (semistable) elliptic curves
over the rationals and Fermat’s Last Theorem relied on his
invention of a modularity lifting method. There were two strands to
the method:
In this talk, I will discuss joint work with Tristan Buckmaster,
Nader Masmoudi, and Vlad Vicol in which we construct
non-conservative solutions to the Euler equations which belong to
the regularity class C0tH1/2−x. The motivation for such
solutions...
I will talk about ongoing work with S. Venugopalan on computing
disk potentials (which are counts of holomorphic disks with
boundary on a Lagrangian) via multi-directional neck stretching.
The focus will be on examples.
Morrey’s conjecture arose from a rather innocent looking
question in 1952: is there a local condition characterizing
"ellipticity” in the calculus of variations? Morrey was not able to
answer the question, and indeed, it took 40 years until
first...
