In this talk, I will construct an S1-equivariant version of the
relative symplectic cohomology developed by Varolgunes. As an
application, I will construct a relative version of Gutt-Hutchings
capacities and a relative version of symplectic (co...
The (small) quantum connection is one of the simplest objects
built out of Gromov-Witten theory, yet it gives rise to a
repertoire of rich and important questions such as the Gamma
conjectures and the Dubrovin conjectures. There is a very
basic...
The rectangular peg problem, an extension of the square peg
problem, is easy to outline but challenging to prove through
elementary methods. In this talk, I discuss how to show the
existence and a generic multiplicity result assuming the
Jordan...
We explore the construction of non-Weinstein Liouville geometric
objects based on Anosov 3-flows, introduced by Mitsumatsu, in the
generalized framework of Liouville Interpolation Systems and
non-singular partially hyperbolic flows. We discuss the...
We will present two results in complex geometry: (1) A Kähler
compactification of ℂn with a smooth divisor complement must be ℙn,
which confirms a conjecture of Brenton and Morrow under the Kähler
assumption; (2) Any complete asymptotically conical...
I will describe a new lower bound on the number of intersection
points of a Lagrangian pair, in the exact setting, using Steenrod
squares on Lagrangian Floer cohomology which are defined via a
Floer homotopy type.
In contact geometry, a systolic inequality aims to give a
uniform upper bound on the shortest period of a periodic Reeb orbit
for contact forms with fixed volume on a given manifold. This
generalizes a well-studied notion in Riemannian geometry. It...
Quantum Steenrod operations are deformations of classical
Steenrod operations on mod p cohomology defined by counts of genus
0 holomorphic curves with a p-fold symmetry, for a prime p. We
explain their relationship with the p-curvature of the...
In this talk I will first define the space of h-cobordisms
associated to a manifold M. This space is known to have many
non-trivial homotopy groups and in stable range (they can often be
computed using Waldhausen's algebraic K-theory of spaces). I...
Kaledin established a Cartier isomorphism for cyclic homology of
dg-categories over fields of characteristic p, generalizing a
classical construction in algebraic geometry. In joint work with
Paul Seidel, we showed that this isomorphism and related...
