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...
Based on the exotic Lagrangian tori constructed in CP2
by Vianna and Galkin-Mikhalkin, we construct for each Markov
triple three monotone Lagrangian tori in the 4-ball, and for
triples with distinct entries show that these tori lie in
different...
This talk will be about joint work with Fabian Ziltener in which
we show that a compact n-rectifiable subset of R^2n with vanishing
n-Hausdorff measure can be displaced from itself by a Hamiltonian
diffeomorphism arbitrarily close to the identity...
We introduce an SFT-type invariant for Legendrian knots in R^3,
which is a deformation of the Chekanov-Eliashberg differential
graded algebra. The differential includes components that count
index zero pseudoholomorphic disks with up to two positive...
One of the earliest achievements of mirror symmetry was the
prediction of genus zero Gromov-Witten invariants for the quintic
threefold in terms of period integrals on the mirror. Analogous
predictions for open Gromov-Witten invariants in closed...
We show that two generic, open, convex or concave toric domains
in R4 are symplectomorphic if and only if they agree up to
reflection. The proof uses barcodes in positive S1-equivariant
symplectic homology, or equivalently in cylindrical contact...
