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...
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...
