arXiv research

Real Lagrangian tori in $S^2 imes S^2$ are Hamiltonian isotopic to the Clifford torus.

New construction of Fukaya-Seidel categories using complex gradient flow equation.

We prove that the number of Reeb chords between a Legendrian submanifold and its contact Hamiltonian push-off is at least the sum of the $\mathbb{Z}_2$-Betti numbers of the submanifold, provided that the contact isotopy is sufficiently small when compared to the smallest Reeb chord on the Legendrian. Moreover, the esta…

Nearby pinwheels are isotopic, solving Arnold's conjecture.

Study elliptic operators on glued manifolds, reducing to finite-dimensional systems.

Manifolds with boundary and with corners form categories ${\bf Man}\subset{\bf Man^b}\subset{\bf Man^c}$. A manifold with corners $X$ has two notions of tangent bundle: the tangent bundle $TX$, and the b-tangent bundle ${}^bTX$. The usual definition of smooth structure uses $TX$, as $f:X\to\mathbb{R}$ is defined to be …