Video Lectures

We consider a class of Lagrangian sections L contained in certain Calabi-Yau Lagrangian fibrations (mirrors of toric weak Fano manifolds). We prove that a form of the Thomas-Yau conjecture holds in this case: L is Hamiltonian isotopic to a special...

The r-colour Ramsey number Rr(k) is the minimum n∈ℕ such that every r-colouring of the edges of the complete graph Kn on n vertices contains a monochromatic copy of Kk. We prove, for each fixed r≥2, that

Rr(k)≤e−δkrrk

for some constant δ=δ(r)>0 and...

In this talk, I will introduce a class of numerical invariants associated with matrix factorizations, constructed to mirror open Gromov–Witten invariants. Matrix factorizations are algebraic objects expected to correspond, under mirror symmetry, to...

This talk is based on joint work with Naichung Conan Leung. We study the mirror symmetry of nonabelian group actions on symplectic manifolds. We show that the presence of a nonabelian symmetry imposes constraints on non-displaceable Lagrangian...