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...