School of Mathematics

Given a Hamiltonian H∈C∞(S1×M), what is the relationship between the dynamics of the isotopy generated by H and the various Floer-theoretic invariants associated to H? In this talk I will discuss how — in the case where M is a closed surface —one...

We will go in-depth into the proof that for all functions t(n) greater than or equal to n, every multitape Turing machine running in time t can be simulated in space only O(tlogt‾‾‾‾‾√). We will attempt to be completely self-contained. To that end...

The field of unlikely Intersections presents a robust paradigm for problems in which several subjects intermingle: arithmetic, o-minimality, and hodge theory. The goal of this talk will be to introduce some of those connections. My aim is to...

A linear extension of P is a linear ordering compatible with the poset relations. Let p(x less than y) be the probability that x

precedes y in a uniformly random linear extension, and let δ(x,y)=min(p(x less than y),p(y less than x)) and δ(P) be the...

I will describe a recent extension of the classical PAC (Probably Approximately Correct) learning framework [Vapnik and Chervonenkis, 1970s; Valiant, 1980s]. This extension makes it possible to model a wide range of common and practical data...

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...

We prove the quilted Floer cochain complexes form $(A_\infty,n)$ modules over the Fukaya category $Fuk(M \times M^-)$. Then we prove that when we restrict the input to mapping cones of product Lagrangians and graphs, the resulting bar-type complex...