Jakob Stein, University College London
This seminar will be held jointly online and in person:
Vasileos (Hector) Papoulias, Oxford University
Daniel Fadel, Peking University
John Huerta, University of Lisbon
**NOTE NEW TIME**
Qaasim Shafi, Imperial College London
Derek Harland, University of Leeds
Kateryna Tatarko, Department of Pure Mathematics, University of Waterloo
Izar Alonso Lorenzo, Oxford University
When considering compactifications of heterotic string theory, systems of PDEs involving geometric structures arise. In this talk, we will describe heterotic systems in six and seven dimensions and then study the existence of the G-structures required by them in the cohomogeneity one setting. In the first part of the talk, we provide a non-existence result for balanced non-Kähler SU(3)-structures which are invariant under a cohomogeneity one action on a simply connected six-manifold. In the second part, we find a family of coclosed $G_2$-structures on certain seven-dimensional cohomogeneity one manifolds. The first part of this talk is based on a joint work with F. Salvatore.
MC 5417
Daniel Platt, King's College London
Associative submanifolds are certain 3-dimensional manifolds in 7-dimensional manifolds. They are calibrated, and therefore minimal surfaces, and there is a research programme that attempts to count them in order to define numerical invariants of manifolds, similar to Gromov-Witten invariants. However, not many examples of associative submanifolds are known, which is one of the difficulties in working out the details of this programme. In the talk I will explain how to construct some dozens of associatives whose existence had previously been predicted by physicists. They are different from all previously known associatives in that their volume goes to zero as the ambient manifold converges to a certain singular limit.
MC 5417
Duncan McCoy, Université du Québec à Montréal
Dehn surgery is an operation where one constructs a 3-manifold by taking a knot in the 3-sphere, cutting out a tubular neighbourhood and then gluing in another solid torus. We say that a Dehn surgery is an “alternating surgery” if it produces a manifold which arises as the double branched cover of an alternating link. I will try to justify why alternating surgeries are interesting and explain some of what is known about them. In particular, I will discuss the existence of an algorithm to calculate all possible alternating surgeries on a given knot and describe the results of implementing such an algorithm. This is joint work with Ken Baker and Marc Kegel.