Please note that the room of the seminar will change throughout the term.

Vaibhav Gadre (University of Glasgow). Cusp excursions of random Teichmulller geodesics. Friday 3rd May, 1:30-2:30pm. Huxley 308.

Abstract: Dynamics on moduli spaces of Riemann surfaces is often studied by considering analogies with homogeneous dynamics. The talk will begin with a short survey of moduli spaces from this point of view. It will then focus on random geodesics on moduli spaces as a specific context for considering these analogies.

Pierrick Bousseau (ETH Zurich). A relative holomorphic anomaly equation. Friday 10th May, 1:30-2:30pm. Huxley 308.

Abstract: The holomorphic anomaly equation is some recursive relation conjecturally satisfied by higher genus Gromov-Witten invariants of Calabi-Yau 3-folds. I will start reviewing the case of the local projective plane, for which this result is known. The main point of the talk will be to present a new conjectural holomorphic anomaly equation for some family of relative Gromov-Witten invariants related to the projective plane, and a proof in genus one. This is work in progress, joint with Longting Wu.

Nikolaos Tziolas (University of Cyprus). Vector fields and moduli of canonically polarized surfaces in positive characteristic. Friday 17th May, 1:30-2:30pm. Huxley 139.

Abstract: The purpose of this talk is to present some results about the geometry of smooth canonically polarized surfaces defined over a field of positive characteristic which have a nontrivial global vector field, equivalently non reduced automorphism scheme, and the implications that the existence of such surfaces has in the moduli problem of canonically polarized surfaces.

Ed Segal (UCL). Mirrors to punctured surfaces. Friday 24th May, 1:30-2:30pm. Huxley 144.

Abstract: There are various known ways to construct a category which is mirror to the Fukaya category of a punctured surface. I’ll discuss some work-in-progress (with Yanki Lekili) where we find algebro-geometric proofs that all the constructions give equivalent categories.

No seminar on Friday 31st May due to this event.

Andreas Krug (University of Marburg). Stability of Tautological Bundles on Symmetric Products of Curves. Friday 7th June, 1:30-2:30pm. Huxley 144.

Abstract: Given a vector bundle E over smooth variety X, there is a natural way to associate a vector bundle, called tautological bundle, on the Hilbert scheme of points on X. In this talk, we will discuss stability of tautological bundles in the case that X is a curve.

Vera Vértesi (University of Strasbourg). Additivity of the minimal genus for tight contact structures. Friday 14th June, 1:30-2:30pm. Huxley 144.

Abstract: A corollary of Haken’s Lemma from 1968 gives that the minimal genus of Heegaard splittings of 3-manifolds is additive under connected sum. In this talk I generalise this result for contact 3-manifolds. As a consequence of Giroux’s 2002 paper about open book decompositions, contact 3-manifolds have contact Heegaard splittings i.e. contact 3-manifolds decompose as the union of two contact handlebodies. After the basics of contact geometry I describe the main idea of the proof, that the minimal genus for contact Heegaard splittings of tight contact structures is additive under connected sum.

Hamid Ahmadinezhad (Loughborough University). Two decades on birational rigidity of del Pezzo fibration. Friday 21st June, 1:30-2:30pm. Huxley 144.

Abstract: Birational rigidity of Mori fibre spaces is a central problem in post MMP birational classification. In this talk, I will focus on 3-fold Mori fibre spaces with fibre dimension two, the so-called del Pezzo fibrations. I will discuss the importance of the problem and give an overview of the central results, with some recent progress.