Matt Kerr (Washington University in St. Louis). K2 of curves and mirror symmetry Friday 10th Jan, 1:30-2:30pm. Huxley 140.
Abstract: In their simplest form, K2 classes on curves are just pairs of rational functions; what makes them interesting is the regulator map and its interaction with arithmetic of curves and differential equations. I’ll discuss a couple of applications to mirror symmetry: (i) via their close relationship to Hori-Vafa models, K2 cycles explain the asymptotic growth rate of local Gromov-Witten invariants of toric Fano surfaces; and (ii) they help to settle a conjecture on eigenvalues of quantum curves arising in the topological string/spectral theory correspondence.
Wendelin Lutz (University of Massachusetts). The Morrison Cone Conjecture under deformation Friday 17th Jan, 1:30-2:30pm. Huxley 140.
Abstract: Let Y be a Calabi—Yau variety. The Morrison Cone Conjecture is a fundamental conjecture in Algebraic Geometry on the geometry of the nef cone and the movable cone of Y: while these cones are usually not rational polyhedral, the cone conjecture predicts that the action of Aut(Y) on Nef(Y) admits a rational polyhedral fundamental domain, and that the action of Bir(Y) on Mov(Y) admits a rational polyhedral fundamental domain.
Even though the conjecture has been settled in special cases, it is still wide open in dimension at least 3.
We prove that if the cone conjecture holds for a smooth Calabi-Yau threefold Y, then it also holds for any smooth deformation of Y.
Samuel Muñoz Echániz (Cambridge). Mapping class groups of h-cobordant manifolds Friday 24th Jan, 1:30-2:30pm. Huxley 140.
Abstract: A cobordism W between compact manifolds M and M’ is an h-cobordism if the inclusions of M and M’ into W are both homotopy equivalences. This kind of cobordisms plays an important role in the classification of high-dimensional manifolds, as h-cobordant manifolds are often diffeomorphic.
With this in mind, given two h-cobordant manifolds M and M’, how different can their diffeomorphism groups Diff(M) and Diff(M’) be? The homotopy groups of these two spaces are the same “up to extensions” in a range of strictly positive degrees. Contrasting this fact, I will present examples of h-cobordant manifolds with different mapping class groups. In doing so, I will review the classical theory of h-cobordisms and introduce several moduli spaces of manifolds that help in answering this question.
Samuel Stephanie Baines (Imperial). TBA Friday 31th Jan, 1:30-2:30pm. Huxley 140.
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TBA Friday 7th Feb, 1:30-2:30pm. Huxley 140.
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Benjamin Briggs (Imperial). TBA Friday 14th Feb, 1:30-2:30pm. Huxley 140.
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Michael Schmalian (Oxford). TBA Friday 21st Feb, 1:30-2:30pm. Huxley 140.
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Aleksander Doan (UCL). TBA Friday 28th Feb, 1:30-2:30pm. Huxley 140.
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Nattalie Tamam (Imperial). TBA Friday 14 Mar, 1:30-2:30pm. Huxley 140.
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