Samuel Borza (Vienna). Measure contraction properties for sub-Riemannian structures beyond step 2 Friday 2nd May, 1:30-2:30pm. Huxley 140.
Abstract: I will introduce Carnot groups, and their quotients, as metric measure spaces. These are examples of Carnot–Carathéodory spaces, or sub-Riemannian manifolds, and include the Heisenberg group, the Engel group, and the Martinet flat structure, to name but a few. Once we have a good grasp of these geometric structures, I will outline some open problems in the field before shifting focus to the study of curvature and the so-called metric contraction properties. These analytic inequalities aim to define, in a synthetic way, a lower bound on the Ricci curvature. The new results I will present show how these properties can be preserved by taking quotients, and how this affects their validity or failure. This is joint work with Luca Rizzi from SISSA.
Masafumi Hattori (Nottingham). K-moduli of quasimaps and quasi-projectivity of K-stable Calabi-Yau fibrations over curves Friday 9th May, 1:30-2:30pm. Huxley 140.
Abstract: K-stability is an important notion in algebraic geometry, which is introduced to detect the existence of constant scalar curvature Kahler metrics, as the Yau-Tian-Donaldson conjecture predicted. On the other hand, this notion is also closely related to GIT and moduli theory. Odaka predicted that we can construct a moduli space (K-moduli) by using K-stability and Xu et. al. constructed K-moduli theory for log Fano pairs with an ample CM line bundle, which is a line bundle canonically defined. However, Odaka’s K-moduli conjecture is still open for general polarized varieties.
In this talk, we introduce uniform adiabatic K-stability for Calabi-Yau fibrations, that is a uniform notion of K-stability when the polarization is very close to the base line bundle, and we construct K-moduli theory of Calabi-Yau fibrations over curves. Moreover, we will construct K-moduli theory for log Fano quasimaps and apply it to the quasi-projectivity for K-moduli of Calabi-Yau fibrations.
Shaked Bader (Oxford). Hyperbolic subgroups of type FP_2(Ring) Friday 16th May, 1:30-2:30pm. Huxley 140.
Abstract: In 1996 Gersten proved that if G is a word hyperbolic group of cohomological dimension 2 and H is a subgroup of type FP_2, then H is hyperbolic as well. In this talk, I will present a project with Robert Kropholler and Vlad Vankov generalising this result to show that the same is true if G is only assumed to have cohomological dimension 2 over some ring R and H is of type FP_2(R).
Matt Booth (Imperial). Reflexive dg categories in algebra and topology Friday 23rd May, 1:30-2:30pm. Huxley 140.
Abstract: Reflexive dg categories, introduced recently by Kuznetsov and Shinder, satisfy strong duality properties which in particular place restrictions on invariants like their Hochschild (co)homology, derived Picard groups, and semiorthogonal decompositions. Examples include various derived categories of proper schemes, as well as finite dimensional algebras. I’ll define what it means for a dg category to be reflexive before giving some examples arising from algebraic geometry, algebraic topology, and symplectic geometry. This talk is based on work in progress joint with Isambard Goodbody and Sebastian Opper.
Yuhan Sun (Imperial). Rigid fibers in symplectic and contact manifolds Friday 30th May, 1:30-2:30pm. Huxley 140.
Abstract: Given a Hamiltonian integrable system on a closed symplectic manifold, Entov-Polterovich proved it has at least one rigid fiber. We will first survey several ideas of the proof and recent enhancements. Then we will present a rigid fiber theorem for contact manifolds. Based on joint works with Mak, Uljarevic and Varolgunes.
Matthew Hedden (Michigan State University). TBA Friday 6th June, 1:30-2:30pm. Huxley 140.
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Anya Nordskova (University of Hasselt). TBA Friday 13th June, 1:30-2:30pm. Huxley 140.
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Daniel Bath (KU Leuven). TBA Friday 20th June, 1:30-2:30pm. Huxley 140.
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Silvia Sabatini (University of Cologne). TBA Friday 27th June, 1:30-2:30pm. Huxley 140.
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