Geometry and Analysis Seminar

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series
29 January 2018
14:15
Abstract

First, we will discuss sequences of closed minimal hypersurfaces (in closed Riemannian manifolds of dimension up to 7) that have uniformly bounded index and area. In particular, we explain a bubbling result which yields a bound on the total curvature along the sequence and, as a consequence, topological control in terms of index and area. We then specialise to minimal surfaces in ambient manifolds of dimension 3, where we use the bubbling analysis to obtain smooth multiplicity-one convergence under bounds on the index and genus. This is joint work with Lucas Ambrozio, Alessandro Carlotto, and Ben Sharp

  • Geometry and Analysis Seminar
5 February 2018
14:15
Ailsa Keating
Abstract

In real dimension two, the symplectic mapping class group of a surface agrees with its `classical' mapping class group, whose properties are well-understood. To what extend do these generalise to higher-dimensions? We consider specific pairs of symplectic manifolds (S, M), where S is a surface, together with collections of Lagrangian spheres in S and in M, say v_1, ...,v_k and V_1, ...,V_k, that have analogous intersection patterns, in a sense that we will make precise. Our main theorem is that any relation between the Dehn twists in the V_i must also hold between Dehn twists in the v_i. Time allowing, we will give some corollaries, such as embeddings of certain interesting groups into auto-equivalence groups of Fukaya categories.

 

  • Geometry and Analysis Seminar
19 February 2018
14:15
Abstract

For many moduli problems, in order to construct a moduli space as a geometric invariant theory quotient, one needs to impose a notion of (semi)stability. Using recent results in non-reductive geometric invariant theory, we explain how to stratify certain moduli stacks in such a way that each stratum admits a coarse moduli space which is constructed as a geometric quotient of an action of a linear algebraic group with internally graded unipotent radical. As many stacks are
naturally filtered by quotient stacks, this involves describing how to stratify certain quotient stacks. Even for quotient stacks for reductive group actions, we see that non-reductive GIT is required to construct the coarse moduli spaces of the higher strata. We illustrate this point by studying the example of the moduli stack of coherent sheaves over a projective scheme. This is joint work with G. Berczi, J. Jackson and F. Kirwan.

  • Geometry and Analysis Seminar
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