Observance
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Speaker:   Shah Faisal
Title:   Progress on the Lagrangian capacity
Abstract:   The symplectic area of a Lagrangian submanifold L in a symplectic manifold is defined as the minimal positive symplectic area of a smooth 2-disk with boundary on L. The Lagrangian capacity of a symplectic manifold is defined as the supremum of these minimal areas taken over all embedded Lagrangian tori. In this talk, I will describe several conjectures concerning Lagrangian capacity and report on the progress we have made so far. This talk is partially based on ongoing joint work with Yin Li.

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Spring break: no talk this week

Speaker:   Peter Cameron
Title:   Spacetime extensions in low regularity
Abstract:   It has been shown that the interior of a dynamical black hole spacetime (of the sort believed to occur in nature) contains a horizon to which the spacetime metric extends continuously. However, Penrose's strong cosmic censorship conjecture states that in any such extension, the Christoffel symbols should fail to be locally square integrable (and consequently evolution via the Einstein equations must break down, thus preserving the deterministic nature of the theory). Motivated by proving such an inextendibility statement, I will discuss recent work with Jan Sbierski where we study the uniqueness of continuous spacetime extensions in 1+1 dimensions.

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No seminar this week: Della Pietra lecture

Title:    UNDERSTANDING COINCIDENCES

Abstract:   Coincidences astound us. They can affect where we live (and with whom), work and all sorts of things. I will review ideas of Freud and Jung on the psychology of coincidences. I will also show that sometimes, a bit of thought shows 'it's not so surprising after all'. A small set of tools and examples lead to a checklist and ways of quantifying things. This is a math talk, but aimed at a very general audience.