Tuesday, 29 October 2024, 4-5pm Location: B.4.04 - LT2 Cruciform Building (Google Maps location)

• Speaker: Alexander Strohmaier (Hannover)
  
  Title: Analytic microlocal analysis, unique continuation and its implications in QFT and inverse problems
  
  Abstract:
I will give a short informal explanation of the timelike tube theorem in QFT on curved spacetimes and lay out what mathematical ingredients were used in its proof. I will then give a short and more elementary overview of various notions of wavefront sets in the analytic category based on the FBI transform and illustrate how it can be used to give a simple proof to Boman’s flatness theorem. (Based in parts on joint work with E. Witten)

Tuesday, 12 November 2024, 4-5pm Location: B05 Darwin Building Google Maps location)

• Speaker: Laura Monk (Bristol)
  
  Title: The probabilistic method in hyperbolic geometry
  
  Abstract: The aim of this talk is to illustrate how a probabilistic viewpoint can be incredibly fruitful in all fields of mathematics, even "fundamental" fields such as hyperbolic geometry. The probabilistic method consists in establishing properties that are true "for most X" rather than "for all X", using a random model to sample the object X we wish to study. It allows to prove results in spite of some pathological counter-examples, and also to benefit from powerful additional tools. I will narrate the story of this idea in hyperbolic geometry, from the first combinatorial model by Brooks and Makover, to more recent models, based on random covers and Weil-Petersson geometry. The main character we will follow during this journey is the diameter, a very simple quantity that cannot be bounded a priori, but is now well-understood thanks to this new approach.

Tuesday, 3 December 2024, 4-5pm Location: 124 Gideon Schreier, Bentham House (Google Maps location)

• Speaker: Euan Spence (Bath)
  
  Title: A case study in using semiclassical analysis in the numerical analysis of high-frequency wave problems.
  
  Abstract: The main focus of my research for the last ~10 years has been in using tools from semiclassical analysis, that is, the tools and techniques designed for studying high-frequency solutions to PDEs, in the numerical analysis of these PDEs. This talk will showcase a recent result in this research direction, namely, the first frequency-explicit convergence results about domain-decomposition methods for the high-frequency Helmholtz equation. (No prior knowledge of domain decomposition methods will be needed to understand this talk!)

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You'll find the old colloquium schedules here.