Research lectures, seminars and events
The events listed in this area are research seminars, workshops and lectures hosted by Durham University departments and research institutes. If you are not a member of the University, but wish to enquire about attending one of the events please contact the organiser or host department.
|October 2019||December 2019|
Events for 11 November 2019
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MÃ¡rton BalÃ¡zs: Nonexistence of bi-infinite geodesics in exponential last passage percolation - a probabilistic way (Joint work with Ofer Busani and Timo SeppÃ¤lÃ¤inen)
Take a point on the 2-dimensional integer lattice and another one North-East from the first. Place i.i.d. Exponential weights on the vertices of the lattice; the point-to-point geodesic between the two points is the a.s. unique path of North and East steps that collects the maximal sum of these weights.
A bi-infinite geodesic is a doubly infinite North-East path such that any segment between two of its points is a point-to-point geodesic. We show that this thing a.s. does not exist (except for the trivial case of the coordinate axes). The intuition is roughly this: transversal fluctuations of a point-to-point geodesic are in the order of the 2/3rd power of its length, which becomes infinite for a bi-infinite geodesic. This and coalescence of geodesics result in not seeing this path anywhere near the origin which, combined with translation invariance, a.s. excludes its existence.
One needs to make this more quantitative to prove that even after taking the union for all possible directions we cannot see a bi-infinite geodesic, a program sketched by Newman. This has recently been completed rigorously by Basu, Hoffman and Sly with inputs from integrable probability. In this work we instead build on purely probabilistic arguments, such as couplings and maxima of drifted random walks, to arrive to this result.
Over the last few years, something (possibly a mid-life crisis) has made me become concerned about the reliability of modern mathematics, and about how the methods we mathematicians have traditionally used to prove theorems are scaling with the advent of the internet /ArXiv, and pressure on academics to get big results out there. I have started experimenting with a formal computer proof verification system called Lean, integrating it into my undergraduate teaching at Imperial and pushing it to see if it can handle modern mathematical definitions such as perfectoid spaces and the other ideas which got Peter Scholze a Fields Medal in 2018. I personally believe that Lean is part of what will become a paradigm shift in the way humans do mathematics, and that people who do not switch will ultimately be left behind. Am I right? Only time will tell. This talk will be suitable for a general scientific audience -- mathematics undergraduates, computer scientists and philosophers will all find it comprehensible.
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Dr Kimberley A. Fowler: Asceticism in Late-Antique Egypt as Told by the Book of Thomas the Contender (NHC II, 7)
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Compact stellar objects such as white dwarfs (WDs) have been proposed as potential probes to set constraints on dark matter (DM) particles. When DM scatters off nuclei, kinetic energy is transferred to the star that can give rise to an observational signal. Previous works did not consider relativistic effects on the calculation of the DM capture rate in WDs. However, since WDs are very dense objects, these effects can lead to sizeable corrections to the DM scattering cross-section. We present preliminary results of such computation and also study the impact of the inner structure and finite temperature of these stars on the DM capture rate.