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 2020||December 2020|
Events for 6 November 2020
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3d N=2 gauge theories enjoy a twist that allows to study their partition functions on a circle times a closed Riemann surface. These partition functions, known as twisted indices, were computed some time ago using supersymmetric localisation on the Coulomb branch. More recently, we interpreted the indices from the point of view of a supersymmetric quantum mechanics, unveiling interesting connections to geometry. Starting from simple quantum mechanical geometric models, in this talk we want to introduce this point of view and explain how the indices encode interesting geometric phenomena such as wall-crossing and, in the case of N=4 gauge theories, symplectic duality of quasi-maps. The talk is based on arxiv:1802.10120, arxiv:1812.05567, arxiv:1912.9591, arxiv:2007.11603.
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Consider a diploid population (one in which each individual carries two copies of each gene) living in one spatial dimension. Suppose a particular gene appears in two forms (alleles) A and a, and that individuals carrying AA have a higher fitness than aa individuals, while Aa individuals have a lower fitness than both AA and aa individuals. The proportion of advantageous A alleles expands through the population approximately according to a travelling wave. We can prove that on a suitable timescale, the genealogy of a sample of A alleles taken from near the wavefront converges to a Kingman coalescent as the population density goes to infinity. This contrasts with the case of directional selection in which the corresponding limit is thought to be the Bolthausen-Sznitman coalescent.
Joint work with Alison Etheridge.
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