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.
|September 2018||November 2018|
Events for 15 October 2018
Richard H Clayton: Adventures with Gaussian process emulators and models of electrical activity in the heart
Electrical activation of the heart muscle acts to initiate and synchronise contraction, and results from the movement of ions across the cell membrane. Over the last 50 years, models of electrical activity in single cells have been developed. These models are coupled systems of stiff and nonlinear ODEs, and as experimental techniques have developed they have become increasingly complex and time consuming to solve. Cell models can be coupled into PDE representations of heart tissue, and form the building blocks for multi-scale models of whole heart function, which can be used to simulate the heart of an individual patient. However, electrical activity in real cells is a variable process, with subtle differences in the time course of activation and recovery between different cells, and from one beat to the next in an individual cell. Part of the reason for this is that some model parameters represent quantities that are not fixed constants. Further uncertainty and variability in whole heart models arises from assumptions and simplifications in the models themselves, as well as in the way that medical images are used to construct a mesh representing the heart of a real patient. These problems are beginning to be addressed in the heart modelling community. In the seminar I will describe our work in Sheffield, in which we have used Gaussian process emulators to shed light on cell models and cell model calibration, and work in collaboration with King's College London where we aim to infer uncertain activation times based on noisy and incomplete data from real patients.
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In this talk, we will consider 2d field theories invariant under the BMS3 algebra, putatively dual to 3d Minkowski spacetimes and discuss the notion of a version of modular invariance in these theories. We will revisit the derivation of the BMS-Cardy formula and its reproduction of the entropy of cosmological horizons in flat space. We would then discuss in detail the construction of characters for these 2d field theories.
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I will review some properties of the famous Klein quartic and its automorphism group, and sketch how it can be used to give an alternative construction of the lattices in PU(2,1) obtained by the author in joint work with John Parker and Julien Paupert. Most of these lattices turn out to be non-arithmetic.
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