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.
|December 2019||February 2020|
Events for 20 January 2020
Connor Armstrong: Loops, Leading Singularities and On-Shell Diagrams for Super Yang-Mills and Supergravity
On-shell diagrams are a useful tool for calculating and manipulating amplitudes. For N=4 SYM, they can be used to recurse amplitudes to all loop orders but their application to supergravity is less clear.
I will review how to calculate tree level amplitudes in these theories using recursion relations and on-shell diagrams. I'll then look at what they can tell us about 1-loop amplitudes and their leading singularities, hinting at possible new expressions for n-point MHV supergravity amplitudes at 1-loop.
Contact Daniel Martin
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One of the fundamental problems in dynamics is to understand the attractor of a system, i.e. the set where most orbits spent most of the time. As soon as the existence of an attractor is determined, one would like to know if it persists in a family of systems and in which way i.e. its stability. Attractors of one dimensional systems are well understood, and their stability as well. I will discuss attractors of two dimensional systems, starting with the special case of Henon maps. In this setting very little is understood. Already to determine the existence of an attractor is a very difficult problem. I will survey the known results and discuss the new developments in the understanding of attractors, coexistence of attractors and their stability for two dimensional dynamical systems.
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Planar random growth processes occur widely in the physical world. Examples include diffusion-limited aggregation (DLA) for mineral deposition and the Eden model for biological cell growth. One approach to mathematically modelling such processes is to represent the randomly growing clusters as compositions of conformal mappings. In 1998, Hastings and Levitov proposed one such family of models, which includes versions of the physical processes described above. An intriguing property of their model is a conjectured phase transition between models that converge to growing disks, and 'turbulent' non-disk like models. In this talk I will describe a natural generalisation of the Hastings-Levitov family in which the location of each successive particle is distributed according to the density of harmonic measure on the cluster boundary, raised to some power. In recent joint work with Norris and Silvestri, we show that when this power lies within a particular range, the macroscopic shape of the cluster converges to a disk, but that as the power approaches the edge of this range the fluctuations approach a critical point, which is a limit of stability. This phase transition in fluctuations can be interpreted as the beginnings of a macroscopic phase transition from disks to non-disks analogous to that present in the Hastings-Levitov family.
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