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Applied Maths Seminar Series
Located in Academic Departments / Mathematics / Research
Atomistic thin film growth using extended time scale techniques
Professor Roger Smith, Loughborough University
Located in Academic Departments / Mathematics / Research
Rigorous numerical estimates on dynamically defined numbers
Prof Mark Pollicott, Warwick University
Located in Academic Departments / Mathematics / Research
Applied Maths Seminar Archive
Located in Academic Departments / Mathematics / Research
Long-time behaviour for monostable equations with non-local diffusion (Dr Dmitri Finkelshtein, Swansea University)
Abstract: We consider a class of monostable non-linear equations with non-local diffusion in R^d with bounded solutions. If the non-local diffusion is given through an anisotropic probability kernel decaying at least exponentially fast in a direction and if the initial condition has the similar property, then the solution propagates in this direction at most linearly in time. For a particular equation arising in population ecology, we study then travelling waves and a detailed description of the front of propagation. In contrast, for the general equation, if either the kernel or the initial condition have appropriately regular heavy tails, then an acceleration of the front propagation for solutions is observed. We present sharp estimates for the time-space zone which separates the region of convergence to the unstable zero solution with the region of convergence to the stable positive constant solution. We consider differences between the case when the initial condition decays in all directions at infinity with the case of the initial condition decreasing along all coordinate axes only. We obtain new estimates for solutions to a linear non-local equation as well.
Located in Academic Departments / Mathematics / Research
Long timescale modelling of atomistic processes
Professor Steven David Kenny Loughborough University
Located in Academic Departments / Mathematics / Research
Mathematical sociology is not an oxymoron
Professor Martin G Everett, University of Manchester
Located in Academic Departments / Mathematics / Research
USING FUZZY RANDOM VARIABLES IN LIFE ANNUITIES PRICING (Dr. Laura González-Vila Puchades, Universitat de Barcelona)
This session develops life annuity pricing with stochastic representation of mortality and fuzzy quantification of interest rates. We show that modelling the present value of annuities with fuzzy random variables allows quantifying their expected price and risk resulting from the uncertainty sources considered. So, we firstly describe fuzzy random variables and define some associated measures: the mathematical expectation, the variance, distribution function and quantiles. Secondly we show several ways to estimate the discount rates to price annuities. Subsequently the present value of life annuities is modelled with fuzzy random variables. We finally show how an actuary can quantify the price and the risk of a portfolio of annuities when their present value is given by means of fuzzy random variables.
Located in Academic Departments / Mathematics / Research
"Metastability of the condensate in zero-range process", Professor Michail Loulakis (NTU Athens)
Abstract: I will explain the concept of metastability in the context of Markov processes and a general framework to tackle problems of the sort, the "martingale approach" proposed by Beltran and Landim. Then, I will present the zero-range process, an interacting particle model that goes through a phase transition when the particle density exceeds a critical value, with the emergence of a condensate. Finally, I will show how the martingale approach can be used to derive the scaling limit of the process that describes the movement of the condensate in the thermodynamic limit.
Located in Academic Departments / Mathematics / Research
Taming Infinities (Professor Martin Hairer (FRS), University of Warwick)
Abstract: Some physical and mathematical theories have the unfortunate feature that if one takes them at face value, many quantities of interest appear to be infinite! Various techniques, usually going under the common name of “renormalization” have been developed over the years to address this, allowing mathematicians and physicists to tame these infinities. We will tip our toes into some of the mathematical aspects of these techniques and we will see how they have recently been used to make precise analytical statements about the solutions of some equations whose meaning was not even clear until now.
Located in Academic Departments / Mathematics / Research

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