

School of Mathematics ColloquiumTuesday 9 February 2010Sir Michael Atiyah (University of Edinburgh)Topology and Quantum Physics 5.15pm, Rupert Beckett Lecture Theatre, Michael Sadler Building Classical Physics has a long and intimate relation with Geometry, going back to Galileo and Newton, in which force bends (or curves) the motion of a particle. This broad idea carries over to Maxwell's Electromagnetism and Einstein's General Relativity. However in the 20th century quantum mechanics altered the picture, but at the same time geometers widened their horizons by taking up topology. I will try to explain how the force curvature link extends to a quantumtopology one. Interestingly a prime example of a topological problem is that of distinguishing knots, and Kelvin in the 1870's suggested that knots might explain the structure of atoms. Although, with the advent of quantum mechanics, Kelvin's theory was discarded it was too beautiful an idea to waste In a sense Kelvinâ€™s basic idea has survived but applied at the subatomic level. The new understanding of the QuantumTopology link has had a profound effect on both mathematics and theoretical physics, as I hope to indicate. This colloquium is run jointly between the Schools of Mathematics and Physics & Astronomy
Wednesday 1 July 2009Professor Stanislav Molchanov (University of North Carolina at Charlotte, USA)Reactiondiffusion equations for growth processes and applications to spatial dynamics of biological populations 4.30pm MALL Seminar Room, School of Mathematics, Level 8 The central topic of the talk will be the mathematical models of the evolution of biological populations (such as plankton). The space distribution of the particles can be described by the reactiondiffusion (or KPP) equations, perhaps with the negative feedback (in the spirit of the classical works by Fisher and KolmogorovPetrovskiiPiskunov). The distribution of the masses of particles is described by a nonstandard differentialfunctional equation (which must catch the mitosis processes) coupled with the KPP equation. The talk will present several analytic results and limit theorems on the spacemass distribution of the particles. The talk will be preceded by tea at 4.10pm and followed by a wine
reception, both in the level 9 foyer of the
School of Mathematics.
Thursday 26 February 2009Professor Niels Gronbaek (Department of Mathematical Sciences, University of Copenhagen)Thematic Projects  making Real Analysis real 4.30pm MALL Seminar Room, School of Mathematics, Level 8 In the talk I will describe a development project aiming at furthering independent student work and developing mathematical competencies The talk will be preceded by tea at 4.10pm and followed by a wine reception, both in the level 9 foyer of the School of Mathematics.Tuesday 2 December 2008Professor Nick Trefethen FRS (Oxford University Computing Laboratory)CHEBFUNS: A NEW KIND OF NUMERICAL COMPUTING 4.00pm MALL Seminar Room, School of Mathematics, Level 8 For a long time there have been two kinds of mathematical computation: symbolic and numerical. Symbolic computing manipulates algebraic expressions exactly, but it is unworkable for many applications since the space and time requirements tend to grow combinatorially. Numerical computing avoids the combinatorial explosion by rounding to 16 digits at each step, but it works just with individual numbers, not algebraic expressions. This talk will describe a new kind of computing that aims to combine the feel of symbolics with the speed of numerics. The idea is to represent functions by Chebyshev expansions whose length is determined adaptively to maintain an accuracy of close to machine precision. Our "chebfun" system is implemented in objectoriented Matlab, with familiar vector operations such as sum and diff being overloaded to analogues for functions such as integration and differentiation. The system is surprisingly effective, and a demonstration will be given together with a discussion of the underlying mathematics and of the prospects for the future. The chebfun system is a joint project with Zachary Battles, Ricardo Pachon, Rodrigo Platte, and Toby Driscoll. The talk will be preceded by tea at 3.30pm and followed by a wine reception, both in the level 9 foyer of the School of Mathematics.Tuesday 11 November 2008Professor Robert Pego (Carnegie Mellon)Selfsimilarity and the scaling attractor for models of coagulation and clustering 4.00pm MALL Seminar Room, School of Mathematics, Level 8 We study limiting behavior of rescaled size distributions in several models of clustering or coagulation dynamics, `solvable' in the sense that the Laplace transform converts them into nonlinear PDE. The scaling analysis that emerges has many connections with the classical limit theorems of probability theory, and a surprising application to the study of shock clustering in the inviscid Burgers equation with randomwalk initial data. I'll focus on recent progress regarding a `mindriven' clustering model related to domain coarsening dynamics in the AllenCahn equation. The talk will be preceded by tea at 3.30pm and followed by a wine reception, both in the level 9 foyer of the School of Mathematics.Tuesday 17 June 2008Professor Paul Martin (Leeds)Representation theory inspired by computational statistical mechanics and Professor Simon Ruijsenaars (Leeds) CalogeroMoser systems: A crossroads in mathematics and physics 4.00pm MALL Seminar Room, School of Mathematics, Level 8 This colloquium will be given jointly by two professors who joined the School of Mathematics this academic year. It will be preceded by tea at 3.30pm and followed by a wine reception, both in the level 9 foyer of the School of Mathematics. Tuesday 29 April 2008Professor Valerie Isham (UCL)SpaceTime Models for Soil Moisture Dynamics 4.30pm MALL Seminar Room, School of Mathematics, Level 8 Abstract: Soil moisture provides the physical link between soil, climate and vegetation. It increases via the infiltration of rainfall and decreases through evapotranspiration, runoff and leakage, all these effects being dependent on the existing soil moisture level. During wet periods, soil moisture tends largely to be driven by the topography, while evapotranspiration has more influence in dry periods. In this talk, I will describe models for soil moisture dynamics in which marked Poisson processes are used to model the temporal process of rainfall input to the soil moisture dynamics, and storms are allowed to have both spatial and temporal extents. Losses due to evapotranspiration depend on vegetation cover and the models allow for variable, and possibly random, vegetation processes. Under arid/semiarid conditions, many transient and equilibrium properties of these models can be determined analytically and used for comparison with data on soil moisture dynamics. The talk will be preceded by tea at 4pm and followed by a wine reception, both in the level 9 foyer of the School of Mathematics.Tuesday 12 February 2008Dr John Ockendon FRS (Oxford Centre for Industrial and Applied Mathematics)The ups and downs of Maths in Industry 4.30pm MALL Seminar Room, School of Mathematics, Level 8 This talk will be about the work of OCIAM and its various international imitators, and the new mathematical challenges posed by industrial questions. The talk will be preceded by tea at 4pm and followed by a wine reception, both in the level 9 foyer of the School of Mathematics.Tuesday 4 December 2007Prof. Robin Wilson (Open University)Euler  300 years on 4.30pm MALL Seminar Room, School of Mathematics, Level 8 Abstract: In this talk we look at the life, labours and legacy of Leonhard Euler (17071783), the most prolific mathematician of all time. The talk will be preceded by tea at 4pm and followed by a wine reception, both in the level 9 foyer of the School of Mathematics.Tuesday 6 November 2007Prof. Mike Steel (University of Canterbury)Phylogenetics: Interactions between mathematics and evolution 4.30pm MALL Seminar Room, School of Mathematics, Level 8 Abstract: Phylogenetics is the reconstruction and analysis of 'evolutionary' trees and graphs in biology (and related areas of classification such as linguistics). Several areas of mathematics, statistics and computer science play an increasingly important part in the underlying theory. I will describe some of the ways in which techniques from combinatorics and probability have helped provide insights into certain fundamental questions relevant to evolutionary biology, and outline some open problems. The talk will be preceded by tea at 4pm and followed by a wine reception, both in the level 9 foyer of the School of Mathematics.Thursday 8 March 2007Prof. Martin Barlow FRS (University of British Columbia)Nash, the heat equation, and percolation 4pm Roger Stevens Lecture Theatre 14 Abstract: In the late 1950s de Giogi, Moser and Nash made fundamental advances in proving regularity for divergence form elliptic and parabolic PDE. These ideas have been extended to manifolds, and more recently graphs. I will describe how these methods can be developed to give information on random walks on percolation clusters. The talk will be preceded by tea at 3.40pm and followed by a wine reception, both in the level 9 foyer of the School of Mathematics.Thursday 1 February 2007Prof. Brian Davies FRS (King's College)Beyond Mathematical Platonism 4pm Roger Stevens Lecture Theatre 14 The talk will be preceded by tea at 3.40pm and followed by a wine reception, both in the level 9 foyer of the School of Mathematics. Thursday 2 November 2006Prof. Kjeld Laursen (University of Copenhagen)Can our classroom mathematics be more like our research mathematics? 4pm Roger Stevens Lecture Theatre 14 Abstract: William Thurston posed the question "What is it that mathematicians accomplish?" and he rephrases it to "How do mathematicians advance human understanding of mathematics?", after which he gives this aspect of an answer: "What we are doing is finding ways for people to understand and think about mathematics." In this light, some of the barriers between research mathematics and taught mathematics crumble. In this talk I will make some observations and give some specific examples on our possibilities of contributing to this 'crumbling'. The talk will be preceded by tea at 3.40pm in the level 9 foyer of the School of Mathematics.Thursday 5 October 2006Prof. Robert MacKay FRS (University of Warwick)12 Mathematics Lessons from the Triple Linkage 4pm Roger Stevens Lecture Theatre 14 Abstract: The triple linkage is a mechanical device introduced by Thurston and Weeks to illustrate the idea of a manifold (its configuration space is a surface of genus 3). I will use it to also illustrate concepts from geometry and dynamics. The configuration space carries a natural Riemannian metric (the kinetic energy). Study of this metric with Tim Hunt reveals a parameter regime where the frictionless dynamics is Anosov (uniformly hyperbolic) on each energy level. Uniform hyperbolicity is the mathematically nicest form of chaos, but no physically realistic example was known before. It leads to many consequences, in particular, equivalence to a stochastic process on a partition and Brownian motion at the large scale on any Abelian cover. To make the system really physical, one has to allow friction, but various aspects of the chaos survive this if compensating external forcing is provided. The talk will be preceded by tea at 3.45pm and followed by a wine reception, both in the level 9 foyer of the School of Mathematics.Thursday 13 April 2006Prof. Alexander Kirillov (University of Pennsylvania)Geometry, analysis and arithmetic of fractals 4pm Classroom H, School of Mathematics (note change of venue) Abstract: This is a brief survey of my book "A tale of two fractals", to be published by Moscow Independent University in 2006. The goal is to attract young mathematicians to some beautiful facts and open problems arising in the study of selfsimilar fractals. We consider only two examples: the Sierpinski and Apollonian gaskets (and their manydimensional analogues). The main subject in the first example: analytic and arithmetic properties of harmonic functions. In the second example the main object is the geometric properties of discs and arithmetic properties of their curvatures. We also show some applications of generalized numerical systems to computations with fractals. I believe that this essay gives a good opportunity for young people to test their ability at creative work in mathematics. I mean here not only the solution of wellposed problems, but the recognition of hidden pattern and the formulation of new problems. The talk will be preceded by tea at 3.45pm and followed by a wine reception, both in the level 9 foyer of the School of Mathematics.Thursday 1 December 2005Prof. John Toland FRS (University of Bath)Linking, the Calculus of Variations, and Periodic Orbits of Indefinite Hamiltonian Systems 4pm Roger Stevens Lecture Theatre 13 The talk will be preceded by tea at 3.45pm and followed by a wine reception, both in the level 9 foyer of the School of Mathematics. Thursday 22 September 2005Prof. Jon Keating (University of Bristol)Random matrix theory and the Riemann zeta function 4pm Roger Stevens Lecture Theatre 4 (note change of venue) Abstract: I will review the conjectural link between the Riemann zeros and the eigenvalues of random matrices. I will then describe recent applications of random matrix theory to the value distribution of the Riemann zeta function, and to the distribution of ranks of elliptic curves. The talk will be preceded by tea at 3.40pm and followed by a wine reception, both in the level 9 foyer of the School of Mathematics.This talk is part of a 3 day zeta function/random matrix theory event. The other talks, by Sir Michael Berry (Bristol) and Prof. Boris Altshuler (Princeton) are being organized by Vadim Kuznetsov. Tuesday 26 April 2005Prof. Sir Michael Berry FRS (University of Bristol)Two Universal Asymptotic Oscillatory Phenomena 4pm Roger Stevens Lecture Theatre 20 The talk will be preceded by tea at 3.40pm and followed by a wine reception, both in the level 9 foyer of the School of Mathematics. Tuesday 1 March 2005Prof. Sir Michael Atiyah FRS (University of Edinburgh)The Soliton 4pm Roger Stevens Lecture Theatre 2 Abstract: Solitons, localized solutions of certain partial differential equations which behave like "particles", ie preserve their identity under "collisions", were one of the most remarkable mathematical discoveries of the latter part of the twentieth century. They have been studied extensively by pure mathematicians, applied mathematicians,physicists and engineers . They are a perfect example of something important that transcends traditional boundaries. I will give a survey of past and present developments suitable for a general audience. The talk will be preceded by tea at 3.40pm and followed by a wine reception, both in the level 9 foyer of the School of Mathematics. 
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