# School of Mathematics

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## School Colloquium

There will be a short reception after the talk on level 9. All are very welcome to attend!

Wednesday 28th February, 2018

TBA, 4:00 PM

**Professor Jon Dawes**(

*University of Bath*)

Unpublished patterns of thought: Alan Turing’s later work on morphogenesis

TBA

Thursday 12th October, 2017

MALL, 4:00 PM

**Professor Tom Ward**(

*University of Leeds*)

The space of group automorphisms

I will discuss some of the issues thrown up by attempts to describe the space of all compact group automorphisms modulo various equivalence relations of dynamical significance. Many of the questions are strongly connected to number theory.

Thursday 16th February, 2017

MALL, 4:00 PM

**Dr Lara Alcock**(

*Loughborough University*)

Tilting the Classroom: Engaging Students in Large Lectures

There is much discussion currently about flipping the classroom or otherwise making dramatic adjustments to teaching. But for most lecturers, especially those with large classes, this is not practical. My view is that lectures are not inherently bad, and that that there are numerous ways to make them more engaging without dramatic changes. This talk will be about 18 approaches that I use - these work well together, but each can be implemented independently so they can be tried out according to personal taste. There will be lots of examples and some light-touch discussion of how this approach relates to evidence from psychological research on learning.

Thursday 9th June, 2016

Roger Stevens 16, 4:00 PM

**Professor Rebecca Hoyle**(

*University of Southampton*)

Maternal effects, phenotypic plasticity and environmental change

Maternal effects are the influences of the maternal phenotype on offspring phenotypes by routes other than direct genetic transmission. Potentially they provide an additional means of adaptation to changing environmental conditions over and above that afforded by within-generation phenotypic plasticity. I will present results from a quantitative genetics model of the coevolution of maternal effects and phenotypic plasticity following an abrupt environmental change and during cyclical environmental fluctuations such as seasonal variation. We find that generally the strongest maternal effects occur for traits that experience very strong selection and for which plasticity is severely constrained. For traits experiencing weak selection, phenotypic plasticity enhances the evolutionary scope of maternal effects, but maternal effects attain much smaller values throughout. As weak selection is common, our results suggest that finding substantial maternal influences on offspring phenotypes may be more challenging than anticipated.

Monday 7th March, 2016

MALL 1 & 2, 3:00 PM

**Prof Ernesto Estrada**(

*Department of Mathematics and Statistics, University of Strathclyde*)

Communicability and spatial efficiency of networks

Tuesday 24th November, 2015

MALL, 4:00 PM

**Professor Victor Buchstaber**(

*Moscow State University and Steklov Institute*)

Combinatorial Topology of carbon molecular structures

The talk is devoted to mathematical problems concerning the following carbon molecular structures:
- fullerenes (buckminsterfullerene C60, was prepared in 1985,
- nanotubes(the first macroscopic production was made in 1992),
- grafenes (first measurably produced and isolated in the lab in 2003,
- nonobuds (a material discovered and synthesized in 2006).
At that moment the problem of mathematical classification of such carbon molecular structures is well-known and is vital due to applications in chemistry, physics, biology and nanotechnology.
We will formulate tasks concerning molecular carbon structures in terms of convex polytopes and polygonal partitions of 2-surfaces. The connection of these tasks with known and new mathematical problems will be discussed.
The talk is prepared jointly with N.Yu.Erokhovets. All necessary notions will be explained during the lecture.

Tuesday 17th February, 2015

Roger Stevens 14, 4:00 PM

**Yuji Kodama**(

*Ohio State*)

Combinatorics and geometry of KP solitons and applications to tsunami

Let Gr(N,M) be the real Grassmann variety defined by the set of all N-dimensional
subspaces of R^M. Each point on Gr(N,M) can be represented by an NxM matrix A
of rank N. If all the NxN minors of A are nonnegative, the set of all points associated with those
matrices forms the totally nonnegative part of the Grassmannian, denoted by Gr(N,M)^+.
In this talk, I start to give a realization of Gr(N,M)^+ in terms of the (regular) soliton solutions of the KP
(Kadomtsev-Petviashvili) equation which is a two-dimensional extension of the KdV equation.
The KP equation describes small amplitude and long waves on a surface of shallow water.
I then construct a cellular decomposition of Gr(N,M)^+ with the asymptotic form of the soliton solutions.
This leads to a classification theorem of all solitons solutions of the KP equation, showing that
each soliton solution is uniquely parametrized by a derrangement of the symmetric group S_M.
Each derangement defines a combinatorial object called the Le-diagram (a Young diagram with zeros in
particular boxes). Then I show that the Le-diagram provides a complete classification of the ''entire'' spatial patterns
of the soliton solutions coming from the Gr(N,M)^+ for asymptotic values of the time.
I will also present some movies of real experiments of shallow water waves which represent
some of those solutions obtained in the classification problem.
Finally I will discuss an application of those results to analyze the Tohoku-tsunami on March 2011.
The talk is elementary, and shows interesting connections among combinatorics, geometry and integrable systems.

Tuesday 27th January, 2015

Roger Stevens 21, 4:00 PM

**Professor Sir Michael Berry**(

*University of Bristol*)

Divergent series: from Thomas Bayes’s bewilderment to today’s resurgence via the rainbow

It is important to understand divergent series, because most series encountered in physical applications diverge. Following the discovery by Bayes in 1747 that Stirling’s series for the factorial is divergent, the study of asymptotic series has today reached the stage of enabling summation of the divergent tails of many series with an accuracy far beyond that of the smallest term. Several of these advances sprang from developments of Airy’s theory of waves near optical caustics such as the rainbow. Key understandings by Euler, Stokes, Dingle and Écalle unify the different series corresponding to different parameter domains, culminating in the concept of resurgence: quantifying the way in which the low orders of such series reappear in the high orders.

Friday 14th November, 2014

Roger Stevens 19, 4:00 PM

**Sid Redner**(

*Santa Fe Institute and Department of Physics, Boston University*)

Fate of the Kinetic Ising and Potts Model

What happens when the Ising model that is initially at infinite temperature is suddenly cooled to zero temperature and subsequently evolves by single spin-flip dynamics? In two dimensions, the ground state is reached only about 2/3 of the time, and the evolution is characterized by two distinct time scales, the longer of which arises from topological defects. There is also an intriguing and deep connection between domain topologies and continuum percolation. In three dimensions, the ground state is never reached and (i) domains at long times are topologically complex, with average genus growing algebraically with system size; (ii) "blinker" spins always arise that can flip ad infinitum with no energy cost; (iii) the relaxation time grows exponentially with system size. The zero-temperature coarsening of the q-state Potts model is richer still. In two dimensions, macroscopic avalanches may occur at long times that drive apparently frozen systems to the ground state.

Tuesday 28th October, 2014

Roger Stevens 4, 4:00 PM

**Professor Ben Green**(

*University of Oxford*)

Points and lines

Suppose you have n points in the plane, not all on a line. A famous result called the Sylvester-Gallai theorem states that there must be at least one "ordinary line", by which we mean a line through precisely two points of the set. I will discuss this theorem and then turn to some more recent developments connected with the question of how many ordinary lines there must be. Perhaps unexpectedly, this involves considerations about elliptic curves as well as some results from additive number theory. The talk should be accessible to a general mathematical audience (you won't need to know what an elliptic curve is).

Wednesday 25th June, 2014

MALL 1, 3:00 PM

**Percy Deift**(

*NYU*)

Long-time asymptotics for solutions of the NLS equation with a delta potential and even initial data (LMS Hardy Lecture in Leeds)

We consider the one-dimensional focusing Nonlinear Schroedinger Equation (NLS) with a delta potential at the origin and even initial data. The problem is equivalent to the solution of the initial/boundary problem for NLS on a half-line with Robin boundary conditions at the origin. We study the asymptotic stability of the stationary 1-soliton solution of the equation under perturbation by applying the nonlinear steepest -descent method for Riemann-Hilbert problems.

Friday 28th February, 2014

MALL, School of Mathematics, 4:00 PM

**Professor Michael Keyl**(

*Technische Universität München*)

From the central limit theorem to quantum memory -- fluctuation operators and their applications

Fluctuation operators are introduced in mean field theory to measure
fluctuations of a mean field observable around its expectation value. In
statistical mechanics they can be used to prove a quantum analog of the
central limit theorem: if the particle number goes to infinity and if
correlations decay exponentially fast, the fluctuations of a quantum spin
system behave like a bosonic system (e.g. a harmonic oscillator) in a Gaussian state. We will use this as a starting point to discuss a number of applications of fluctuation operators, which connect different aspects of quantum mechanics, quantum statistics, functional analysis and group theory. This includes in particular: a new class of operators -- called Schwartz operators -- which can be regarded as a non-commutative version of Schwartz functions, the theoretical description of experiments with quantum memory by E. Polzik and others, the asymptotics (large dimensions) of irreducible representations of unitary groups, and (approximate) joint distributions for measurements of non-commuting quantum observables.

Tuesday 23rd October, 2012

MALL, 4:00 PM

**Phil Boyland**(

*University of Florida*)

Entropy efficiency of fluid stirring protocols

When a two-dimensional fluid is stirred by the motion of rods
undergoing a sufficiently complicated topological pattern it
results in exponential growth of the lengths of
material lines (arcs) in the fluid. This, in turn,
implies the growth of gradients of advected scalars
as well as the length of the interface between different
fluid regions. Thus the exponential growth of material
lines is often correlated with enhanced mixing. The
Thurston-Nielsen theory provides techniques for computing
the rates of growth associated with various topological
classes of stirring protocols. We use this theory to optimize
the rate of growth per unit motion of the stirrers for
a class of stirring protocols. The main tool is the
generalized spectral radius as well as its nonlinear
analog, the entropy efficiency.

Tuesday 18th October, 2011

MALL, 4:00 PM

**Professor Megan Clark**(

*School of Mathematics, Statistics and Operations Research, Victoria University of Wellington*)

Transition from Secondary School to University Mathematical Sciences

There is an assumption throughout much of the English-speaking world that the transition from secondary school study in mathematics to first year university should be made a smooth as possible to maximise learning. On the basis of that assumption foundation courses and other mechanisms have been established to address deficits students may have. Based on my work with Lovric (McMaster) this talk argues for a different model of transition that is as least as well justified and may be more effective and satisfying for students.

Tuesday 9th February, 2010

Rupert Beckett Lecture Theatre, Michael Sadler Building, 5:15 PM

**Prof. Sir Michael Atiyah**(

*University of Edinburgh*)

Topology and Quantum Physics (joint with School of Physics & Astronomy)

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 quantum-topology 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 Kelvin’s basic idea has survived but applied at the subatomic level.
The new understanding of the Quantum –Topology link has had a profound effect on both mathematics and theoretical physics, as I hope to indicate.

Wednesday 1st July, 2009

MALL, 4:30 PM

**Professor Stanislav Molchanov**(

*University of North Carolina at Charlotte*)

Reaction-diffusion equations for growth processes and applications to spatial dynamics of biological populations

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 reaction-diffusion (or KPP) equations, perhaps with the negative feedback (in the spirit of the classical works by Fisher and Kolmogorov-Petrovskii-Piskunov). The distribution of the masses of particles is described by a non-standard differential-functional equation (which must catch the mitosis processes) coupled with the KPP equation. The talk will present several analytic results and limit theorems on the space-mass distribution of the particles.

Thursday 26th February, 2009

MALL, 4:30 PM

**Professor Niels Gronbaek**(

*Department of Mathematical Sciences, University of Copenhagen*)

Thematic Projects - making Real Analysis real

In the talk I will describe a development project aiming at furthering independent student work and developing mathematical competencies.

Tuesday 2nd December, 2008

MALL, 4:00 PM

**Professor Nick Trefethen FRS**(

*Oxford University Computing Laboratory*)

CHEBFUNS: A NEW KIND OF NUMERICAL COMPUTING

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 object-oriented 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.

Tuesday 11th November, 2008

MALL, 4:00 PM

**Professor Robert Pego**(

*Carnegie Mellon*)

Self-similarity and the scaling attractor for models of coagulation and clustering

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 random-walk initial data. I'll focus on recent progress regarding a `min-driven' clustering model related to domain coarsening dynamics in the Allen-Cahn equation.

Tuesday 17th June, 2008

MALL, 4:00 PM

**Professor Paul Martin**(

*Leeds*)

Representation theory inspired by computational statistical mechanics

Tuesday 17th June, 2008

MALL, 4:00 PM

**Professor Simon Ruijsenaars**(

*Leeds*)

Calogero-Moser systems: A crossroads in mathematics and physics

Tuesday 29th April, 2008

MALL, 4:30 PM

**Professor Valerie Isham**(

*UCL*)

Space-Time Models for Soil Moisture Dynamics

Soil moisture provides the physical link between soil, climate and vegetation. It increases via the infiltration of rainfall and decreases through evapotranspiration, run-off 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/semi-arid conditions, many transient and equilibrium properties of these models can be determined analytically and used for comparison with data on soil moisture dynamics.

Tuesday 12th February, 2008

MALL, 4:30 PM

**Dr John Ockendon FRS**(

*Oxford Centre for Industrial and Applied Mathematics*)

The ups and downs of Maths in Industry

This talk will be about the work of OCIAM and its various international imitators, and the new mathematical challenges posed by industrial questions.

Tuesday 4th December, 2007

MALL Seminar Room, School of Mathematics, Level 8, 4:30 PM

**Prof. Robin Wilson**(

*Open University*)

Euler --- 300 years on

Abstract: In this talk we look at the life, labours and legacy of Leonhard Euler (1707-1783), 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.

### Colloquia

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