Lewis Fry Richardson Lectures

2023, Feb 22

4.30pm

Professor Joern Sesterhenn (Bayreuth)

Title: Of big whirls and little whirls and how to find them in a turbulent flow

Abstract: Our brain readily sees structure in a turbulent flow -- but how can we quantify structures? Over the last decades a multitude of methods were
proposed. Most of them are either defined in Fourier-space or based on
the velocity gradient tensor. Both types of methods are inherently quasi-stationary. Other methods look at material lines in the flow which form a barrier which no mass can pass. These "particle-based" methods are time-dependent, but material by construction. Structures based on energy will not be detected. When considering for example a vortex, angular momentum, which is at the root of the conservation of the motion, will play no direct role in their identification.

In this talk we propose a dynamical approach: Analogous to what one thinks is a wave, we define as a structure something, which is transported in the flow with as little change as possible and is recognized later on as such. In mathematical terms, this means that we introduce a space-time transform such that in this new reference frame some hyper-surface of the flow quantities is constant along the time-like direction, akin to a characteristic surface in hyperbolic equations.

This is achieved by an optimization for finding the characteristic direction and a Dynamic Mode Decomposition in the transformed space to identify the long-lived structures. The result, after transformation back to the physical frame of reference, is a set of structures which can divided rather unambiguously in three groups: Big Whirls, little whirls and lesser whirls. Big and little whirls -- they are but a few -- are able to reproduce the energy spectrum of the full flow. The lesser whirls can be shown to feed on the big ones and to dissipate the turbulent kinetic energy.

2019, Oct 16

Professor Pablo Shmerkin (T. Di Tella University and CONICET)

Title: Distance sets: the problems of Erdös and Falconer

Abstract: What is the relationship between the sizes of a subset of the plane and the set of distances spanned by pairs of points in the set? This very simple question gave rise to deep problems, many of which remain open. In the talk I'll give a general introduction to these problems and present some recent contributions obtained jointly with T. Keleti

2019, Jan 31

Professor Richard John Samworth (University of Cambridge)

Title: Statistical challenges with Big Data

Abstract: The ability to collect and store data on previously unimaginable scales has transformed the field of Statistics, creating both enormous opportunities and fundamental new challenges. I will try to give some indication of the ways in which the landscape has changed, with a focus on the modern problem of variable selection.

2018, Jun 14

Professor Samuel James Patterson (Universität Göttingen)

Title: Chains, drums and the Riemann Hypothesis

2018, Jan 31

Professor Gary Gibbons FRS (University of Cambridge)

Title: Applying null geodesic in a Lorentzian spacetimes to problems unconnected with General Relativity

Abstract: The problem of finding null geodesics in a stationary spacetime may be reduced to solving a Zermelo problem or a Randers--Finsler problem in a Riemannian manifold and conversely those two problems can be lifted to the null geodesic problem in a stationary spacetime. More generally, any natural dynamical problem may be lifted to the null-geodsic flow of a Lorentzian manifold.  In my talk I will explain this connection and give some recent examples of its use.

2017, Nov 15

Professor Julia Yeomans FRS (University of Oxford)

Title: Dense active matter: topology in biology

Abstract: Active materials such as bacteria, molecular motors and self-propelled colloids, are Nature’s engines. They continuously transform chemical energy from their environment to mechanical work. Dense active matter shows mesoscale turbulence, the emergence of chaotic flow structures characterised by high vorticity and topological defects. I shall discuss how dense active matter might be harnessed to provide energy, the transition to mesoscale turbulence in channels, and its relevance to cell motility and cell division. In particular I shall give examples of how topological defects, which are important in the physics of liquid crystals, may be of relevance in biological systems.

2017, Jun 01

Professor Dominic Joyce FRS (University of Oxford)

Title: What is a derived manifold?

Abstract: The Derived Algebraic Geometry of Jacob Lurie and Toen-Vezzosi is a generalization of classical Algebraic Geometry in which schemes and stacks are replaced by infinity-categories of "derived schemes" and "derived stacks", which have a richer geometric structure. There is a much less well-known subject of Derived Differential Geometry, a generalization of classical Differential Geometry in which smooth manifolds and orbifolds are replaced by "derived manifolds” and “derived orbifolds”, and this talk will give an introduction to it.
Derived manifolds and orbifolds live in a 2-category, or an infinity-category, depending on the model. As topological spaces, derived manifolds may be very singular — for example, the Mandelbrot set can be made into a derived manifold — but nonetheless much of the geometry of manifolds extends to derived manifolds in a nice way. One property important for applications is that compact, oriented derived manifolds have "virtual cycles” in integral homology, generalizing the fundamental class of a compact oriented manifold, so derived manifolds can be used in the theory of enumerative invariants. Moduli spaces of solutions of nonlinear elliptic equations on compact manifolds, which are important in several areas of geometry, have the structure of derived manifolds or derived orbifolds. "Kuranishi spaces" in symplectic geometry are actually a kind of derived orbifold.

2017, Jan 11

Professor Martin Hairer FRS (University of Warwick)

Title: Taming the Infinities

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.

2016, Oct 26

Professor Kenneth Falconer FRSE (University of St Andrews)

Title: Projections of Fractals - Old and New

Abstract: I will discuss dimensional and other properties of orthogonal projections of fractals. The subject has a history going back over 60 years but there have been some very interesting recent developments involving ideas from dynamics and ergodic theory.

2016, Mar 2

Professor Jens Marklof FRS (University of Bristol)

Title: Emerging applications of homogeneous flows: From discrete mathematics to statistical physics

Abstract: The theory of homogeneous flows provides a powerful mathematical toolkit that has recently contributed to the solution of a number of longstanding problems. I will survey some of the recent progress, including a study of distances in multi-loop networks (circulant graphs), the coin exchange problem and the derivation of a new kinetic equation which captures surprising transport phenomena in crystals and quasicrystals. This lecture is aimed at a broad audience.

2015, Nov 11

The inaugural LFR lecture

Professor Julian C R Hunt FRS, Baron Hunt of Chesterton

Title: Systems, patterns, and idealism -- Lewis Fry Richardson's inspiration

Abstract: http://www.annualreviews.org/doi/abs/10.1146/annurev.fluid.30.1.0