Past Forthcoming Seminars

14 November 2017
14:00
Federico Danieli
Abstract

Time parallelisation techniques provide an additional direction for the parallelisation of the solution of time-dependent PDEs or of systems of ODEs. In particular, the Parareal algorithm has imposed itself as the canonical choice to achieve parallelisation in time, also because of its simplicity and flexibility. The algorithm works by splitting the time domain in chunks, and iteratively alternating a prediction step (parallel), in which a "fine" solver is employed to achieve a high-accuracy solution within each chunk, to a correction step (serial) where a "coarse" solver is used to quickly propagate the update between the chunks. However, the stability of the method has proven to be highly sensitive to the choice of fine and coarse solver, even more so when applied to chaotic systems or advection-dominated problems.


In this presentation, an alternative formulation of Parareal is discussed. This aims to conduct the update by estimating directly the sensitivity of the solution of the integration with respect to the initial conditions, thus eliminating altogether the necessity of choosing the most apt coarse solver, and potentially boosting its convergence properties.

 

  • Numerical Analysis Group Internal Seminar
14 November 2017
12:45
Abstract

Many species of insects adhere to vertical and inverted surfaces using footpads that secrete thin films of a mediating fluid. The fluid bridges the gap between the foot and the target surface. The precise role of this liquid is still subject to debate, but it is thought that the contribution of surface tension to the adhesive force may be significant. It is also known that the footpad is soft, suggesting that capillary forces might deform its surface. Inspired by these physical ingredients, we study a model problem in which a thin, deformable membrane under tension is adhered to a flat, rigid surface by a liquid droplet. We find that there can be multiple possible equilibrium states, with the number depending on the applied tension and aspect ratio of the system. The presence of elastic deformation significantly enhances the adhesion force compared to a rigid footpad. A mathematical model shows that the equilibria of the system can be controlled via two key parameters depending on the imposed separation of the foot and target surface, and the tension applied to the membrane. We confirm this finding experimentally and show that the system may transition rapidly between two states as the two parameters are varied. This suggests that different strategies may be used to adhere strongly and then detach quickly.

  • Junior Applied Mathematics Seminar
14 November 2017
12:00
to
13:15
Tim Adamo
Abstract

We consider two-dimensional chiral, first-order conformal field theories governing maps from the Riemann sphere to the projective light cone inside Minkowski space -- the natural setting for describing conformal field theories in two fewer dimensions. These theories have a SL(2) algebra of local bosonic constraints which can be supplemented by additional fermionic constraints depending on the matter content of the theory. By computing the BRST charge associated with gauge fixing these constraints, we find anomalies which vanish for specific target space dimensions. These critical dimensions coincide precisely with those for which (biadjoint) cubic scalar theory, gauge theory and gravity are classically conformally invariant. Furthermore, the BRST cohomology of each theory contains vertex operators for the full conformal multiplets of single field insertions in each of these space-time CFTs. We give a prescription for the computation of three-point functions, and compare our formalism with the scattering equations approach to on-shell amplitudes.

14 November 2017
12:00
Andrew Mellor
Abstract

Temporal networks are increasingly being used to model the interactions of complex systems. 
Most studies require the temporal aggregation of edges (or events) into discrete time steps to perform analysis.
In this article we describe a static, behavioural representation of a temporal network, the temporal event graph (TEG).
The TEG describes the temporal network in terms of both inter-event time and two-event temporal motifs.
By considering the distributions of these quantities in unison we provide a new method to characterise the behaviour of individuals and collectives in temporal networks as well as providing a natural decomposition of the network.
We illustrate the utility of the TEG by providing examples on both synthetic and real temporal networks.

13 November 2017
17:00
Brendan Owens
Abstract

I will report on a joint project with Frank Swenton whose goal is to develop an algorithm to determine whether an alternating knot is ribbon.  We can’t do this yet but we have an algorithm that has been remarkably, and indeed mysteriously, successful in finding a great deal of new slice knots.

13 November 2017
17:00
Allan McRobie
Abstract

There is a deep connection between the stability of oil rigs, the bending of light during gravitational lensing and the act of life drawing. To understand each, we must understand how we view curved surfaces. We are familiar with the language of straight-line geometry – of squares, rectangles, hexagons - but curves also have a language – of folds, cusps and swallowtails - that few of us know.

Allan will explain how the key to understanding the language of curves is René Thom’s Catastrophe Theory, and how – remarkably – the best place to learn that language is perhaps in the life drawing class. Sharing its title with Allan's new book, the talk will wander gently across mathematics, physics, engineering, biology and art, but always with a focus on curves.

Warning: this talk contains nudity.

Allan McRobie is Reader in Engineering, University of Cambridge

Please email external-relations@maths.ox.ac.uk to register

13 November 2017
16:00
Anna Siffert
Abstract

We prove that for closed surfaces of fixed topological type, orientable or non-orientable, there exists a unit volume metric, smooth away from finitely many conical singularities, that
maximizes the first eigenvalue of the Laplace operator among all unit volume metrics. The key ingredient are several monotonicity results, which have partially been conjectured to hold before. This
is joint work with Henrik Matthiesen.

  • Partial Differential Equations Seminar
13 November 2017
15:45
Lisa Carbone
Abstract

The Monster Lie algebra m, which admits an action of the Monster finite simple group M, was constructed by Borcherds as part of his program to solve the Conway-Norton conjecture about the representation theory of M. We associate the analog of a Lie group G(m) to the Monster Lie algebra m. We give generators for large free subgroups and we describe relations in G(m).

13 November 2017
15:45
KURUSCH EBRAHIMI-FARD
Abstract

Abstract: Butcher’s B-series is a fundamental tool in analysis of numerical integration of differential equations. In the recent years algebraic and geometric understanding of B-series has developed dramatically. The interplay between geometry, algebra and computations reveals new mathematical landscapes with remarkable properties. 

The shuffle Hopf algebra,  which is fundamental in Lyons’s groundbreaking work on rough paths,  is based on Lie algebras without additional properties.  Pre-Lie algebras and the Connes-Kreimer Hopf algebra are providing algebraic descriptions of the geometry of Euclidean spaces. This is the foundation of B-series and was used elegantly in Gubinelli’s theory of Branched Rough Paths. 
Lie-Butcher theory combines Lie series with B-series in a unified algebraic structure based on post-Lie algebras and the MKW Hopf algebra, which is giving algebraic abstractions capturing the fundamental geometrical properties of Lie groups, homogeneous spaces and Klein geometries. 

In these talks we will give an introduction to these new algebraic structures. Building upon the works of Lyons, Gubinelli and Hairer-Kelly, we will present a new theory for rough paths on homogeneous spaces built upon the MKW Hopf algebra.

Joint work with: Charles Curry and Dominique Manchon

  • Stochastic Analysis Seminar

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