Oxford Mathematics and the Clay Mathematics Institute Public Lectures

Roger Penrose - Eschermatics
24 September 2018 - 5.30pm

Roger Penrose’s work has ranged across many aspects of mathematics and its applications from his influential work on gravitational collapse to his work on quantum gravity. However, Roger has long had an interest in and influence on the visual arts and their connections to mathematics, most notably in his collaboration with Dutch graphic artist M.C. Escher. In this lecture he will use Escher’s work to illustrate and explain important mathematical ideas.

Oxford Mathematics is hosting this special event in its Public Lecture series during the conference to celebrate the 20th Anniversary of the foundation of the Clay Mathematics Institute. After the lecture Roger will be presented with the Clay Award for the Dissemination of Mathematical Knowledge.

5.30-6.30pm, Mathematical Institute, Oxford

Please email @email to register.

Watch live:

https://www.facebook.com/OxfordMathematics
https://livestream.com/oxuni/Penrose

The Oxford Mathematics Public Lectures are generously supported by XTX Markets.

Mathematical models based on first principles can describe the interaction between electrical, mechanical and fluid-dynamical processes occurring in the heart. This is a classical multi-physics problem. Appropriate numerical strategies need to be devised to allow for an effective description of the fluid in large and medium size arteries, the analysis of physiological and pathological conditions, and the simulation, control and shape optimisation of assisted devices or surgical prostheses. This presentation will address some of these issues and a few representative applications of clinical interest.

It is at first sight surprising that a minimizer of an integral of the calculus of variations may make the integrand infinite somewhere.

This talk will discuss some examples of this phenomenon, how it can be related to material defects, and related open questions from nonlinear elasticity and the theory of liquid crystals.

Details to follow

Hall algebras of categories of quiver representations and coherent sheaves

on smooth projective curves over F_q recover interesting

representation-theoretic objects such as quantum groups and their

generalizations. I will define and describe the structure of the Hall

algebra of coherent sheaves on a projective variety over F_1, with P^2 as

the main example. Examples suggest that it should be viewed as a degenerate

q->1 limit of its counterpart over F_q.

We discuss the recent achievements in the attractors theory for damped wave equations in bounded domains which are related with Strichartz type estimates. In particular, we present the results related with the well-posedness and asymptotic smoothness of the solution semigroup in the case of critical quintic nonlinearity. The non-autonomous case will be also considered.
 

An important and relevant topic at Thales is 1-3 composite modelling capability. In particular, sensitivity enhancement through design.

A simplistic model developed by Smith and Auld1 has grouped the polycrystalline active and filler materials into an effective homogenous medium by using the rule of weighted averages in order to generate “effective” elastic, electric and piezoelectric properties. This method had been further improved by Avellaneda & Swart2. However, these models fail to provide all of the terms necessary to populate a full elasto-electric matrix – such that the remaining terms need to be estimated by some heuristic approach. The derivation of an approach which allowed all of the terms in the elasto-electric matrix to be calculated would allow much more thorough and powerful predictions – for example allowing lateral modes etc. to be traced and allow a more detailed design of a closely-packed array of 1-3 sensors to be conducted with much higher confidence, accounting for inter-elements coupling which partly governs the key field-of-view of the overall array. In addition, the ability to populate the matrix for single crystal material – which features more independent terms in the elasto-electric matrix than conventional polycrystalline material- would complement the increasing interest in single crystals for practical SONAR devices.

1.“Modelling 1-3 Composite Piezoelectrics: Hydrostatic Response” – IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control 40(1):41-

2.“Calculating the performance of 1-3 piezoelectric composites for hydrophone applications: An effective medium approach” The Journal of the Acoustical Society of America 103, 1449, 1998