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Claudia Scheimbauer

Title: Quantum field theory meets higher categories

Abstract: Studying physics has always been a driving force in the development of many beautiful pieces of mathematics in many different areas. In the last century, quantum field theory has been a central such force and there have been several fundamentally different approaches using and developing vastly different mathematical tools. One of them, Atiyah and Segal's axiomatic approach to topological and conformal quantum field theories, provides a beautiful link between the geometry of "spacetimes” (mathematically described as cobordisms) and algebraic structures. Combining this approach with the physical notion of "locality" led to the introduction of the language of higher categories into the topic. The Cobordism Hypothesis classifies "fully local" topological field theories and gives us a recipe to construct examples thereof by checking certain algebraic conditions generalizing the existence of the dual of a vector space. I will give an introduction to the topic and very briefly mention on my own work on these "extended" topological field theories.

Alberto Paganini

Title: Shape Optimization with Finite Elements

Abstract: Shape optimization means looking for a domain that minimizes a target cost functional. Such problems are commonly solved iteratively by constructing a minimizing sequence of domains. Often, the target cost functional depends on the solution to a boundary value problem stated on the domain to be optimized. This introduces the difficulty of solving a boundary value problem on a domain that changes at each iteration. I will suggest how to address this issue using finite elements and conclude with an application from optics.

Research suggests that students with a 'growth mindset' may do better than those with a 'fixed mindset'.

• What does that mean for our teaching?
• How can we support students to develop a growth mindset?
• What sorts of mindsets do we ourselves have?
• And how does that affect our teaching and indeed the rest of our work?

Jan Sbierski

Title: On the unique evolution of solutions to wave equations

Abstract: An important aspect of any physical theory is the ability to predict the future of a system in terms of an initial configuration. This talk focuses on wave equations, which underlie many physical theories. We first present an example of a quasilinear wave equation for which unique predictability in fact fails and then turn to conditions which guarantee predictability. The talk is based on joint work with Felicity Eperon and Harvey Reall.

Andrew Krause

Title: Surprising Dynamics due to Spatial Heterogeneity in Reaction-Diffusion Systems

Abstract: Since Turing's original work, Reaction-Diffusion systems have been used to understand patterning processes during the development of a variety of organisms, as well as emergent patterns in other situations (e.g. chemical oscillators). Motivated by understanding hair follicle formation in the developing mouse, we explore the use of spatial heterogeneity as a form of developmental tuning of a Turing pattern to match experimental observations of size and wavelength modulation in embryonic hair placodes. While spatial heterogeneity was nascent in Turing's original work, much work remains to understand its effects in Reaction-Diffusion processes. We demonstrate novel effects due to heterogeneity in two-component Reaction-Diffusion systems and explore how this affects typical spatial and temporal patterning. We find a novel instability which gives rise to periodic creation, translation, and destruction of spikes in several classical reaction-diffusion systems and demonstrate that this periodic spatiotemporal behaviour appears robustly away from Hopf regimes or other oscillatory instabilities. We provide some evidence for the universal nature of this phenomenon and use it as an exemplar of the mostly unexplored territory of explicit heterogeneity in pattern formation.
 

Both in the real and in the p-adic case, I will talk about recent results about C^r-parameterizations and their diophantine applications.  In both cases, the dependence on r of the number of parameterizing C^r maps plays a role. In the non-archimedean case, we get as an application new bounds for rational points of bounded height lying on algebraic varieties defined over finite fields, sharpening the bounds by Sedunova, and making them uniform in the finite field. In the real case, some results from joint work with Pila and Wilkie, and also beyond this work, will be presented, 
in relation to several questions raised by Yomdin. The non-archimedean case is joint work with Forey and Loeser. The real case is joint work with Pila and Wilkie, continued by my PhD student S. Van Hille.  Some work with Binyamini and Novikov in the non-archimedean context will also be mentioned. The relations with questions by Yomdin is joint work with Friedland and Yomdin. 

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.

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

The Simonyi Lecture is an annual lecture under the auspices of the Charles Simonyi Professor for the Public Understanding of Science, Marcus du Sautoy. It is not part of the Oxford Mathematics Public Lectures series but its themes and topics touch not only on mathematics but the wider natural sciences and beyond. All are very welcome and there is no need to register.

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In this year’s Simonyi Lecture Geoffrey West discusses universal laws that govern everything from growth to mortality in plants, animals, cities and companies. These remarkable laws originate in the networks that sustain life from circulatory to social systems and help us address big, urgent questions from population explosion, urbanization, lifespan and cancer, to the accelerating pace of life and global sustainability. Why do we stop growing and live about 100 years rather than 1000, or just two like mice? Why do we sleep eight hours a day and not three like elephants? Why do all companies and people die whereas cities keep growing? How are these related to innovation, wealth creation, and “singularities”? And is any of this sustainable? 

Geoffrey West is a theoretical physicist whose primary interests have been in fundamental questions in physics, biology and social organizations  West is a distinguished professor at the Sante Fe Institute, where he served as the president from 2004-2008. He is author of the recent best-selling book 'Scale'.