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Johann Sebastian Bach was the most mathematical of composers. Oxford Mathematician and Cambridge organ scholar James Sparks will explain just how mathematical and City of London Sinfonia will elaborate with a special performance of the Goldberg Variations. 

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James Sparks - Bach and the Cosmos (30 minutes)

City of London Sinfonia - J S Bach arr. Sitkovetsky, Goldberg Variations (70 minutes)

Alexandra Wood - Director/Violin

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Watch live:
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https://www.livestream.com/oxuni/Bach-Cosmos

The Oxford Mathematics Public Lectures are generously supported by XTX Markets

Consider a network of agents connected by communication links, where each agent holds a real value. The gossip problem consists in estimating the average of the values diffused in the network in a distributed manner. Current techniques for gossiping are designed to deal with worst-case scenarios, which is irrelevant in applications to distributed statistical learning and denoising in sensor networks. We design second-order gossip methods tailor-made for the case where the real values are i.i.d. samples from the same distribution. In some regular network structures, we are able to prove optimality of our methods, and simulations suggest that they are efficient in a wide range of random networks. Our approach of gossip stems from a new acceleration framework using the family of orthogonal polynomials with respect to the spectral measure of the network graph (joint work with Raphaël Berthier, and Pierre Gaillard).

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.