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In recognition of a lifetime's contribution across the mathematical sciences, we are initiating a series of annual Public Lectures in honour of Roger Penrose. The first lecture will be given by his long-time collaborator and friend Stephen Hawking.

Unfortunately the lecture is now sold out and we have a full waiting list. However, we will be podcasting the lecture live (and also via the University of Oxford Facebook page).

A cubic polynomial equation in four or more variables tends to have many integer solutions, while one in two variables has a limited number of such solutions. There is a body of work establishing results along these lines. On the other hand very little is known in the critical case of three variables. For special such cubics, which we call Markoff surfaces, a theory can be developed. We will review some of the tools used to deal with these and related problems.

Joint works with Bourgain/Gamburd and with Ghosh
 

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  ignificantly 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.

Inelastic surface growth associated with continuous creation of incompatibility on the boundary of an evolving body is behind a variety of both natural processes (embryonic development,  tree growth) and technological processes (dam construction, 3D printing). Despite the ubiquity of such processes, the mechanical aspects of surface growth are still not fully understood. In this talk we present  a new approach to surface growth that allows one to address inelastic effects,  path dependence of the growth process and the resulting geometric frustration. In particular, we show that incompatibility developed during deposition can be fine-tuned to ensure a particular behaviour of the system in physiological (or working) conditions. As an illustration, we compute an explicit deposition protocol aimed at "printing" arteries, that guarantees the attainment of desired stress distributions in physiological conditions. Another illustration is the growth starategy for explosive plants, allowing a complete release of residual elastic energy with a single cut.

In this talk Michael Bonsall will explore how we can use mathematics to link between scales of organisation in biology. He will delve in to developmental biology, ecology and neurosciences, all illustrated and explored with real life examples, simple games and, of course, some neat maths.

Michael Bonsall is Professor of Mathematical Biology in Oxford.

7 February 2018, 5pm-6pm, Mathematical Institute, Oxford

Please email @email to register or watch online: https://livestream.com/oxuni/bonsall

Archimedes, who famously jumped out of his bath shouting "Eureka", also invented $\pi$. 

Euler invented $e$ and had fun with his formula $e^{2\pi i} = 1$

The world is full of important numbers waiting to be invented. Why not have a go ?

Michael Atiyah is one of the world's foremost mathematicians and a pivotal figure in twentieth and twenty-first century mathematics. His lecture will be followed by an interview with Sir John Ball, Sedleian Professor of Natural Philosophy here in Oxford where Michael will talk about his lecture, his work and his life as a mathematician.

Please email @email to register.

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

Prime numbers have intrigued, inspired and infuriated mathematicians for millennia and yet mathematicians' difficulty with answering simple questions about them reveals their depth and subtlety. 

Join Vicky to learn about recent progress towards proving the famous Twin Primes Conjecture and to hear the very different ways in which these breakthroughs have been made - a solo mathematician working in isolation, a young mathematician displaying creativity at the start of a career, a large collaboration that reveals much about how mathematicians go about their work.  

Vicky Neale is Whitehead Lecturer at the Mathematical Institute, University of Oxford and Supernumerary Fellow at Balliol College.

Please email @email to register.

In our Oxford Mathematics Christmas Lecture Alex Bellos challenges you with some festive brainteasers as he tells the story of mathematical puzzles from the middle ages to modern day. Alex is the Guardian’s puzzle blogger as well as the author of several works of popular maths, including Puzzle Ninja, Can You Solve My Problems? and Alex’s Adventures in Numberland.

Please email @email to register.

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 @email to register

Can mathematics really help us in our fight against infectious disease? Join Julia Gog as we explore some exciting current research areas where mathematics is being used to study pandemics, viruses and everything in between, with a particular focus on influenza.

Julia Gog is Professor of Mathematical Biology, University of Cambridge and David N Moore Fellow at Queens’ College, Cambridge.

Please email: @email to regsiter