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Euler’s equation, the ‘most beautiful equation in mathematics’, startlingly connects the five most important constants in the subject: 1, 0, π, e and i. Central to both mathematics and physics, it has also featured in a criminal court case and on a postage stamp, and has appeared twice in The Simpsons. So what is this equation – and why is it pioneering?

Robin Wilson is an Emeritus Professor of Pure Mathematics at the Open University, Emeritus Professor of Geometry at Gresham College, London, and a former Fellow of Keble College, Oxford.

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

Please email @email to register

Dr Nicola Beer heads up the Department of Stem Cell Engineering at the new Novo Nordisk Research Centre Oxford. Her team will use human stem cells to derive metabolically-relevant cells and tissues such as islets, hepatocytes, and adipocytes todiscover novel secreted factors and corresponding signalling pathways which modify cell function, health, and viability. Bycombining in vitro-differentiated human stem cell-derived models with CRISPR and other genomic targeting techniques, the teamassay cell function from changes in a single gene up to a genome-wide scale. Understanding the genes and pathways underlying cell function (and dysfunction) highlights potential targets for new Type 2 Diabetes therapeutics. Dr Beer will talk about the work ongoing in her team, as well as more broadly about the role of human stem cells in drug discovery and patient treatment.

Oxford Mathematics Public Lectures
Hooke Lecture

Michael Berry - Chasing the dragon: tidal bores in the UK and elsewhere
15 November 2018 - 5.15pm

In some of the world’s rivers, an incoming high tide can arrive as a smooth jump decorated by undulations, or as a breaking wave. The river reverses direction and flows upstream.

Understanding tidal bores involves

· analogies with tsunamis, rainbows, horizons in relativity, and ideas from  quantum physics;

· the concept of a ‘minimal model’ in mathematical explanation;

· different ways in which different cultures describe the same thing;

· the first unification in fundamental physics.

Michael Berry is Emeritus Professor of Physics, H H Wills Physics Laboratory, University of Bristol

5.15pm, Mathematical Institute, Oxford

Please email @email to register.

Watch live:

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

Oxford Mathematics Public Lectures are generously supported by XTX Markets.

In this lecture Persi Diaconis will take a look at some of our most primitive images of chance - flipping a coin, rolling a roulette wheel and shuffling cards - and via a little bit of mathematics (and a smidgen of physics) show that sometimes things are not very random at all. Indeed chance is sometimes confused with frequency and this confusion caries over to a confusion between chance and evidence. All of which explains our wild misuse of probability and statistical models.

Persi Diaconis is world-renowned for his study of mathematical problems involving randomness and randomisation. He is the co-author of 'Ten Great Ideas about Chance (2017) and is the Mary V. Sunseri Professor of Statistics and Mathematics at Stanford University. 

Please email @email to register.

Watch live:

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

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

Richard Wade:   Classifying spaces, automorphisms, and right-angled Artin groups 

Right-angled Artin groups (otherwise known as partially commutative groups, or graph groups), interpolate between free abelian groups and free groups. These groups have seen a lot of attention recently, much of this due to some surprising links to the world of hyperbolic 3-manifolds.We will look at classifying spaces for such groups and their associated automorphism groups. These spaces are useful as they give a topological way to understand algebraic invariants of groups. This leads us to study some beautiful mathematical objects: deformation spaces of tori and trees. We will look at some recent results that aim to bridge the gap between these two families of spaces.
 
Andrey Kormilitzin:   Learning from electronic health records using the theory of rough paths

In this talk, we bring the theory of rough paths to the study of non-parametric statistics on streamed data and particularly to the problem of regression and classification, where the input variable is a stream of information, and the dependent response is also (potentially) a path or a stream.  We informally explain how a certain graded feature set of a stream, known in the rough path literature as the signature of the path, has a universality that allows one to characterise the functional relationship summarising the conditional distribution of the dependent response. At the same time this feature set allows explicit computational approaches through machine learning algorithms.

Finally, the signature-based modelling can be applied to some real-world problems in medicine, in particular in mental health and gastro-enterology.

Laura Capuano's talk 'Pell equations and continued fractions in number theory'

The classical Pell equation has an extraordinary long history and it is very useful in many different areas of number theory. For example, they given a way to write a prime congruent to 1 modulo 4 as a sum of two squares, or they can also be used to break RSA excryption when the decription key is too small. In this talk, I will present some properties of this wonderful equation and its relation with continued fractions. I will also treat the case of Pell equations in other contexts, such as the ring of polynomials, showing the differences with the classical case. 

Noemi Picco's talk 'Cortical neurogenesis: how humans (and mathematicians) can do more than macaque, with less'

The cerebral cortex is perhaps the crowning achievement of evolution and is the region of the brain that distinguishes us from other species. Studying the developmental programmes that generate cortices of different sizes and neuron counts, is the key to understanding both brain evolution and disease. I will show what mathematical modeling has to say about cortex evolution, when data resolution is poor. I will then discuss why humans are so special in the way they create their cortex, and how we are just like everybody else in many other aspects of brain development.

It is thought that the hairy legs of water walking arthropods are able to remain clean and dry because the flexibility of the hairs spontaneously moves drops off the hairs. We present a mathematical model of this bending-induced motion, or bendotaxis, and study how it performs for wetting and non-wetting drops. Crucially, we show that both wetting and non-wetting droplets move in the same direction (using physical arguments and numerical solutions). This suggests that a surface covered in elastic filaments (such as the hairy leg of insects) may be able to universally self-clean. To quantify the efficiency of this effect, we explore the conditions under which drops leave the structure by ‘spreading’ rather than translating and also how long it takes to do so.

The theory of metric measure spaces with Ricci curvature from below is growing very quickly, both in the "Riemannian" class RCD and the general  CD one. I will review some of the most recent results, by illustrating the key identification results and technical tools (at the level of calculus in metric measure spaces) underlying these results.