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The show goes on and that means the vital role of explaining what we do and what you need to do to join us as a student in Oxford Mathematics.

Our two Open Days will do just that. Admissions Guru James Munro will be live, talking about life in Oxford, explaining the Admissions process and, together with some of our students, answering any questions you want to ask. In addition there will be talks covering different aspects of the curriculum.

So please join us. All you have to do is go to this page a few minutes before 10.30am on each of the next two Saturdays (25 April & 2 May) and all will be explained, including how to ask questions in real time. The talks will all remain available after the livestream finishes.

Take care all

Yesterday, April 8th, Oxford Mathematician Robin Thompson gave a hugely well-received Oxford Mathematics Online Public Lecture on how mathematicians model infectious diseases such as COVID-19. We hope that it will continue to provide a useful introduction to mathematical models of infectious disease outbreaks (and how they can inform public health measures). It would be impossible to answer all of the questions that have been submitted, but we have selected eleven at random (we are mathematicians after all), and Robin has answered them here.

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Thanks for the lecture. Just a quick question: in the models, why do social distancing measures affect the infection rate (beta)?
Chris, via email

Thanks for your question, Chris. The parameter beta represents the infection rate between pairs of infectious and susceptible hosts. Beta therefore depends on the contact rate between infectious and susceptible hosts, as well as the probability of infection per contact. If a social distancing strategy is introduced, then the contact rate between infectious and susceptible hosts decreases (everyone in the population has fewer contacts). As a result, beta decreases.

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Is it clear that the R state exists for coronavirus?
Nic, via Vimeo live chat

The epidemiology of the novel coronavirus is still not fully understood. However, it is unlikely that individuals who have recovered from COVID-19 can be reinfected soon afterwards, due to the body’s antibody response. How long this antibody response lasts for is as yet unknown, but immunologists think that it is likely to be months or years.

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Why is the contact matrix not symmetric?
Jerome, via Vimeo live chat

A few different people asked this question. Any two specific individuals will of course have the same number of contacts with each other. However, in general, an individual of age x may have a different number of contacts with individuals of age y than an individual of age y has with individuals of age x. This is because there are different numbers of individuals in different age groups.

For example, imagine a tiny population of five people, consisting of a grandparent and their four grandchildren. Suppose that the grandparent contacts each grandchild once per week. Then, in this small population, the grandparent would have four contacts per week with younger individuals, but each younger individual would only have one contact per week with grandparents.

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How do you estimate uncertainty in your parameter estimation?
Alexey, via Vimeo live chat

Great question, Alexey. I am guessing that you are a mathematician, so I can give a relatively technical answer! There are a number of ways to include uncertainty in estimates of the parameters governing disease transmission. For the stochastic simulation models, one way to do this is to estimate parameter values using a statistical inference technique such as Markov chain Monte Carlo, which generates a (joint) posterior distribution for the parameter values. Then, in each forward simulation, we sample the parameter values at random from the posterior, giving a wide range of possible future dynamics. It is really important that this entire range of forecasts is communicated to policy-makers who are making decisions about which public health measures to introduce.

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Thank you from Spain. I’m a mathematician, not an expert in this area, and I would like to ask for some bibliography regarding epidemiological models, and their mathematical properties. I’m mainly interested in deterministic models.
Jorge, via Facebook

There are some excellent resources about epidemiological modelling that are available. One book that I have found particularly useful is Keeling and Rohani’s 'Modeling Infectious Diseases in Humans and Animals'. Another useful book for mathematicians about the mathematical properties of epidemic models is 'Mathematical Epidemiology of Infectious Diseases' by Diekmann and Heesterbeek. But there are lots of other resources out there – some of which are online and available for free!

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For data on values such as Beta and Lambda, do researchers rely on pre-existing processed data or do they gather data in real time and process it?
Omar, via Facebook

This is a great question, Omar. Usually, epidemiological modellers rely on both of these approaches – some parameter values are estimated using existing data (or observations from previous outbreaks, for diseases that cause recurring outbreaks) and others are estimated and updated in real-time as an outbreak is ongoing. This real-time estimation is usually carried out by fitting the transmission model to data on, for example, the numbers of cases or deaths per day.

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The parameter beta in the SI model is the same for the S-equation and the I-equation – why is that?
Ana, via Facebook

Hi Ana, thanks for your question. The idea there is that individuals move from the susceptible class (S) to the infectious class (I) when they contract the virus – so the same number of individuals leave S as enter I. The parameter beta determines the rate at which individuals leave S and enter I, and so it is the same in both equations (one equation for leaving S, and the other for entering I).

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How do we/can we understand the different outcomes between a relatively light and relatively strict lockdown?
Andrew, via Twitter

Models can be used to explore how case numbers are likely to change under different potential control measures. To consider the difference between a light and strict lockdown, the key change is likely to be the number of contacts that individuals in the population make. This can be adjusted in the models by changing the value of the infection rate parameter, beta.

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Why don’t the models of lockdown account for the economic impact and the downstream suicide rate?
Richard, via Email

This is a very important question. The potential economic impacts of control interventions and mental health effects should definitely be factored into decisions being made by policy-makers. Outputs from the models presented here could in theory be taken and used for additional analyses assessing the economic impacts and downstream suicide rates. Crucially, the output from models like those presented here represents only one of a range of factors that policy-makers should consider when deciding which interventions to introduce. Responses to infectious disease outbreaks rely on expertise from individuals in a range of fields.

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Superb talk! How is R0 affected by COVID-19’s ability to remain infectious on surfaces?
Sarah, via Twitter

This is a great question – thanks Sarah! COVID-19 infections can occur via a number of different routes, including inhalation of droplets, transfer via contaminated surfaces, and possibly faecal-oral transmission. In principle, R0 can be split up according to each of these different components. R0 can then be calculated as the sum of the reproduction number values for each mode of transmission. 

An excellent study by Christophe Fraser’s team here in Oxford looked recently at dividing the reproduction number up between asymptomatic transmission (i.e. transmissions from infectious individuals that never show symptoms), presymptomatic transmission (i.e. transmissions from individuals that show clear symptoms, before those symptoms develop), symptomatic transmission and environmental transmission.

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What it the rate of transmission of COVID-19?
Amaan1001, via Instagram

The transmissibility of the novel coronavirus is governed by the reproduction number, which represents the average number of individuals that an infectious host is likely to infect over their course of infection. Initial reproduction number estimates for COVID-19 were roughly in a range of between 2 and 3, although it depends on the precise setting. However, the number of individuals that any infectious host is likely to infect can be reduced substantially by public health measures such as social distancing, which is why we must all follow social distancing guidelines. You might be interested in this tracker of reproduction number estimates through time in different countries (full disclosure: I am involved in it, but the hard work is being done by Dr Sam Abbott and the rest of Dr Seb Funk’s excellent team at LSHTM!).

Models. They are dominating our Lockdown lives. But what is a mathematical model? We hear a lot about the end result, but how is it put together? What are the assumptions? And how accurate can they be?

In our first online only lecture Robin Thompson, Research Fellow in Mathematical Epidemiology in Oxford, will explain. Robin is working on the ongoing modelling of Covid-19 and has made many and varied media appearances in the past few weeks. We are happy to take questions after the lecture.

Wednesday 8 April 2020
5.00-6.00pm

Watch live:
https://twitter.com/oxunimaths?lang=en
https://www.facebook.com/OxfordMathematics/
https://livestream.com/oxuni/Thompson

Oxford Mathematics Public Lectures are generously supported by XTX Markets

Oxford Mathematician Konstantin Ardakov has been awarded the 2020 Adams Prize. The Adams Prize is awarded jointly each year by the Faculty of Mathematics, University of Cambridge and St John’s College, Cambridge to UK-based researchers, under the age of 40, doing first class international research in the Mathematical Sciences. This year’s topic was “Algebra”, and the prize has been awarded jointly to Konstantin and Michael Wemyss (University of Glasgow).

Professor Mihalis Dafermos, Chair of the Adams Prize Adjudicators, said: "Prof Ardakov has made substantial contributions to noncommutative Iwasawa theory, and to the p-adic representation theory of p-adic Lie groups. In a long-term collaboration with Simon Wadsley, he has developed a p-adic analogue of the classical theory of D-modules, of significance both in representation theory and to the local Langlands program.

The Adams Prize is named after the mathematician John Couch Adams and was endowed by members of St John’s College, Cambridge. It is currently worth approximately £15,000. It commemorates Adams’s role in the discovery of the planet Neptune, through calculation of the discrepancies in the orbit of Uranus.

The University has announced numerous steps to prioritise the health and welfare of staff, students and visitors in the light of the UK’s escalating coronavirus situation. This is an unprecedented and challenging time for our university and department community, and I would ask that you please support each other wherever you can, and follow University guidance, which is continuously updated. MI staff and students should also check their emails regularly for further guidance.

Mike Giles, Head of Department

Oxford Mathematicians Derek Moulton and Alain Goriely together with their colleague Régis Chirat (University of Lyon) have won the 2019 PNAS Cozzarelli Prize in the Engineering and Applied Sciences category for their paper 'Mechanics unlocks the morphogenetic puzzle of interlocking bivalved shells.'

The paper describes how two groups of animals—brachiopods and bivalve mollusks—sport interlocking shells that help guard against predators and environmental perturbations, and explains how those shells are formed.

The Cozzarelli Prize is awarded annually to six research teams whose PNAS (Proceedings of the National Academy of Sciences of the United States of America) articles have made outstanding contributions to their fields. Each team represents one of the six classes of the National Academy of Sciences.

Oxford Mathematicians occasionally have time to write and edit books. Their range of topics - from Topology and Geometry to Stochastic Methods and Chaos via the International Congress of 1936 and a candid account of a life escaping from poverty and living with polio - is a testament to how much maths reaches in to our lives. Some are for specialists, some for aspiring specialists, but all give you a flavour of the mathematical life.

Here are some of the those works that have already been published or will appear soon. The Oxford Mathematician (and their individual page) is highlighted in blue along with relevant links to the book itself.

Stochastic Modelling of Reaction-Diffusion Processes - Radek Erban, S. Jonathan Chapman
Stochastic methods have been used by researchers in Oxford Mathematics to model a number of biological systems, ranging in size from molecular dynamics simulations of small biomolecules to stochastic modelling of groups of animals.

This book can be used both for self-study and as a supporting text for advanced undergraduate or beginning graduate-level courses in applied mathematics. It discusses the essence of mathematical methods which appear (under different names) in a number of interdisciplinary scientific fields bridging mathematics and computations with biology and chemistry (including mathematical biology, non-equilibrium statistical physics, computational chemistry, soft condensed matter, physical chemistry or biophysics).

Chaos - An Introduction for Applied Mathematicians - Andrew Fowler and Mark McGuinness
This is a textbook on chaos and nonlinear dynamics, written by applied mathematicians for applied mathematicians. It aims to tread a middle ground between the mathematician's rigour and the physicist’s pragmatism.

The Wonder Book of Geometry - David Acheson
David transports us into the world of geometry, a fundamental and ancient branch of mathematics and argues that geometry can provide the quickest route into the whole spirit of mathematics at its best, especially for the young.

Topology: A Very Short Introduction - Richard Earl
The twentieth century was the century of topology – or so said Jean Dieudonné. From a nascent, intuitively understood subject in the time of Riemann, topology would become a significant area of mathematics, influencing the foundations of mathematics, through to applications in physics and data science.

Meeting under the Integral Sign? The Oslo Congress of Mathematicians on the Eve of the Second World War - Christopher D. Hollings and Reinhard Siegmund-Schultze
This book examines the historically unique conditions under which the International Congress of Mathematicians took place in Oslo in 1936. This Congress was the only one on this level to be held during the period of the Nazi regime in Germany (1933–1945) and after the wave of emigrations from it. Relying heavily on unpublished archival sources, the authors consider the different goals of the various participants in the Congress, most notably those of the Norwegian organisers, and the Nazi-led German delegation. They also investigate the reasons for the absence of the proposed Soviet and Italian delegations.

My Gift of Polio ~ An unexpected Life ~ From Scotland’s Rustic Hills to Oxford’s Hallowed Halls & Beyond - James D Murray
James Murray was the youngest of six children born into a poor working-class family in Moffat, a very small isolated town in rural Scotland, during the Depression of the early 1930s. He caught polio as a baby and his future looked bleak. This profusely illustrated memoir describes his early years growing up in poverty and follows his serendipitous life beyond - taking him from degrees at the University of St. Andrews to international renown in the world of academia at Harvard, Oxford, Paris and other universities around the world.

Conformal Maps and Geometry – Dmitry Belyaev
Geometric function theory is one of the most interesting parts of complex analysis, an area that has become increasingly relevant as a key feature in the theory of Schramm–Loewner evolution. Though Riemann mapping theorem is frequently explored, there are few texts that discuss general theory of univalent maps, conformal invariants, and Loewner evolution. This textbook provides an accessible foundation of the theory of conformal maps and their connections with geometry.

Leading Within Digital Worlds: Strategic Management for Data Science - Peter Grindrod
With rapidly evolving emerging technologies, the business world is entering a phase of reform. Within times of change, transformative and disruptive environments as well as uncertain futures have created a difficult landscape for leaders within business. This book is written for business leaders who want to remain at the forefront of the business world in these times of technological and digital evolution.

Lectures and Surveys on G2-Manifolds and Related Topics - Spiro Karigiannis, Naichung Conan Leung and Jason Lotay (Eds.)
This book, one of the first on G2 manifolds in decades, collects introductory lectures and survey articles largely based on talks given at a workshop held at the Fields Institute in August 2017, as part of the major thematic program on geometric analysis. It provides an accessible introduction to various aspects of the geometry of G2 manifolds, including the construction of examples, as well as the intimate relations with calibrated geometry, Yang-Mills gauge theory, and geometric flows. It also features the inclusion of a survey on the new topological and analytic invariants of G2 manifolds that have been recently discovered. 

Geometric Group Theory – Cornelia Drutu and Misha Kapovich
The book contains proofs of several fundamental results of geometric group theory, such as Gromov's theorem on groups of polynomial growth, Tits's alternative, Stallings's theorem on ends of groups, Dunwoody's accessibility theorem, the Mostow Rigidity Theorem, and quasiisometric rigidity theorems of Tukia and Schwartz. This is the first book in which geometric group theory is presented in a form accessible to advanced graduate students and young research mathematicians.

Probability and Random Processes, 4th edition, & One Thousand Exercises in Probability, 3rd edition - Geoffrey Grimmett and David Stirzaker

Probability and Random Processes:
This book provides an extensive introduction to probability and random processes. It is intended for those working in the many and varied applications of the subject as well as for those studying more theoretical aspects.

One Thousand Exercises in Probability:
This volume contains more than 1300 exercises in probability and random processes together with their solutions. The new edition extends the previous edition by the inclusion of numerous new exercises, and several new sections devoted to further topics in aspects of stochastic processes. Since many exercises have multiple parts, the total number of interrogatives exceeds 3000.

INTERNATIONAL WOMEN’S DAY EVENT - Mathematical Institute, Lecture Theatre 3, Friday 6th March 2020, 12-2pm

In conjunction with the Mathematical, Physical and Life Sciences Equality & Diversity team, Oxford Mathematics, Department of Statistics and Department of Computer Science invite you to attend an event celebrating women in science and showcasing the achievements of women in our University.  Three speakers from across the departments will talk about their research and careers to date.  The presentations will be followed by a networking lunch and poster session. 

Our speakers are:
Ms Klaudia Krawiecka, DPhil student in Cyber Security, Department of Computer Science
Dr Priya Subramanian, Hooke Research Fellow, Mathematical Institute
Dr Cora Mezger, Director of Statistical Consultancy Services, Department of Statistics

The event is free to attend but please register to attend by emailing @email by midday on 28th February 2020, noting any dietary or access requirements.

There will also be a poster session, at which Early Career Researchers, undergraduates and postgraduates are invited to present posters that showcase their work or work relating to International Women’s Day.   Posters will be judged by a panel of experts and vouchers awarded to the three best entries (£100 for first place; £50 for second place and £25 for third place).  

To apply to present a poster, please email @email by midday on 21st February 2020 with your poster title and abstract (no more than 150 words).  Posters should be A0 in size.  Funds are available for printing costs.