Forthcoming events in this series
How might you prepare talks for different audiences (specialised seminar, colloquium-style talk, talk to a non-mathematical audience, job interview)? Join us for advice on this, and on how to connect with your audience and get them to feel involved.
There are many opportunities within Oxford to communicate your excitement about mathematics and your own research to a wider audience, whether adults or school students. In this session we'll hear about some of those opportunities, and have some training on how to write a press release, so that you are well placed to share your next research paper with the public.
Featuring
Rebecca Cotton-Barratt, Schools Liaison Officer and Admissions Coordinator in the Mathematical Institute
Mareli Grady, Schools Liaison Officer in the Statistics Department and Mathemagicians Coordinator in the Mathematical Institute
Stuart Gillespie, Media Relations Officer for the University of Oxford
What are the national maths societies for? What can they do for us? What can we do for them?
Featuring representatives from the Institute of Mathematics and its Applications, the London Mathematical Society, the OR Society, and the Royal Statistical Society.
Cluster algebras: from finite to infinite -- Sira Gratz
Abstract: Cluster algebras were introduced by Fomin and Zelevinsky at the beginning of this millennium. Despite their relatively young age, strong connections to various fields of mathematics - pure and applied - have been established; they show up in topics as diverse as the representation theory of algebras, Teichmüller theory, Poisson geometry, string theory, and partial differential equations describing shallow water waves. In this talk, following a short introduction to cluster algebras, we will explore their generalisation to infinite rank.
Modelling the effects of data streams using rough paths theory -- Hao Ni
Abstract: 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 where the input variable is a stream of information, and the dependent response is also (potentially) a path or a stream. We 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 linear regression. We give several examples to show how this low dimensional statistic can be effective to predict the effects of a data stream.
What is the point of giving a talk? What is the point of going to a talk? In this presentation, which is intended to have a lot of audience participation, I would like to explore how one should prepare talks for different audiences and different occasions, and what one should try to get out of going to a talk.
From the finite Fourier transform to topological quantum field theory -- Bruce Bartlett
Abstract: In 1979, Auslander and Tolimieri wrote the influential "Is computing with the finite Fourier transform pure or applied mathematics?". It was a homage to the indivisibility of our two subjects, by demonstrating the interwoven nature of the finite Fourier transform, Gauss sums, and the finite Heisenberg group. My talk is intended as a new chapter in this story. I will explain how all these topics come together yet again in 3-dimensional topological quantum field theory, namely Chern-Simons theory with gauge group U(1).
Defects in liquid crystals: mathematical approaches -- Giacomo Canevari
Abstract: Liquid crystals are matter in an intermediate state between liquids and crystalline solids. They are composed by molecules which can flow, but retain some form of ordering. For instance, in the so-called nematic phase the molecules tend to align along some locally preferred directions. However, the ordering is not perfect, and defects are commonly observed.
The mathematical theory of defects in liquid crystals combines tools from different fields, ranging from topology - which provides a convenient language to describe the main properties of defects -to calculus of variations and partial differential equations. I will compare a few mathematical approaches to defects in nematic liquid crystals, and discuss how they relate to each other via asymptotic analysis.
Some models for climate change, the good the bad and the ugly
Modelling climate presents huge challenges for mathematicians and scientists, and has a large effect on policy makers. Climate models themselves vary from simple to complex with a huge range in between. But how good and/or reliable are they?
In this talk I will describe some of the various mathematical models of climate that are both used to understand past climate and also to predict future climate. I will also try to show that an understanding of non-smooth effects in dynamical systems can give us useful insights into the behaviour and analysis of these models.
What is the purpose of journals? How should you choose what journal to submit a paper to? Should it be open access? And how would you like your work to be evaluated?
Who are you? What motivates you? What's important to you? How do you react to challenges and adversities? In this session we will explore the power of self-awareness (understanding our own characters, values and motivations) and introduce assertiveness skills in the context of building positive and productive relationships (with colleagues, collaborators, students and others).
Computing distinct solutions of differential equations -- Patrick Farrell
Abstract: TBA
Triangles and equations -- Yufei Zhao
Abstract: I will explain how tools in graph theory can be useful for understanding certain problems in additive combinatorics, in particular the existence of arithmetic progressions in sets of integers.
Writing is a part of any career in science or mathematics. I will make some remarks about the role writing has played in my life and the role it might play in yours.
Finding rational points on curves - Jennifer Balakrishnan (Mathematical Institute, Oxford)
From cryptography to the proof of Fermat's Last Theorem, elliptic curves are ubiquitous in modern number theory. Much activity is focused on developing methods to discover their rational points (those points with rational coordinates). It turns out that finding a rational point on an elliptic curve is very much like finding the proverbial needle in the haystack. In fact, there is no algorithm known to determine the group of rational points on an elliptic curve.
Hyperelliptic curves are also of broad interest; when these curves are defined over the rational numbers, they are known to have finitely many rational points. Nevertheless, the question remains: how do we find these rational points?
I'll summarize some of the interesting number theory behind these curves and briefly describe a technique for finding rational points on curves using (p-adic) numerical linear algebra.
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Analysis, prediction and control of technological progress - François Lafond (London Institute for Mathematical Sciences, Institute for New Economic Thinking at the Oxford Martin School, United Nations University - MERIT)
Technological evolution is one of the main drivers of social and economic change, with transformative effects on most aspects of human life. How do technologies evolve? How can we predict and influence technological progress? To answer these questions, we looked at the historical records of the performance of multiple technologies. We first evaluate simple predictions based on a generalised version of Moore's law, which assumes that technologies have a unit cost decreasing exponentially, but at a technology-specific rate. We then look at a more explanatory theory which posits that experience - typically in the form of learning-by-doing - is the driver of technological progress. These experience curves work relatively well in terms of forecasting, but in reality technological progress is a very complex process. To clarify the role of different causal mechanisms, we also study military production during World War II, where it can be argued that demand and other factors were exogenous. Finally, we analyse how to best allocate investment between competing technologies. A decision maker faces a trade-off between specialisation and diversification which is influenced by technology characteristics, risk aversion, demand and the planning horizon.
Derived geometry and approximations - Pavel Safronov
Derived geometry has been developed to address issues arising in geometry from a consideration of spaces with intrinsic symmetry or some singular spaces arising as complicated intersections. It has been successful both in pure mathematics and theoretical physics where derived geometric structures appear in quantum gauge field theories such as the theory of quantum electrodynamics. Recently Lurie has developed a transparent approach to deformation theory, i.e. the theory of approximations of algebraic structures, using the language of derived algebraic geometry. I will motivate the theory on a basic example and explain one of the theorems in the subject.
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How magnets and mathematics can help solve the current water crisis - Ian Griffiths
Although water was once considered an almost unlimited resource, population growth, drought and contamination are straining our water supplies. Up to 70% of deaths in Bangladesh are currently attributed to arsenic contamination, highlighting the essential need to develop new and effective ways of purifying water.
Since arsenic binds to iron oxide, magnets offer one such way of removing arsenic by simply pulling it from the water. For larger contaminants, filters with a spatially varying porosity can remove particles through selective sieving mechanisms.
Here we develop mathematical models that describe each of these scenarios, show how the resulting models give insight into the design requirements for new purification methods, and present methods for implementing these ideas with industry.