Past Fridays@4

4 November 2016
Emilie Dufresne + Robert Van Gorder

What is the minimal size of a separating set? -- Emilie Dufresne

Emilie Dufresne

Abstract: The problem of classifying objects up to certain allowed transformations figures prominently in almost all branches of Mathematics, and Invariants are used to decide if two objects are equivalent. A separating set is a set of invariants which achieve the desired classification. In this talk we take the point of view of Invariant Theory, where the objects correspond to points on an affine variety (often a vector space) and equivalence is given by the action of an algebraic group on this affine variety. We explain how the geometry and combinatorics of the group action govern the minimal size of separating sets.


Predator-Prey-Subsidy Dynamics and the Paradox of Enrichment on Networks -- Robert Van Gorder

Robert Van Gorder

Abstract: The phrase "paradox of enrichment" was coined by Rosenzweig (1971) to describe the observation that increasing the food available to prey participating in predator-prey interactions can destabilize the predator's population. Subsequent work demonstrated that food-web connectance on networks can stabilize the predator-prey dynamics, thereby dampening the paradox of enrichment in networked domains (such as those used in stepping-stone models). However, when a resource subsidy is available to predators which migrate between nodes on such a network (as is actually observed in some real systems), we may show that predator-prey systems can exhibit a paradox of enrichment - induced by the motion of predators between nodes - provided that such networks are sufficiently densely connected. 

28 October 2016
Professor Mike Giles & Professor Ursula Martin

Some relish the idea of working with users of research and having an impact on the outside world - some view it as a ridiculous government agenda which interferes with academic freedom.  We’ll give an overview of  the political and practical aspects of impact and identify things you might want to consider when deciding whether, and how, to get involved.

14 October 2016

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.

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

10 June 2016
Wondering about how to organise your DPhil? How to make the most of your supervision meetings?

In this session we will explore these and other questions related to what makes a successful DPhil with help from faculty members, postdocs and DPhil students.

In the first half of the session Helen Byrne and Roger Heath-Brown will give short talks on their experiences as PhD students and supervisors. 

The second part of the session will be a panel discussion, and the panel will consist of Emily Cliff, Benjamin Green, Paul Taylor and Andrew Thompson. Senior faculty members will be kindly asked to leave the lecture theatre - to ensure that students feel comfortable with discussing their experiences with later year students and postdocs/research fellows without any senior faculty present.
At 5pm senior and junior faculty members, postdocs and students will reunite in the common room for the happy hour.

About the speakers and panel members:
Helen Byrne received her DPhil from Oxford under the supervision of John Norbury. She was a Professor of Applied Mathematics in Nottingham from 2003 to 2011, when she moved to Oxford where she is a Professor in Mathematical Biology.
Roger Heath-Brown received his PhD from Cambridge under the supervision of Alan Baker. He moved to Oxford in 1979, where he has been a Professor of Pure Mathematics since 1999.
Emily Cliff received her DPhil from Oxford in 2015 under the supervision of Kobi Kremnitzer, and she is now a postdoc in the Geometry and Representation Theory group.
Benjamin Green and Paul Taylor are both fourth year DPhil students; Benjamin Green is a member of the Number Theory group,
while Paul Taylor is in the Mathematical Biology group.
Andrew Thompson received his PhD from the University of Edinburgh in 2012 under the supervision of Coralia Cartis and Jared Tanner, and he has been a Lecturer in Computational Mathematics at Oxford since 2014.
20 May 2016
Sira Gratz + Hao Ni

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.

13 May 2016
Professor Philip Maini

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.

6 May 2016
Bruce Bartlett + Giacomo Canevari

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.

29 April 2016
Professor Chris Budd

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.