Past Fridays@4

11 May 2018
Vicky Neale

Research suggests that students with a 'growth mindset' may do better than those with a 'fixed mindset'.

  • What does that mean for our teaching?
  • How can we support students to develop a growth mindset?
  • What sorts of mindsets do we ourselves have?
  • And how does that affect our teaching and indeed the rest of our work?
27 April 2018
Jan Sbierski and Andrew Krause

Jan Sbierski

Title: On the unique evolution of solutions to wave equations

Abstract: An important aspect of any physical theory is the ability to predict the future of a system in terms of an initial configuration. This talk focuses on wave equations, which underlie many physical theories. We first present an example of a quasilinear wave equation for which unique predictability in fact fails and then turn to conditions which guarantee predictability. The talk is based on joint work with Felicity Eperon and Harvey Reall.

Andrew Krause

Title: Surprising Dynamics due to Spatial Heterogeneity in Reaction-Diffusion Systems

Abstract: Since Turing's original work, Reaction-Diffusion systems have been used to understand patterning processes during the development of a variety of organisms, as well as emergent patterns in other situations (e.g. chemical oscillators). Motivated by understanding hair follicle formation in the developing mouse, we explore the use of spatial heterogeneity as a form of developmental tuning of a Turing pattern to match experimental observations of size and wavelength modulation in embryonic hair placodes. While spatial heterogeneity was nascent in Turing's original work, much work remains to understand its effects in Reaction-Diffusion processes. We demonstrate novel effects due to heterogeneity in two-component Reaction-Diffusion systems and explore how this affects typical spatial and temporal patterning. We find a novel instability which gives rise to periodic creation, translation, and destruction of spikes in several classical reaction-diffusion systems and demonstrate that this periodic spatiotemporal behaviour appears robustly away from Hopf regimes or other oscillatory instabilities. We provide some evidence for the universal nature of this phenomenon and use it as an exemplar of the mostly unexplored territory of explicit heterogeneity in pattern formation.

9 March 2018
Radu Cimpeanu and Liana Yepremyan

Speaker: Radu Cimpeanu
Title: Crash testing mathematical models in fluid dynamics

Abstract: In the past decades, the broad area of multi-fluid flows (systems in which at least two fluids, be they liquids or mixtures of liquid and gas, co-exist) has benefited from simultaneous innovations in experimental equipment, concentrated efforts on analytical approaches, as well as the rise of high performance computing tools. This provides a wonderful wealth of techniques to approach a given challenge, however it also introduces questions as to which path(s) to take. In this talk I will explore the symbiotic relationship between reduced order modelling and fully nonlinear direct computations, each of their strengths and weaknesses and ultimately how to use a hybrid strategy in order to gain an understanding over larger subsets of often vast solution spaces. The discussion will take us through a number of interesting topics in fluid mechanics on a wide range of scales, from electrohydrodynamic control in microfluidics, to nonlinear waves in channel flows and violent drop impact scenarios.

Speaker: Liana Yepremyan
Title: Turan-type problems for hypergraphs

Abstract: One of the earliest results in extremal graph theory is Mantel's Theorem  from 1907, which says that for given number of vertices, the largest triangle-free graph on these vertices is the complete bipartite graph with (almost) equal sizes. Turan's Theorem from 1941 generalizes this result to all complete graphs. In general, the Tur'\an number of a graph G (or more generally, of  a hypergraph) is the largest number of edges in a graph (hypergraph) on given number of vertices containing no copy of G as a subgraph. For graphs a lot is known about these numbers,  a result by Erd\Hos, Stone and Simonovits determines the correct order of magnitude of Tur\'an numbers  for all non-bipartite graphs. However, these numbers are known only for few  hypergraphs. We don't even know what is the Tur\'an number of the complete 3-uniform hypergraph on 4 vertices. In this talk I will give some  introduction  to these problems and brielfly describe some of the methods used, such as the stability method and the Lagrangian  function, which are interesting on their own.

23 February 2018
Dave Hewett and Alison Trinder

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.

9 February 2018
Yalong Cao and Doireann O'Kiely

Yaolong Cao: Gauge Theories on Geometric Spaces
In this talk, I will very briefly discuss gauge theories on various geometric spaces, including Riemann surfaces, 4-manifolds and manifolds with special or exceptional holonomy. More details on Calabi-Yau 4-folds will be mentioned, which are related to my research interests.

Doireann O'Kiely: Dynamic Wrinkling of Elastic Sheets
Our lives contain many scenarios in which thin structures wrinkle: a piece of tin foil or cling film crumples in our hand, and creases form in our skin as we age. In this talk I will discuss experimental and theoretical work by researchers in the Mathematical Institute on wrinkling of elastic sheets.
We study the impact of a solid onto an elastic sheet floating at a liquid-air interface. We observe a wave that is reminiscent of the ripples caused by dropping a stone in a pond, as well as spoke-like wrinkles, whose wavelength evolves in time. We describe these phenomena using a combination of asymptotic analysis, numerical simulations and scaling arguments.

2 February 2018
Mike Giles

In this talk I will discuss the upcoming REF2021 and its significance for early career researchers (research fellows and postdocs) including

  • why it is so important to all UK maths departments
  • why the timing of it could have important career consequences for ECRs
  • publication issues such as quality versus quantity, and choice of journal
  • the importance of Impact Case Studies
26 January 2018

A panel discussion and Q&A, looking at some of the challenges and opportunities available for mathematicians outside universities. Featuring:

Madeleine Copin – North London Collegiate School
Josephine French – Health Data Insight, working in partnership with Public Health England
Martin Gould – Spotify
Dan Jones – Quadrature Capital
Adam Sardar – e-therapeutics

19 January 2018
Dan Ciubotaru, Philip Maini, Thomas Wasserman, Renee Hoekzema, Jaroslav Fowkes, Carolina Matte Gregory

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 Dan Ciubotaru and Philip Maini will give short talks on their experiences as PhD students and supervisors.
  • The second part of the session will be a panel discussion with final-year Dphil students and early postdocs.

The panel will consist of Thomas Wasserman, Renee Hoekzema, Jaroslav Fowkes and Carolina Matte Gregory. Senior faculty members will be kindly asked to leave the lecture theatre to ensure that students feel comfortable discussing their experiences with other students and postdocs without any senior faculty present.

24 November 2017
Richard Wade and Andrey Kormilitzin

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.