Past Fridays@4

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.

10 November 2017
Laura Capuano and Noemi Picco

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.

16 June 2017
Lisa Lamberti + Jaroslav Fowkes

Lisa Lamberti

Geometric models in algebra and beyond

Many phenomena in mathematics and related sciences are described by geometrical models.

In this talk, we will see how triangulations in polytopes can be used to uncover combinatorial structures in algebras. We will also glimpse at possible generalizations and open questions, as well as some applications of geometric models in other disciplines.

Jaroslav Fowkes

Jaroslav Fowkes

Optimization Challenges in the Commercial Aviation Sector

The commercial aviation sector is a low-margin business with high fixed costs, namely operating the aircraft themselves. It is therefore of great importance for an airline to maximize passenger capacity on its route network. The majority of existing full-service airlines use largely outdated capacity allocation models based on customer segmentation and fixed, pre-determined price levels. Low-cost airlines, on the other hand, mostly fly single-leg routes and have been using dynamic pricing models to control demand by setting prices in real-time. In this talk, I will review our recent research on dynamic pricing models for the Emirates route network which, unlike that of most low-cost airlines, has multiple routes traversing (and therefore competing for) the same leg.