# Abstracts

# Plenary talks

## Dr Anna Felikson, Durham University

### Cluster algebras, mutations and triangulated surfaces

Cluster algebras were introduced by Fomin and Zelevinsky in 2002. Since then it turned out that this notion is connected to numerous different fields in mathematics (such as Poisson geometry, representation theory, integrable systems, combinatorics of polytopes, Teichmuller theory, dilogarithm identities, probability theory and many others). In this talk we will introduce cluster algebras and show some connections to triangulated surfaces. More precisely, we will see how an experience in the classification of hyperbolic Coxeter polytopes helped to solve some classification problem in cluster algebras. This work is joint with Pavel Tumarkin and Michael Shapiro.

## Professor Xue-Mei Li, Imperial College London

### Perturbations, Stochastic Equations, and Averaging

Perturbation and approximations underlies almost all applications of physical mathematical models. The averaging method, first introduced for periodic motions, is now widely used for a large class of problems in both pure and applied mathematics. The aim of the perturbation theory is easy to describe. Take for example a differential equation or a stochastic differential equation, few stochastic equations have exact solutions. We can however approximate them with equations, either exactly solvable or at least we have good knowledge of the behaviour of their solutions. In this talk discuss stochastic averaging for stochastic differential equations, and describe the latest developments.

## Professor Jing Ping Wang, University of Kent

### Classification of Integrable equations and Number Theory

Among nonlinear partial differential equations(PDE) there is an exceptional class of integrable equations, which can be studied with the same completeness as linear PDEs, at least in principle. They possess a rich set of exact solutions and many hidden properties. Classification of integrable equations of a given family of nonlinear PDEs is an important topic in the field of soliton theory. There are many approaches to this problem, among which the symmetry approach has proved to be very efficient and powerful. In this talk, I’ll give a brief account of recent development of the symmetry approach. The progress has been achieved mainly due to a symbolic representation of the ring of differential polynomials, which enables us to use results from algebraic geometry and number theory.

## Dr Flavia Poma, Lloyds Banking Group

### Harnessing information through NLP and Machine Learning

Data is generated in a continuous stream; the majority of this data exists in textual form, which is highly unstructured in nature. In order to produce significant and actionable insights from text data we use text analysis and natural language processing (NLP) to transform text into structured data to analyse and build models upon. During the presentation we will take a walk through NLP tools and techniques, highlighting some of the main challenges and ways to overcome them. We will also look at different real-life applications using machine learning techniques with particular focus on two of them: text classification and sentiment analysis.

# Contributed talks

## Ms Oana Lang, Imperial College London

### Well-posedness Analysis for the Stochastic Great Lake Equations with Transport Noise

The great lake equations are a family of shallow water equations which model the circulation of an inviscid fluid in a shallow water basin with varying bottom topography. They generalize the 2D Euler equations in the sense that the vorticity field is not just the curl of the velocity, but a more general linear operator (with good regularity properties) applied to the velocity field. The aim of introducing transport-type stochasticity in this context is to model in a physically consistent way the small scale geophysical processes which usually cannot be resolved in a deterministic framework. The well-posedness of the stochastic Euler equation with transport-type noise has been proved in [1]. We discuss the extension of this result to the great lake equations with the same type of stochasticity.

[1] D. Crisan, O. Lang, Well-posedness for a stochastic 2D Euler equation with transport noise (in preparation)

## Dr Constanze Roitzheim, University of Kent

### Stable homotopy groups of spheres

Stability is a phenomenon that adds a lot of structure to algebraic topology, particularly to homotopy groups. I will explain and motivate the construction of stable homotopy groups and give a brief overview of examples, known results and open challenges. This talk does not require any previous knowledge in topology.

## Ms Ana Rojo-Echeburúa, University of Kent

### Variational Systems with an Euclidean Symmetry using the Rotation Minimizing Frame

In this talk, I will study variational systems with an Euclidean symmetry, using the Normal, or Rotation Minimizing frame. The Rotation Minimizing frame has many advantages when considering the evolution of curves in computer aided design environments. Lie group based moving frames is the subject of many recent studies, however, the powerful symbolic computational methods derived for them which have proved so useful in the applications, do not apply to the Normal frame, as this frame is not defined by algebraic equations on the jet variables at a given point, but rather is defined by a differential equation. I will present the Rotation Minimizing frame and show how to use the known symbolic techniques despite the fact that it does not readily fit the known framework needed for these techniques. I will derive the invariant differentiation formulae and the syzygy operator needed to obtain Noether’s laws for variational problems with a Euclidean symmetry using the Rotation minimising frame and present some application in biological problems such as the modelization of proteins, nucleid acids and polymers.