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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 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.

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.

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?

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.

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.

Let X be a complex algebraic variety containing a point x. One of the central ideas of deformation theory is that the local structure of X near the point x can be encoded by a differential graded Lie algebra. In this talk, Jacob Lurie will explain this idea and discuss some generalizations to more exotic contexts.

In this seminar, I aim to go through the "main prequel" of the talk I gave during the first Advanced Class of this term, and provide a "simple" answer to Abraham Robinson's original question that he posed in 1973 regarding the (un)decidability of finitely generated extensions of undecidable fields. I will provide a quick introduction to, and some classical results from, the mathematical discipline of Field Arithmetic, and using these results show that one can construct undecidable (large) fields that have finitely generated extensions which are decidable. Of course, as I had mentioned in the advanced class, a counterexample to the "simple" question that I have been working on unfortunately does not seem to lie within this class of large fields. If time permits, I will provide a sneak peek into the possible "sequel" by briefly talking about what the main issue of solving the "simple" problem is, and how a "hide-and-seek" method might come in handy in tackling that problem.

I will discuss some reaction-diffusion equations of bistable type motivated by biology and medicine. The aim is to understand the effect of the shape of the domain on propagation or on blocking of advancing waves. I will first describe the motivations of these questions and present a result about the existence of generalized “transition waves”. I will then discuss various geometric conditions that lead to either blocking, or partial propagation, or complete propagation. These questions involve new qualitative results for some non-linear elliptic and parabolic partial differential equations. I report here on joint work with Juliette Bouhours and Guillemette Chapuisat.