For a prime number p, we will consider completed group algebras, or Iwasawa algebras, of the form kG, for G a complete p-valued group of finite rank, k a field of characteristic p. Classifying the ideal structure of Iwasawa algebras has been an ongoing project within non-commutative algebra and representation theory, and we will discuss ideas related to this topic based on previous work and try to extend it. An important concept in studying ideals of group algebras is the notion of controlling ideals, where we say a closed subgroup H of G controls a right ideal I of kG if I is generated by a subset of kH. It was proved by Konstantin Ardakov in 2012 that for G nilpotent, every faithful prime ideal of kG is controlled by the centre of G, and it follows that the prime spectrum of kG can be realised as the disjoint union of commutative strata. I am hoping to extend this to a more general case, perhaps to when G is solvable. A key step in the proof is to consider a faithful prime ideal P in kG, and an automorphism of G, trivial mod centre, that fixes P. By considering the Mahler expansion of the automorphism, and approximating the coefficients, we can examine sequences of bounded k-linear functions of kG, and study their convergence. If we find that they converge to an appropriate quantized divided power, we can find proper open subgroups of G that control P. I have extended this notion to larger classes of automorphisms, not necessarily trivial mod centre, using which this proof can be replicated, and in some cases extended to when G is abelian-by-procyclic. I will give some examples, for G with small rank, for which these ideas yield results.

In this presentation, we give an overview of the numerical methods used in commercial oil and gas reservoir simulation. The models are described by flow through porous media and are solved using a series of nested numerical methods. Most of the computational effort resides in solving large linear systems resulting from Newton iterations. Therefore, we will go in greater detail about the iterative linear solvers and preconditioning techniques.

Note: This talk will cover similar topics to the InFoMM group meeting talks on Friday 28th April, but I will discuss more mathematical details for this JAMS talk.

I will give an overview of the complexes used in algebraic topology using the language of abstract complexes.

This is a lunch seminar, so feel free to bring your lunch along!

We will discuss the Chapter "Cohomology" from the book "Elementary applied topology" by Robert Ghrist (available at https://www.math.upenn.edu/~ghrist/notes.html).

This is a lunch seminar, so feel free to bring your lunch along!

Liquid crystals are classical examples of mesophases or materials that are intermediate in character between conventional solids and liquids. There are different classes of liquid crystals and we focus on the simplest and most widely used nematic liquid crystals. Nematic liquid crystals are simply put, anisotropic liquids with distinguished directions and are the working material of choice for the multi-billion dollar liquid crystal display industry. In this workshop, we briefly review the mathematical theories for nematic liquid crystals, the modelling framework and some recent work on modelling experiments on confined liquid crystalline systems conducted by the Aarts Group (Chemistry Oxford) and experiments on nematic microfluidics by Anupam Sengupta (ETH Zurich). This is joint work with Alexander Lewis, Peter Howell, Dirk Aarts, Ian Griffiths, Maria Crespo Moya and Angel Ramos.
We conclude with a brief overview of new experiments on smectic liquid crystals in the Aarts laboratory and questions related to the recycling of liquid crystal displays originating from informal discussions with Votechnik ( a company dealing with automated recycling technologies , http://votechnik.com/).