Postgraduate seminar series

I am in charge of the seminar series from June 2014 – December 2014, details of seminars will appear here.

There is a calendar at the bottom of the page.

 

Thursday 18th December 2014 (s0.31) – 13.00-14.00 – No speakerSocial coffee instead
Thursday 11th December 2014 (s0.31) – 13.00-14.00 – Joint: new students (UEA) – List of speakers below
Thursday 4th December 2014 (s0.31) – 13.00-14.00 – Tanmay Inamdar (UEA) – The Maharam Problem
Thursday 27th November 2014 (s0.31) – 13.00-14.00 – Peter Latham (UEA) – Types in p-adic groups
Thursday 20th November 2014 (s0.31) – 13.00-14.00 – Thomas Coleman (UEA) – Types of morphisms
Thursday 13th November 2014 (s0.31) – 13.00-14.00 – Alberto Villois (UEA) – Scattering of line-ring vortices in a superfluid
Thursday 6th November 2014 (s0.31) – 13.15-14.00 – Robin Cussol (UEA) – Homological methods in representation theory
Thursday 30rd October 2014 (s0.31) – 13.00-14.00 – Rob Henderson (UEA) – Independence in exponential fields
Thursday 23rd October 2014 (ARTS 01.02) – 13.00-14.00 – Martin Walters (UEA) – Bending a block under tension
Thursday 16th October 2014 (s3.05) – 13.00-14.00 – Jodie Cullum (UEA) – How to (theoretically) melt some more of the polar ice caps
Friday  13th June 2014 (s0.31) – 15.30-16.30 – Davide Maestrini (UEA) – Vortex Dynamics in confined 2D regions and negative temperature states
Friday 6th June 2014 (s0.31)- 13.30-14.00 – Xiaozhou Li (Delft University of Technology) – SIAC filtering of DG methods – Boundary and nonuniform mesh
– 14.00-14.30 – Thea Vuik (Delft University of Technology) – Multiwavelet troubled-cell indicator for discontinuity detection of discontinuous Galerkin schemes

 

Abstracts:

Free surface flow over bottom topography (Jack Keeler)
The Null-space of Graph (Ali Al-Tarimshawy)
The Southern Ocean: Barrier or Blender? (Natasha Senior)
Categorification and 2-representation theory (Francesco Bonesi)
Mathematical Modelling and Investigation of Explosive, Pinch Friction and Shear Problems (Robert Timms)

The Maharam Problem (Tanmay Inamdar)
The Maharam Problem (named after Dorothy Maharam) was, till its solution by Michel Talagrand in 2006, “one of the longest standing classical questions of measure theory”. The aim of my talk will be to give some of the motivations (measure-theoretic and set-theoretic) for considering this problem. As a start, I will explain how a certain type of Boolean algebra (and I’ll explain what those are as well), a ‘measure algebra’, arises naturally in measure theory. A natural weakening of a measure algebra is a ‘submeasure algebra’ or ‘Maharam algebra’, which arises from ‘submeasure spaces’ as opposed to measure spaces (where the functional is not expected to be additive, as would be the case with a measure, but merely subadditive). The Maharam Problem asks if every Maharam algebra is in fact a measure algebra (in vaguer terms, whether every submeasure is ‘close to being a measure’). Talagrand constructed a Maharam algebra which is not a measure algebra, and I hope to explain the various advances that went into the solution of the Maharam Problem. Then, if time permits, I would like to talk about a closely related unsolved problem in set theory, the Prikry Conjecture (named after Karel Prikry), which the Boolean algebra constucted by Talagrand could potentially settle.

Types in p-adic groups (Peter Latham)
p-adic groups are big objects with a very complicated representation theory, which is somehow dominated by the “supercuspidal” representations, int he sense that any representation may be described in terms of supercuspidal  representations of (possibly smaller) groups. Conjecturally, it should be possible to define these infinite-dimensional representations in terms of some finite-dimensionsal data known as “types”. I’ll explain how this has been resolved in a few simple cases, and tell you about some unicity properties relating to these types.

Types of morphisms (Thomas Coleman)
A common theme in pure mathematics is the comparison of similar structures using functions known as morphisms. There are many different types of morphism depending on how the function is defined and how well the morphism preserves the structure of its domain. In this talk, I will hopefully illustrate the distinctions between certain types of morphisms on first order structures, talk about some of the work I do with them, and explain why you should never define an isomorphism as a bijective homomorphism ever again.

Scattering of line-ring vortices in a superfluid (Alberto Villois)
We study the scattering of vortex rings by a superfluid line vortex using the Gross-Pitaevskii equation in a parameter regime where a hydrodynamic description based on a vortex filament approximation is applicable. By using a vortex extraction algorithm, we are able to track the location of the vortex ring as a function of time. Using this, we show that the scattering of the vortex ring in our Gross-Pitaevskii simulations is well captured by the local induction approximation of a vortex filament model for a wide range of impact parameters. The scattering of a vortex ring by a line vortex is characterised by the initial offset of the centre of the ring from the axis of the vortex. We find that a strong asymmetry exists in the scattering of a ring as a function of this initial scattering parameter.

Homological methods in representation theory (Robin Cussol)
This is the title under which Vanessa advertised her research project – Francesco, Keith, Ruari and I all applied for this very project. Even though we all work on different things, I would like to give you an overview of what those two research areas entail; I will first take you on a journey through Representation Theory, for you to contemplate the history, richness and beauty of the subject. Subsequently, I will introduce Homological Algebra to you, going back to its topological origins, displaying some nice pictures and some mysterious numbers (!), to then wade through some more recent (and exotic) tools which are more relevant to my project. Finally, to make you all want to listen to me again some time soon, I will reveal the real title of my project.

Bending a block under tension (Martin Walters)
This talk will focus on the problem of bending a semi-infinite block under tension. In the set up of the problem, we have a semi-infinite block with its short edge clamped onto a boundary fixed at some angle to the normal direction of the block . A tension is then applied to the block in the axial direction, forcing the block to bend from its position at the clamped boundary to a position parallel to the axial direction. A model is derived for this mechanic and some surprising results are found. This talk will have a mixture of discussion about the methods involved and the results obtained, so there should be something for everyone!

How to (theoretically) melt some more of the polar ice caps (Jodie Cullum)
The heat distribution over the surface of a terrestrial planet is one of the crucial factors in the consideration of its habitability. The primary carriers of heat around a planet, including Earth, are the ocean and atmosphere. The talk will focus on the ocean component of the system. In particular, how the heat transported by the ocean responds to changes in a fundamental parameter. At the beginning of the talk I will give some brief introduction to the oceanic processes and concepts which are involved in the main results of the talk. I will also maintain a physical perspective throughout, so the talk should be accessible to everybody.

Vortex Dynamics in confined 2D regions and negative temperature states (Davide Maestrini)
Two dimensional systems are difficult to reproduce in nature, but nowadays this problem has been overcome. These systems show a peculiarity which is not possible to find in three dimensional systems, the so called negative temperature. A peculiarity of these systems is the emergence of unexpected phenomenon: the clusterization of point vortices. This talk will introduce the concept of negative temperature and will present how it is possible to describe the dynamics of point vortices in confined 2D geometries. The presentation will make use of movies through which it is possible to observe the clusterization.

SIAC filtering of DG methods – Boundary and nonuniform mesh (Xiaozhou Li)
Smoothness-Increasing Accuracy-Conserving (SIAC) filtering is a technique which helps to improve the smoothness and accuracy of approximations generated by high order methods, such as the discontinuous Galerkin (DG) method. SIAC filtering is ideally designed to be applied to linear equations with periodic boundary conditions over a uniform mesh. However, the real world is not ideal. Addressing any one of these three challenges alone is difficult, especially when computational efficiency is also taken into account.
In this talk, we address two of those three challenges: boundary problems and nonuniform meshes. (1) We show how a new boundary filtering technique can be applied over nonuniform meshes. (2) We also compare the new boundary filter with previous boundary filters including accuracy and computational efficiency aspects. Meanwhile, we show that the new boundary filtering improves accuracy for sufficiently refined meshes, and achieves a higher order convergence rate compared with the original DG approximation.

Multiwavelet troubled-cell indicator for discontinuity detection of discontinuous Galerkin schemes (Thea Vuik)
In my presentation, I will focus on the approximation of the solution of nonlinear hyperbolic PDE’s. Usually, these solutions contain shocks, or develop discontinuities. In numerical approximations, this can lead to spurious oscillations, which we do not want to get. In order to get rid of these oscillations, we apply a limiter. The cells where such treatment is necessary are referred to as troubled cells. To efficiently apply numerical methods in the case of discontinuous solutions, it is useful to have an accurate troubled-cell indicator.  In this presentation I will discuss the use of multiwavelets for troubled-cell indication applied to discontinuous Galerkin (DG) methods.

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