This is a one-day conference for graduate students working in analysis. The event is organised in connection with the Taught Course Centre (a collaboration between the Mathematics Departments at the Universities of Bath, Bristol, Imperial, Oxford and Warwick); but students from other institutions are welcome, too. We invite research students to give a talk and discuss their work in an informal and relaxed atmosphere. There will also be time to mingle and compare experiences.
Registration and Funding Schedule Venue Getting here MapsRegistration is now closed. For questions concerning participation, please contact the organisers.
Funding is provided by the Taught Course Centre.
| Time | Speaker | Title/Abstract |
|---|---|---|
| 10.15 | Coffee and arrivals | |
| 11.00 | Christopher Hopper Oxford |
Partial Regularity of Constrained Minimisers Abstract |
| 11.30 | Charles Sonnenberg Bristol |
Micromagnetics of Nanowires An introductory talk about micromagnetics. We shall explore the analysis involved in studying the micromagnetic energy of soft ferromagnetic nanowires. Using Gamma convergence techniques we will see how the energy for wires with a small radius cross-section can be reduced to a simpler 1D energy. The roles of magnetic domains and domain walls will also be discussed. |
| 12.00 | Mark Wilkinson Oxford |
The Statistical Scaling Hypothesis in the Landau-de Gennes Q-tensor Theory of Nematic Liquid Crystals Abstract |
| 12.30 | Lunch | |
| 2.00 | Gareth Speight Warwick |
Porosity, Doubling and Approximate Differentiability Recently there has been much interest in differentiable structures for Lipschitz functions on metric measure spaces. It has been shown that if a metric measure space admits a differentiable structure, in the sense of Cheeger, then necessarily porous sets have measure zero and hence the measure is pointwise doubling almost everywhere. By an explicit construction, similar to the construction of Laakso's spaces, we show these results no longer hold if differentiability is replaced by approximate differentiability. That is, we construct an example of a space in which Lipschitz functions are approximately differentiable almost everywhere and the measure is non doubling almost everywhere. |
| 2.30 | David Bate Warwick |
Structure of measure in Lipschitz differentiability spaces Rademacher's theorem is a classical result asserting the almost everywhere differentiability of a real valued Lipschitz function defined on Euclidean space. This has been recently generalised by Cheeger to metric measure spaces satisfying a Poincare inequality. This talk will present work giving necessary conditions for a space to satisfy Rademacher's theorem, in particular that the measure must have an Alberti representation. |
| 3.00 | Tea | |
| 3.45 | Chuei Yee Chen Oxford |
Coercivity and Almost Minimality in the Calculus of Variations It is well-known that existence of minimizers can be established by use of the direct method, and that, in the vectorial multi-dimensional case, lower semicontinuity is essentially equivalent to quasiconvexity in the sense of Morrey. In the talk, we discuss the connection between mean coercivity and quasiconvexity. We also briefly discuss the notion of almost (or quasi-) minimizers, and mention some recent results concerning these. |
| 4.15 | David Seifert Oxford |
Operator Semigroups and their Growth Bounds Semigroups of operators play an important role in various areas of mathematics including control theory and the analysis of PDEs. The growth bound of a semigroup, providing, as it does, information about the growth or decay of solutions of (abstract) Cauchy problems, is of particular interest. This talk will explain, from a functional analytic perspective, some of the main concepts of semigroup theory and briefly explore a few of the connections that exist between spectral properties of a semigroup generator (typically a differential operator) on the one hand and the growth bound of the associated semigroup on the other. |
| 4.45 | Anthony Masters Bath |
A Primer on Rearrangements I will investigate the interesting subject of rearrangements, presented in an accessible manner, and the problems that it yields, such as maximisation of a functional over given rearrangements. |
The talks will take place in the Maths Department's Wolfson Lecture Theatre (Building 4 West, room 1.7) at the University of Bath.