Oxford mathematician Sir Andrew Wiles, renowned for his proof of Fermat’s Last Theorem, has been appointed by Her Majesty the Queen to be Oxford’s first Regius Professor of Mathematics.
The Regius Professorship – a rare, sovereign-granted title – was granted to Oxford’s Mathematical Institute as part of the Queen’s 90th birthday celebrations. It is the first Regius Professorship awarded to Oxford since 1842.
3d N=2 Chern-Simons-matter theories have a large variety of boundary conditions that preserve 2d N=(0,2) supersymmetry, and support chiral algebras. I'll discuss some examples of how the chiral algebras transform across dualities. I'll then explain how to construct duality interfaces in 3d N=2 theories, and relate dualities *of* duality interfaces to "Pachner moves" in triangulations of 4-manifolds. Based on recent and upcoming work with K. Costello, D. Gaiotto, and N. Paquette.
In this talk, we shall provide a comprehensive variational principle that allows one to apply critical point theory on closed proper subsets of a given Banach space and yet, to obtain critical points with respect to the whole space.
This variational principle has many applications in partial differential equations while unifies and generalizes several results in nonlinear Analysis such as the fixed point theory, critical point theory on convex sets and the principle of symmetric criticality.
If you are ever in the centre of Oxford and are getting tired of the endless beautiful buildings, then make your way to Wytham Woods. Covering 1000 acres of ancient and beautiful woodland 3 miles NW of Oxford, Wytham is exceptionally rich in flora and fauna, with over 500 species of plants, a wealth of woodland habitats, and 800 species of butterflies and moths. And it is so wonderfully peaceful.
The tree amplituhedron A(n, k, m) is a geometric object generalizing the positive Grassmannian, which was introduced by Arkani-Hamed and Trnka in 2013 in order to give a geometric basis for the computation of scattering amplitudes in N=4 supersymmetric Yang-Mills theory. I will give a gentle introduction to the amplituhedron, and then describe what it looks like in various special cases. For example, one can use the theory of sign variation and matroids to show that the amplituhedron A(n, k, 1) can be identified with the complex of bounded faces of a cyclic hyperplane arrangement. I will also present some conjectures relating the amplituhedron A(n, k, m) to combinatorial objects such as non-intersecting lattice paths and plane partitions. This is joint work with Steven Karp, and part of it is additionally joint work with Yan Zhang.
The vast majority of the world's electricity is generated by converting thermal energy into electric energy by use of a steam turbine. Siemens are one of the worlds leading manufacturers of such
turbines, and aim to design theirs to be as efficient as possible. Using an internally built software, Siemens can estimate the efficiency which would result from a turbine design. In this presentation, we present the approaches that have been taken to improve turbine design using mathematical optimisation software. In particular, we focus on the failings of the approach currently taken, the obstacles in place which make solving this problem difficult, and the approach we intend to take to find a locally optimal solution.
In the 80s, Hatcher and Thurston introduced the pants graph as a tool to prove that the mapping class group of a closed, orientable surface is finitely presented. The pants graph remains relevant for the study of the mapping class group, sitting between the marking graph and the curve graph. More precisely, there is a sequence of natural coarse lipschitz maps taking the marking graph via the pants graph to the curve graph.
A second motivation for studying the pants graph comes from Teichmüller theory. Brock showed that the pants graph can be interpreted as a combinatorial model for Teichmüller space with the Weil-Petersson metric.
In this talk I will introduce the pants graph, discuss some of its properties and state a few open questions.
