I will elaborate on some recent developments on the theory of special functions which are relevant to the calculation of Feynman integrals in perturbative quantum field theory, highlighting the connections with some recent ideas in pure mathematics.
The smooth mapping class group of the 4-sphere is pi_0 of the space of orientation preserving self-diffeomorphisms of S^4. At the moment we have no idea whether this group is trivial or not. Watanabe has shown that higher homotopy groups can be nontrivial. Inspired by Watanabe's constructions, we'll look for interesting self-diffeomorphisms of S^4. Most of the talk will be an outline for a program to find a nice geometric generating set for this mapping class group; a few small steps in the program are actually theorems. The point of finding generators is that if they are explicit enough then you have a hope of either showing that they are all trivial or finding an invariant that is well adapted to obstructing triviality of these generators.
The second in our fascinating collaboration with the Orchestra of the Age of Enlightenment (OAE) and Music at Oxford combines the muscial intelligence of the eighteenth century with the artificial intelligence of the twenty-first. Come along and hear the beauty of Bach's Nun komm, der Heiden Heiland (Now come, Saviour of the Gentiles) and the modern beauty of machine learning which may itself be the musical choice of audiences in 300 years' time.
The OAE provide the music (you even get to join in), Marcus delivers the sermon. Maths and Music; saying everything.
We continue with our series of Student Lectures with this first lecture in the 2nd year Course on Differential Equations. Professor Philip Maini begins with a recap of the previous year's work before moving on to give examples of ordinary differential equations which exhibit either unique, non-unique, or no solutions. This leads us to Picard's Existence and Uniqueness Theorem...
Conical Symplectic Resolutions form a broad family of holomorphic symplectic manifolds that are of interest to mathematical physicists, algebraic geometers, and representation theorists; Nakajima Quiver Varieties and Hypertoric Varieties are known as their special cases. In this talk, I will be focused on the Symplectic Geometry of Conical Symplectic Resolutions, and its non-symplectic applications. More precisely, I will talk about my work on finding Exact Lagrangian Submanifolds inside CSRs, and work in progress (joint with Alexander Ritter) about the construction of Symplectic Cohomology on CSRs.
Oxford Mathematician James Maynard has been awarded the 2020 Cole Prize in Number Theory by the American Mathematical Society (AMS) "for his many contributions to prime number theory."
In the seminar, I will talk about a parabolic toy-model for the incompressible Navier-Stokes equations, that satisfies the same energy inequality, same scaling symmetry and which is also super-critical in dimension 3. I will present some partial regularity results that this model shares with the incompressible model and other results that occur only for our model.
