A global analysis of bird plumage patterns reveals no association between habitat and camouflage.
 Somveille, M Marshall, K Gluckman, T PeerJ volume 4 e2658 (09 Jan 2016)
Tue, 07 Feb 2017
14:15
L4

Modular W-algebras and reduced enveloping algebras

Simon Goodwin
(University of Birmingham)
Abstract

We give an overview of joint work with Lewis Topley on modular W-algebras. In particular, we outline the classification 1-dimensional modules for modular W-algebras for gl_n, which in turn this leads to a classification of minimal dimensional modules for reduced enveloping algebras for gl_n.

Tue, 29 Nov 2016
14:00
L3

Stochastic discrete Hamiltonian variational integrators

Tom Tyranowski
(Imperial College)
Abstract

Stochastic Hamiltonian systems with multiplicative noise are a mathematical model for many physical systems with uncertainty. For example, they can be used to describe synchrotron oscillations of a particle in a storage ring. Just like their deterministic counterparts, stochastic Hamiltonian systems possess several important geometric features; for instance, their phase flows preserve the canonical symplectic form. When simulating these systems numerically, it is therefore advisable that the numerical scheme also preserves such geometric structures. In this talk we propose a variational principle for stochastic Hamiltonian systems and use it to construct stochastic Galerkin variational integrators. We show that such integrators are indeed symplectic, preserve integrals of motion related to Lie group symmetries, demonstrate superior long-time energy behavior compared to nonsymplectic methods, and they include stochastic symplectic Runge-Kutta methods as a special case. We also analyze their convergence properties and present the results of several numerical experiments. 

Wed, 30 Nov 2016
11:30
N3.12

Partition Identities, Q-series and the Quest for Rogers-Ramanujan Involutions

Adam Keilthy
(University of Oxford)
Abstract
This talk will introduce some arguably trivial results about partition identities, and generating functions for various counts of partitions. We will discuss methods of proving q-series identities via bijections of partitions, and proving partition identities via analytic methods. We will then comment on the Rogers-Ramanujan identities, their combinatorial interpretation, and their various methods of proof.

Random Walks 3 – The beauty and symmetry of ancient tiles

Beauty is in the eye of the beholder, but what about symmetry? In our final feature on mathematicians let loose in the Ashmolean Museum, Oxford Mathematician Balázs Szendrői investigates the beauty of symmetry in the Museum's Islamic art works. As he explains, no matter what the tile pattern may look like, its underlying symmetry configuration belongs to a small set of possibilities. 

Fri, 25 Nov 2016

15:00 - 16:00
S0.29

Hyperbolic Dehn filling in dimension four

Stefano Riolo
(University of Pisa)
Abstract

By gluing copies of a deforming polytope, we describe some deformations of complete, finite-volume hyperbolic cone four-manifolds. Despite the fact that hyperbolic lattices are locally rigid in dimension greater than three (Garland-Raghunathan), we see a four-dimensional analogue of Thurston's hyperbolic Dehn filling: a path of cone-manifolds $M_t$ interpolating between two cusped hyperbolic four-manifolds $M_0$ and $M_1$.

This is a joint work with Bruno Martelli.

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