Seminars and Colloquia

The mathematics colloquium is held twice a term.

Mathematics Colloquium

During term time seminars are held by the different research groups in the School of Mathematics.

Pure Mathematics

Applied Mathematics

Events this week:

Analysis Seminar: The Interplay of Two Euler-Lagrange Equations in the Context of Self Maps of the Annulus

George Morrison, New York University Shangha
Tuesday 10 March 2020, 14:00
WATN-R17 18, Watson Building
Tea and coffee will be provided after the talk at the common room

The objective of this talk is to classify all critical points of an energy functional associated to an incompressible elastic deformation of an annulus. We principally consider a sub-class of self maps of the domain in the form of whirls. After a study of the relationship between two Euler-Lagrange systems we resolve the main question in the context of a weighted Dirichlet energy. Of particular interest here is a striking discrepancy in the solution sets depending on whether the underlying spatial dimension is odd or even. This is joint work with Dr. Ali Taheri.

Algebra Reading Group on Sporadic Groups: The Griess Algebra and the Monster

Yunxi Shi (University of Birmingham
Tuesday 10 March 2020, 16:00
Watson Building, Room 310

Abstract not available

Optimisation and Numerical Analysis Seminars: A quotient geometry on the manifold of fixed-rank positive-semidefinite matrices

Estelle Massart (NPL-postdoc, University of Oxford)
Wednesday 11 March 2020, 12:00
Physics West 103

Riemannian optimization aims to design optimization algorithms for constrained problems, where the constraints enforce the variables to belong to a Riemannian manifold. Classical examples of Riemannian manifolds include, e.g., the set of orthogonal matrices, the set of subspaces of a given dimension (called the Grassman manifold), and the set of fixed-rank matrices.

After a quick introduction to Riemannian optimization, and more specifically Riemannian gradient descent (RGD), we will present the tools needed to run RGD on the manifold of fixed-rank positive-semidefinite matrices, seen as a quotient of the set of full-rank rectangular matrices by the orthogonal group. We will also present recent results about related geometrical tools on that manifold. This manifold is particularly relevant when dealing with low-rank approximations of large positive-(semi)definite matrices.

Combinatorics and Probability Seminar: Combinatorial discrepancy and a problem of J.E. Littlewood on Flat Polynomials

Julian Sahasrabudhe (University of Cambridge+
Thursday 12 March 2020, 15:00
Watson LTC
Tea, coffee and biscuits will be provided after the talk at the common room

Given a collection of sets A1,...,Am ⊆ [n], the basic problem in combinatorial discrepancy theory is to find a colouring of {1,...,n} with {+1,-1} so that, for each i ∈ [m], the sum of f over the elements A_i is as small in absolute value as possible. In this talk, I will discuss how the sort of combinatorial and probabilistic reasoning used to think about problems in combinatorial discrepancy can be adapted to solve an old conjecture of J.E. Littlewood in harmonic analysis.