Landscapes in Mathematical Sciences

This is our Department Colloquium, with distinguished speakers giving an overview of a topic of general mathematical interest. The talks are aimed at a level to be accessible to all postgraduate students and staff in the department. Advanced undergraduates and members of other departments are also welcome to attend.

Talks last a full hour and, unless otherwise stated, take place in the Wolfson Theatre (4W1.7), beginning at 3:15pm. Tea is available from 30 minutes before the talk in the foyer outside the lecture theatre.

Contact


Next Landscapes Seminar

Date Speaker Title/Abstract
14 December 2018 Alejandro Adem
UBC Vancouver
The Topology of Commuting Matrices
In this talk we will discuss the structure of spaces of commuting elements in a compact Lie group. Their connected components and other basic topological properties will be discussed. We will also explain how they can be assembled to produce a space which classifies certain bundles and represents an interesting cohomology theory. A number of explicit examples will be provided for orthogonal, unitary and projective unitary groups.

Autumn 2018

Date Speaker Title/Abstract
5 October 2018 Philip Maini
Oxford
Does mathematics have anything to do with biology?
In this talk, I will review a number of interdisciplinary collaborations in which I have been involved over the years that have coupled mathematical modelling with experimental studies to try to advance our understanding of processes in biology and medicine. Examples will include somatic evolution in tumours, collective cell movement in epithelial sheets, and pattern formation in slime mould. These are examples where verbal reasoning models are misleading and insufficient, while mathematical models can enhance our intuition.
19 October 2018 Nigel Hitchin
Oxford
Integrable systems and algebraic geometry
Completely integrable Hamiltonian systems form an important concept in many areas of mathematics and include classical examples like the equations for a spinning top or the geodesics on an ellipsoid. A huge range of examples comes from considering the algebraic geometry of moduli spaces of Higgs bundles on a Riemann surface. The talk will focus on the geometry of the singular locus for these systems and how certain constructions in algebraic geometry help to understand the structure of this locus.
9 November 2018 Eugene Shargorodsky
KCL
Some open problems related to Stokes waves
A Stokes wave is a steady periodic wave, propagating under gravity with constant speed on the surface of an infinitely deep irrotational flow. Its free surface is determined by Laplace's equation, kinematic and periodic boundary conditions and by a dynamic boundary condition given by the requirement that pressure in the flow at the surface should be constant (Bernoulli's theorem). The modern theory of Stokes waves has been shaped by the works of L.E. Fraenkel, J.F. Toland, and their collaborators. This part of nonlinear analysis has surprising connections to many other fields ranging from quantum mechanics to number theory. The aim of the talk is to discuss some of those connections and some related open problems.
23 November 2018 Richard Elwes
Leeds
Concrete Incompleteness
In 1931, Kurt Göel proved his famous incompleteness theorems, establishing that any attempt to axiomatize the arithmetic of the natural numbers would necessarily leave gaps: statements which can be neither proved nor disproved.

Gödel's original unprovable statements have a strongly meta-mathematical flavour, with little apparent relevance to mainstream mathematical concerns. In this talk, we will look at various examples of concrete incompleteness: unprovable statements which are also interesting and natural from a broader mathematical perspective. Particularly striking are some simple combinatorial statements, found recently by Harvey Friedman, which can only be resolved with large cardinal axioms.
7 December 2018 Ruth Gregory
Durham
The Decay of the Universe
Phase transitions are part of everyday life, yet are also believed to be part of the history of our universe, where the nature of particle interactions change as the universe settles into its vacuum state. The recent discovery of the Higgs and its mass suggests that our vacuum may not be entirely stable, and that a further phase transition could take place. My talk will review how we find the probability of these phase transitions and I will discuss my recent work on how black holes can dramatically change the result!
14 December 2018 Alejandro Adem
UBC Vancouver
The Topology of Commuting Matrices
In this talk we will discuss the structure of spaces of commuting elements in a compact Lie group. Their connected components and other basic topological properties will be discussed. We will also explain how they can be assembled to produce a space which classifies certain bundles and represents an interesting cohomology theory. A number of explicit examples will be provided for orthogonal, unitary and projective unitary groups.

A list of talks in recent past years can be found here.