Forthcoming events in this series


Tue, 04 Jul 2023
16:00
Lecture Theatre 2

LMS Hardy Lecture Tour 2023: Eva Miranda (UPC Barcelona) - Singular Hamiltonian and Reeb Dynamics: First steps

Eva Miranda
(UPC Barcelona)
Abstract

Floer theory, which mimics an infinite dimensional Morse approach to the study of critical points of smooth functions, appeared as an attempt to prove Arnold conjecture. The theory is more or less well understood in some compact cases.

Non-compact symplectic manifolds can sometimes be compactified as singular symplectic manifolds where the symplectic form "blows up" along a hypersurface in a controlled way (b^m-symplectic manifolds). In natural examples in Celestial mechanics such as the 3-body problem, these compactifications are given by regularization transformations à la Moser/Mc Gehee etc.

I will use the theory of b^m-symplectic/b^m-contact manifolds (introduced by Scott, Guillemin-Miranda Weitsman, and Miranda-Oms) as a guinea pig to propose ways to extend the study of Hamiltonian/Reeb Dynamics to singular symplectic/contact manifolds. This, in particular, yields new results for non-compact symplectic manifolds and for special (but, yet, meaningful) classes of Poisson manifolds.

Inspiration comes from several results extending the Weinstein conjecture to the context of b^m-contact manifolds and its connection to the study of escape orbits in Celestial mechanics and Fluid Dynamics. Those examples motivate a model for (singular) Floer homology.

I'll describe the motivating examples/results and some ideas to attack the general questions.

The Hardy Lectureship was founded in 1967 in memory of G.H. Hardy (LMS President 1926-1928 & 1939-1941). The Hardy Lectureship is a lecture tour of the UK by a mathematician with a high reputation in research.

Mon, 27 Jun 2022
16:15
St Catherine's

The Reddick Lecture 2022: The Benefits of Applied Mathematics in Product Development

Dr Uwe Beuscher, W.L. Gore & Associates, Inc.
Further Information

For more information, and to register your interest, please visit the Reddick Lecture web page

Abstract

Throughout a product development project, many decisions must be made. These include whether to start, stop, continue, or re-direct a project based on the learnings of the project team. Some of these decisions are related to the risk of achieving certain product performance attributes and they are often based on experimental observations in the laboratory or in field applications of early prototypes. Sometimes, these observations provide sufficient insight but often a significant uncertainty remains. Mathematical simulation can provide deeper insight into the mechanisms, may indicate limiting parameters and transport steps, and allows exploration of novel prototypes without actually making them. This talk will illustrate how Mathematics have been used to inform project development projects and their guiding decisions at WL Gore by describing examples from three very different applications.

Thu, 24 Jun 2021

17:00 - 18:00

Equal Opportunity Cities (this lecture is open to everyone)

Sandy Pentland
(MIT)
Further Information

Using data from four continents, we show that diversity of consumption and of diversity of social exposure are perhaps the single most powerful predictor of life outcomes such as increasing neighborhood GDP, increasing individual wealth, and promoting intergenerational mobility, even after controlling for variables such as population density, housing price, and geographic centrality. The effects of diversity in promoting opportunity are causal, and inequality in opportunity stems more from social norms that promote segregation than from physical segregation. Policies to promote more equal opportunities within cities seem practical.

You can register here. Everyone is welcome.

Fri, 18 Jun 2021

13:30 - 17:00

Groups and Geometry in the South East

Piotr Przytycki, Elia Fioravanti, Rylee Lyman
(McGill & Bonn & Rutgers-Newark)
Further Information

Tits Alternative in dimension 2

1:30-2:30PM

Piotr Przytycki (McGill)

A group G satisfies the Tits alternative if each of its finitely generated subgroups contains a non-abelian free group or is virtually solvable. I will sketch a proof of a theorem saying that if G acts geometrically on a simply connected nonpositively curved complex built of equilateral triangles, then it satisfies the Tits alternative. This is joint work with Damian Osajda.

Coarse-median preserving automorphisms

2:45-3:45PM

Elia Fioravanti (Bonn)

We study fixed subgroups of automorphisms of right-angled Artin and Coxeter groups. If Phi is an untwisted automorphism of a RAAG, or an arbitrary automorphism of a RACG, we prove that Fix(Phi) is finitely generated and undistorted. Up to replacing Phi with a power, the fixed subgroup is actually quasi-convex with respect to the standard word metric (which implies that it is separable and a virtual retract, by work of Haglund and Wise). Our techniques also apply to automorphisms of hyperbolic groups and to certain automorphisms of hierarchically hyperbolic groups. Based on arXiv:2101.04415.

Some new CAT(0) free-by-cyclic groups

4:00-5:00PM

Rylee Lyman (Rutgers-Newark)

I will construct several infinite families of polynomially-growing automorphisms of free groups whose mapping tori are CAT(0) free-by-cyclic groups. Such mapping tori are thick, and thus not relatively hyperbolic. These are the first families comprising infinitely many examples for each rank of the nonabelian free group; they contrast strongly with Gersten's example of a thick free-by-cyclic group which cannot be a subgroup of a CAT(0) group.

 

Thu, 01 Oct 2020

16:00 - 17:00
Virtual

Systems Thinking and Problem Solving: Value-based Approaches to Mathematical Innovation (Cancelled)

Professor R. Eddie Wilson
(University of Bristol)
Further Information

More information on the Reddick Lecture.

Abstract

This talk is a personal how-to (and how-not-to) manual for doing Maths with industry, or indeed with government. The Maths element is essential but lots of other skills and activities are equally necessary. Examples: problem elicitation; understanding the environmental constraints; power analysis; understanding world-views and aligning personal motivations; and finally, understanding the wider systems in which the Maths element will sit. These issues have been discussed for some time in the management science community, where their generic umbrella name is Problem Structuring Methods (PSMs).