Wed, 06 Feb 2019
16:00
C1

Cross ratios on boundaries of negatively curved spaces

Elia Fioravanti
(Oxford University)
Abstract

I will give a self-contained introduction to the theory of cross ratios on boundaries of Gromov hyperbolic and CAT(-1) spaces, focussing on the connections to the following two questions. When are two spaces with the 'same' Gromov boundary isometric/quasi-isometric? Are closed Riemannian manifolds completely determined (up to isometry) by the lengths of their closed geodesics?

Wed, 30 Jan 2019
16:00
C1

Residual properties of graphs of p-groups

Gareth Wilkes
(Cambridge University)
Abstract

When groups may be built up as graphs of 'simpler' groups, it is often 
of interest to study how good residual finiteness properties of simpler 
groups can imply residual properties of the whole. The essential case of 
this theory is the study of residual properties of finite groups. In 
this talk I will discuss the question of when a graph of finite 
$p$-groups is residually $p$-finite, for $p$ a prime. I describe the 
previous theorems in this area for one-edge and finite graphs of groups, 
and their method of proof. I will then state my recent generalisation of 
these theorems to potentially infinite graphs of groups, together with 
an alternative and more natural method of proof. Finally I will briefly 
describe a usage of these results in the study of accessibility -- 
namely the existence of a finitely generated inaccessible group which is 
residually $p$-finite.

Wed, 23 Jan 2019
16:00
C1

Commensurator rigidity from actions on graphs

Richard Wade
(Oxford University)
Abstract

I will give a description of a method introduced by N. Ivanov to study the abstract commensurator of a group by using a rigid action of that group on a graph. We will sketch Ivanov's theorem regarding the abstract commensurator of a mapping class group. Time permitting, I will describe how these methods are used in some of my recent work with Horbez on outer automorphism groups of free groups.

Oxford Mathematician Erik Panzer talks about his and colleagues' work on devising an algorithm to compute Kontsevich's star-product formula explicitly, solving a problem open for more than 20 years.

"The transition from classical mechanics to quantum mechanics is marked by the introduction of non-commutativity. For example, let us consider the case of a particle moving on the real line.

From commutative classical mechanics...

Tue, 22 Jan 2019

12:45 - 13:30
C5

Wave attenuation by flexible vegetation

Clint Wong
(Oxford University)
Abstract

Coastal vegetation has a well-known effect of attenuating waves; however, quantifiable measures of attenuation for general wave and vegetation scenarios are not well known. On the plant scale, there are extensive studies in predicting the dynamics of a single plant in an oscillatory flow. On the coastal scale however, there are yet to be compact models which capture the dynamics of both the flow and vegetation, when the latter exists in the form of a dense canopy along the bed. In this talk, we will discuss the open questions in the field and the modelling approaches involved. In particular, we investigate how micro-scale effects can be homogenised in space and how periodic motions can be averaged in time.

Mon, 21 Jan 2019

13:00 - 14:00
N3.12

Mathematrix - Meet Prof Andrew Hodges

Andrew Hodges
Abstract

 Author of Alan Turing: The Enigma, sharing his academic path and experience as activist for LGBTQ+ rights

Thu, 16 May 2019

17:00 - 18:00
L1

Graham Farmelo - The Universe Speaks in Numbers

Graham Farmelo
Further Information

The supreme task of the physicist, Einstein believed, was to understand the 'miraculous' underlying order of the universe, in terms of the most basic laws of nature, written in mathematical language. Most physicists believe that it's best to seek these laws by trying to understand surprising new experimental findings. Einstein and his peer Paul Dirac disagreed and controversially argued that new laws are best sought by developing the underlying mathematics.

Graham will describe how this mathematical approach has led to insights into both fundamental physics and advanced mathematics, which appear to be inextricably intertwined. Some physicists and mathematicians believe they are working towards a giant mathematical structure that encompasses all the fundamental laws of nature. But might this be an illusion? Might mathematics be leading physics astray?

Graham Farmelo is a Fellow at Churchill College, Cambridge and the author of 'The Strangest Man,' a biography of Paul Dirac.

5.00pm-6.00pm
Mathematical Institute
Oxford

Please email @email to register.

Or watch live:

https://www.facebook.com/OxfordMathematics/
https://livestream.com/oxuni/farmelo

The Oxford Mathematics Public Lectures are generously supported by XTX Markets.

Mon, 18 Feb 2019

17:00 - 18:00
L5

A Beautiful Game from the War: Piet Hein, John Nash, Martin Gardner and Hex

Ryan Hayward
(University of Alberta)
Abstract

Seeking income during World War II, Piet Hein created the game now called Hex, marketing it through the Danish newspaper Politiken.  The game was popular but disappeared in 1943 when Hein fled Denmark.

The game re-appeared in 1948 when John Nash introduced it to Princeton's game theory group, and became popular again in 1957 after Martin Gardner's column --- "Concerning the game of Hex, which may be played on the tiles of the bathroom floor" --- appeared in Scientific American.

I will survey the early history of Hex, highlighting the war's influence on Hein's design and marketing, Hein's mysterious puzzle-maker, and Nash's fascination with Hex's theoretical properties.

Tue, 22 Jan 2019
15:00
C1

Cluster Adjacency

Dr Omer Gurdogan
(Southampton)
Abstract

Cluster Adjacency is a geometric principle which defines a subclass of multiple polylogarithms with analytic properties compatible with that of scattering amplitudes and Feynman loop integrals. We use this principle to a priori remove the redundances in the perturbative bootstrap approach and efficiently compute the four-loop NMHV heptagon. Moreover, cluster adjacency is naturally applied to the space of $A_n$ polylogarithms and generates numerous structures therein to be explored further.

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