Mon, 15 May 2017
17:00
L3

Ars sine Scientia Nihil Est: Architecture and Mathematics through history

Snezana Lawrence
(Anglia Ruskin University)
Abstract

Part of the series "What do historians of mathematics do?"  
In the last year of 14th century, a French mathematician/geometer Jean Mignot, was called from Paris to help with the construction of the Cathedral of Milan. Thus was created one of the most famous stories about how mathematics literally supports great works of art, helping them stand the test of time. This talk will look at some patterns that begin to become apparent in the investigations of the relationship between architecture and mathematics and the creativity that is common to the pursuit of both. I will present the case on how this may matter to someone who is interested in the history of mathematics. To make this more intelligible, I will partly talk also of my personal journey in investigating this relationship and the issues I have researched and written about, and how these in turn changed my view of the nature of mathematics education. 

Mon, 08 May 2017
17:00
L3

What is algebra?

Christopher Hollings
(Mathematical Institute)
Abstract

Part of the series "What do historians of mathematics do?"  

I will address this question by turning to another: "What is algebra?"  In answering this second question, and surveying the way that the answer changes as we move through the centuries, I will highlight some of the problems that face historians of mathematics when it comes to interpreting historical mathematics, and give a flavour of what it means to study the history of mathematics.

Thu, 23 Feb 2017
11:00
C5

Non-reduced schemes and Zariski Geometries

Alfonso Ruiz
(Oxford)
Abstract

Using results by Eisenbud, Schoutens and Zilber I will propose a model theoretic structure that aims to capture the algebra (or geometry) of a non reduced scheme over an algebraically closed field. 

The International Congresses of Mathematicians (ICMs) take place every four years at different locations around the globe, and are the largest regular gatherings of mathematicians from all nations.  However, as much as the assembled mathematicians may like to pretend that these gatherings transcend politics, they have always been coloured by world events: the congresses prior to the Second World War saw friction between French and German mathematicians, for example, whilst Cold War political tensions likewise shaped the conduct of later congresses.

Fri, 03 Mar 2017

10:00 - 11:00
L4

Predictions for Roads

Steve Hilditch
(Thales)
Abstract

Road travel is taking longer each year in the UK. This has been true for the last four years. Travel times have increased by 4% in the last two years. Applying the principle finding of the Eddington Report 2006, this change over the last two years will cost the UK economy an additional £2bn per year going forward even without further deterioration. Additional travel times are matched by a greater unreliability of travel times.

Knowing demand and road capacity, can we predict travel times?

We will look briefly at previous partial solutions and the abundance of motorway data in the UK. Can we make a breakthrough to achieve real-time predictions?

Mon, 13 Mar 2017

15:30 - 16:30
L5

Stable twisted cohomology via scanning

Oscar Randal-Williams
(Cambridge)
Abstract

The technique of scanning, or the parameterised Pontrjagin--Thom construction, has been extraordinarily successful in calculating the cohomology of configuration spaces (McDuff), moduli spaces of Riemann surfaces (Madsen, Tillmann, Weiss), moduli spaces of graphs (Galatius), and moduli spaces of manifolds of higher dimension (Galatius, R-W, Botvinnik, Perlmutter), with constant coefficients. In each case the method also works to study the cohomology of moduli spaces of objects equipped with a "tangential structure". I will explain how choosing an auxiliary highly-symmetric tangential structure often lets one calculate the cohomology of these moduli spaces with large families of twisted coefficients, by exploiting the symmetries of the tangential structure and using a little representation theory.

 

Mon, 13 Mar 2017

14:00 - 15:00
L5

Operad groups and the homology of the Higman-Thompson groups

Nathalie Wahl
(Copenhagen)
Abstract

 Markus Szymik and I computed the homology of the Higman-Thompson groups by first showing that they stabilize (with slope 0), and then computing the stable homology. I will in this talk give a new point of view on the computation of the stable homology using Thumann's "operad groups". I will also give an idea of how scanning methods can enter the picture. (This is partially joint work with Søren Galatius.) 

Mon, 13 Mar 2017

11:30 - 12:30
L5

Homotopical properties of the diffeomorphism group of a smooth homotopy sphere

Michael Weiss
(Muenster)
Abstract

It is hard to detect the exotic nature of an exotic n-sphere M 
in homotopical features of the diffeomorphism group Diff(M). The well 
known reason is that Diff(M) contains a big topological subgroup H which 
is identified with the group of diffeomorphisms rel boundary of the 
n-disk, with a small coset space Diff(M)/H which is invariably homotopy 
equivalent to O(n+1). Therefore it seems that our only chance to detect 
the exotic nature of M in homotopical features of Diff(M) is to see 
something in this extension.  (To make sense of "homotopical features of 
Diff(M)" one should think of Diff(M) as a space with a multiplication 
acting on an n-sphere.) I am planning to report on PhD work of O Sommer 
and calculations due to myself and Sommer which, if all goes well, would 
show that Diff(M) has some exotic homotopical properties in the case 
where M is the 7-dimensional exotic sphere of Kervaire-Milnor fame which 
bounds a compact smooth framed 8-manifold of signature 8. The 
theoretical work is based on classical smoothing theory and the 
calculations would be based on ever-ongoing (>30 years) joint work 
Weiss-Williams, and might give me and Williams another valuable 
incentive to finish it.

Mon, 13 Mar 2017

11:00 - 11:30
L5

Diffeomorphism-equivariant configuration spaces with twisted summable labels

Hongyun Yon
(Oxford)
Abstract

We construct the diffeomorphism-equivariant “scanning map” associated to the configuration spaces of manifolds with twisted summable labels. The scanning map is also functorial with respect to embeddings of manifolds. To adapt P. Salvatore's idea of non-commutative summation into twisted setting, we define a bundle of Fulton-MacPherson operads over a manifold M whose fibres are built within tangent spaces of M.

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