23^{rd} September 2016
Durham University
10:30 – 11:00 CM 211 
Coffee in Mathematical Sciences common room 
11:00 – 11:45 CM 103 
Ruben
SanchezGarcia
(University of Southampton) Title: Geometry and Topology of Networks and Data (slides) Abstract: This
will be an overview talk on past and current work in applied graph theory and
topology. I will describe previous work on network symmetry, and spectral
clustering, ways of generalising network methods to higher dimensions via
Laplacian operators, and an application to ranking in horse racing data. 
11:45 – 14:15 
Break for Lunch and Discussions 
14:15 – 15:00 CM 103 
Mark Grant
(University of
Aberdeen) Title: The PoincaréHopf
Theorem for line fields (revisited) (slides) Abstract:
A line field on a manifold is a section of the projectivized
tangent bundle. These objects find applications in soft matter physics, where
they may be used to model ordered media made up of rodshaped molecules, such
as nematic liquid crystals. In this talk I will present an analogue of the PoincaréHopf
theorem for line fields. For a line field with finitely many isolated
topological defects on a closed manifold, this relates the sum of the local
indices of the defects with the Euler characteristic of the manifold. A
version of this result for orientable surfaces was known to H. Hopf. Our result extends Hopf’s
result to higher dimensions, and corrects a result of L. Markus (published in
the Annals of Mathematics in 1955). This is joint work with D. Crowley. 
15:15 – 16:00 CM 103 
Yumi Boote (University of Manchester) Title: Configuration spaces, the octonionic projective plane, and potential applications (slides) Abstract: For
many years configuration spaces have attracted the attention of
mathematicians, physicists, engineers, and scientists in other disciplines.
For example, the elements of a configuration space of a topological space X
may be interpreted as collections of data/particles. In this talk, I
shall focus on the space C_2(X) of unordered pairs of distinct
particles on a cohomologically wellbehaved X,
and summarise my results on the geometry and integral cohomology
rings of C_2(X) and two of its compactifications. As an example,
I shall discuss the case of the octonionic
projective plane OP^2; it has been suggested by Hisham
Sati that OP^2 could play a role in the Mtheory of theoretical
physics. 

List of participants:
1. Dirk Schuetz
(Durham) 2. Patrick Orson (Durham) 3. Yumi Boote
(Manchester) 4. Vitaliy Kurlin (Liverpool) 5. Mark Grant (Aberdeen) 6. David RecioMitter (Aberdeen) 7. Norbert Peyerimhoff
(Durham) 8. Gareth Williams (Open University) 9. Daniel BallesterosChavez (Durham) 10. Mel Chen (Glasgow) 11. Shiping Liu (Durham) 12. Andrew Lobb
(Durham) 13. Ruben SanchezGarcia (Southampton) 