27^{th} May 2016
University of Aberdeen
09:30 – 10:15 Fraser Noble Annex 
Coffee in Mathematical Sciences common room 
10:15 – 11:15 Fraser Noble 156 
Ben Martin
(University of Aberdeen) Title: Manipulation
and comparison of voxel images Abstract: Medical scans
often provide information in terms of a voxel image (voxels are the
3dimensional analogue of pixels). If
the image is of a body organ  say, a brain  then it is reasonable to assume
that the voxel image is homeomorphic to a solid
ball. I will discuss recent work with Raazesh Sainudiin and Josh Voorkamp on how to store and manipulate such images. We can represent the images using
edgelabelled graphs and use graphtheoretic algorithms to tell when two
images are the same (up to translation and exchange of coordinate
axes). The eventual aim is to develop
an automated system to detect whether the scanned organ is healthy or
diseased by comparing it to a standard database of images. To do this, one needs a way to measure
whether two images are similar. This
seems to be a difficult problem. 
11:30 – 12:30 Fraser Noble 156 
Silke Henkes (University of Aberdeen) Title: Applications of Topology in Soft Matter
Physics (slides) Abstract: Liquid crystals are classified by their orientational symmetry into nematic, smectic and chiral, equivalent to a line field, parallel sheets, and twisted helical phases respectively.

12:30 – 14:00 
Lunch break 
14:00 – 15:00 Fraser Noble 156 
Piotr Beben (University
of Southampton) Title: Cohomology and LScategory of MomentAngle Complexes (slides) Abstract: Given a simplicial complex $K$ with $n$ vertices, the momentangle complex $\mathcal{Z}_K$ is a certain subcomplex of $(D^2)^{\times n}$ defined purely in terms of $K$. Despite their simple description, they have connections to several areas of mathematics. At the same time their topology is very intricate. I will discuss their cohomology, LusternikSchnirelmann
category, and homotopy type, and various
mathematical and realworld applications of these. 
15:15 – 16:15 Fraser Noble 156 
Gregory Lupton (Cleveland State University) Title: Topological Complexity: From Robots to
Social Choice Abstract: Suppose the possible states of
some system are represented as points in an appropriate topological
spacethe configuration space of the system. Then a path in the
configuration space corresponds to a transition, through intermediate states
of the system, from an initial to a final state. A continuous
assignment of paths to each pair of states is called a motion
planner for the system. Topological Complexity is a numerical homotopy invariant (of the configuration space) that
may be viewed as an index of the necessary discontinuity in a motion
planner for the system. In this talk, I will begin with an
overview of the basic ideas of the topic. I will describe
some workjoint with Grant and Opreathat provides useful lower bounds
for the Topological Complexity. I will indicate a
possible direction for future work, namely the topic of social choice
from mathematical economics. 

List of participants:
1. Dave Benson (Aberdeen} 2. Piotr Beben (Southampton) 3. Ben Martin (Aberdeen) 4. Dirk Schuetz
(Durham) 5. Mel Chen (Glasgow) 6. John Hubbuck (Aberdeen) 7. Greg Lupton (Cleveland State) 8. Silke Henkes (Aberdeen) 9. Diarmuid Crowley (Aberdeen) 10. David Quinn (Edinburgh) 11. Mark Grant (Aberdeen) 12. Rachael Boyd (Aberdeen) 13. Aaron Tikuisis (Aberdeen) 14. David Recio Mitter (Aberdeen) 15. Ran Levi (Aberdeen) 16. Csaba Nagy (Aberdeen) 