8^{th} June 2015
University of Aberdeen
09:00 – 10:00 Fraser Noble Annex 
Coffee in Mathematical Sciences common room 
10:00 – 11:00 Fraser Noble 156 
Nina Otter
(University of Oxford) Title: A roadmap for the computation of persistent homology (slides) Abstract: Persistent
homology is a method from algebraic topology used in data analysis to
study qualitative features of data, which is robust to noise, dimension
independent and provides statistical summaries of the outputs. Despite recent
progress, the computation of persistent homology for large datasets remains
an open problem. We investigate the challenges of computing persistent
homology by evaluating the different algorithms and data structures, using
the open source implementations currently available and a wide range of
synthetic and real world datasets. 
11:00 – 11:30 Fraser Noble 156 
Short break for discussions 
11:30 – 12:30 Fraser Noble 156 
Subramanian Ramamoorthy (University of Edinburgh) Title: Topological Trajectory Classification with
Persistent Homology (slides) Abstract: A longstanding and important problem for autonomous robotics is to devise encodings of tasks that span the hierarchy from the quantitative sensorimotor signals to more qualitative task specifications. Despite significant recent activity around methods for learning hierarchical representations, e.g., in the area of computer vision, the problem of defining and learning actionoriented symbols remains open. Motivated in this way, we address the problem of trajectory classification. We present a samplingbased approach to trajectory classification which enables automated highlevel reasoning about topological classes of trajectories. Our approach is applicable to general configuration spaces and relies only on the availability of collision free samples. Unlike previous samplingbased approaches in robotics which use graphs to capture information about the pathconnectedness of a configuration space, we construct a multiscale approximation of neighborhoods of the collision free configurations based on filtrations of simplicial complexes. Our approach thereby extracts additional homological information which is essential for a topological trajectory classification. We propose a multiscale classification algorithm for trajectories in configuration spaces of arbitrary dimension and for sets of trajectories starting and ending in two fixed points. Using a cone construction, we then generalize this approach to classify sets of trajectories even when trajectory start and end points are allowed to vary in pathconnected subsets. We furthermore show how an augmented filtration of simplicial complexes based on an arbitrary function on the configuration space, such as a costmap, can be defined to incorporate additional constraints. We present an evaluation of our approach in 2, 3, 4 and 6dimensional configuration spaces in simulation and in realworld experiments using a Baxter robot and motion capture data. We view this work as a step
towards a broader family of algorithms that maintain beliefs and plan actions
in a multiscale fashion. I will conclude my talk with a discussion on this,
in the process giving a high level outline of some related algorithms from
our recent work addressing interactive decision making. 
12:30 – 14:00 
Lunch break 
14:00 – 15:00 Fraser Noble 156 
Problem Session 
15:00 – 16:00 Fraser Noble 156 
David Quinn
(University of Aberdeen) Title: Finite domination and combinatorial Novikov completions Abstract: Joint work with Thomas Huttemann. We say a cochain complex C of modules over a Laurent polynomial ring in several indeterminates is finitely dominated over the ground ring R if it is a homotopy retract of a bounded cochain complex of finitely generated free Rmodules. In the talk we discuss `Novikov' completions of the Laurent ring, where, given a
polytope P, we associate a completion of the Laurent ring to each flag of
faces of P. We can then show that if C, upon tensoring
with each of these completions, becomes an acyclic complex then C is finitely
dominated. The reverse implication also holds but uses different techniques. 

List of participants:
1. Mark Grant, Aberdeen 2. Jarek Kędra,
Aberdeen 3. Rachael Boyd, Aberdeen 4. Richard Hepworth, Aberdeen 5. David Quinn, Aberdeen 6. Subramanian Ramamoorthy, Edinburgh 7. Zur Izhakian, Aberdeen 8. John Hubbuck,
Aberdeen 9. Diarmuid Crowley, Aberdeen 10. Brendan Owens, Glasgow 11. Assaf Libman, Aberdeen 12. Hassan Hamdoun,
Aberdeen 13. Nina Otter, Oxford 14. Adriana Marciuk, Aberdeen 15. Mark Paulin, Aberdeen 