**Queen Mary University of London**

**2 ^{nd} February 2018**

This workshop is a part of the research network "Applied Algebraic Topology" supported by an LMS scheme 3 grant.

Our previous meetings are detailed here.

**Organisers**

**Dr. Ginestra Bianconi**, QMUL (g.bianconi
AT qmul.ac.uk)

**Prof. Michael Farber**, QMUL (m.farber
AT qmul.ac.uk)

**Schedule**

09:00 - 9:30 Scape 1.04 |
Coffee |

9:30 - 10:30 Scape 1.04 |
Abstract: A sequence of finite graphs are called topologically convergent, if for any connected subgraph H, eventually, either all the graphs contain H or none of them contain H. This is the topological analogue of the Benjamini-Schramm (measurable) graph limit theory. I intend to show how some important results of the measurable graph limit theory can be interpreted and proved in the topological situation. |

11:00 - 12:00 Scape 1.04 |
Abstract: There are many data sets where the nodes in the most obvious representation come with a natural order so these are Directed Acyclic Graphs. This order can be interpreted as an arrow of time suggesting that the most natural geometrical setting are spacetimes with their non-Riemannian geometry. I will discuss this idea in terms of simple models and analysis of several citation networks. |

12:00 - 14:00 |
Lunch break |

14:00 - 15:00 Scape 2.01 |
Abstract: While algebraic topology is now well established as an applicable branch of mathematics, its emergence in neuroscience is surprisingly recent. In this talk I will present a summary of an ongoing joint project with mathematician and neuroscientists. I will start with some basic facts on neuroscience and the digital reconstruction of a rat's neocortex by the Blue Brain Project in EPFL. I will then explain how data emerging from this reconstruction can be mapped into abstract graphs that in turn give rise to certain mathematical objects in the realm of algebraic and combinatorial topology. Following a short introduction to some of the basic tools of algebraic topology, I will explain how they can potentially be used in the context of neuroscience. Having set up the scene, I will proceed by presenting the results of an ongoing collaboration with the Blue Brain Project team. In particular I shall demonstrate how the topological techniques give new insights on the behaviour of neural systems and inspire new directions in neuroscience research. |

15:00 - 15:30 Scape 2.01 |
Coffee |

15:30 - 16:30 Scape 2.01 |
Abstract: In 2003, M. Farber introduced a homotopy invariant whose definition is given in an elementary way and motivated by motion planning problems from robotics, the topological complexity (TC) of a space. We will introduce the concept of TC and its relations with the better-known Lusternik-Schnirelmann category of topological spaces. After discussing lower bounds on TC given in terms of cohomology, we will focus on aspherical spaces. We will discuss algebraic methods yielding lower bounds for the TC of aspherical spaces and present a recent result of M. Farber and the speaker about aspherical spaces with hyperbolic fundamental groups. |

**Participants**