Quantitative Discrete Homotopy Theory
Emily Roff (University of Edinburgh)
Monday 13th October 15:00-16:00
Maths 311B
Abstract
"Discrete homotopy theory" refers to the use of homotopy-theoretic concepts and tools to study combinatorial structures such as graphs. The standard approach admits a quantitative variant, in which one tracks the lengths of homotopies between maps, leading to an infinite hierarchy of homotopy theories for graphs. In this talk, I will present recent work with Richard Hepworth describing a family of homological invariants associated with these theories. I will also discuss an ongoing collaboration with Muriel Livernet and Sarah Whitehouse, in which we seek presentations for the corresponding homotopy categories.
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