|Title||$\infty$-groupoids and the Homotopy Hypothesis|
|Presenter||Edoardo Lanari (Macquarie University)|
|Author(s)||Mr Edoardo Lanari|
|Session||Category Theory, Algebraic Topology, K-Theory|
In this talk I will introduce a globular model for weak $\infty$-groupoids, due to A.\,Grothendieck, and illustrate the basic features of their homotopy theory. It is conjectured that the $(\infty,1)$ category they present models homotopy types (this is the so called `Homotopy Hypothesis'), which has been proven to hold true for essentially every other existing model of $\infty$-groupoids (e.g., Kan complexes). I will also outline original ideas and results of my work, along with important results in the literature on this topic, to give an idea on how to prove this conjecture.