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Graduate Student Colloquium

Date:
-
Location:
Zoom
Speaker(s) / Presenter(s):
Matias von Bell

Title: The 'main theorem' of discrete Morse theory.

Abstract: If you're anything like me, proving that two topological spaces are homotopy equivalent can be quite an intimidating task. If you're further like me you'll catch yourself thinking "If only there was a way to turn such problems into discrete math". This turns out to be more than just wishful thinking thanks to the 'main theorem' of discrete Morse theory! Given polyhedral complexes (or more generally CW complexes), the 'main theorem' lets us turn questions of homotopy equivalence into finding certain acyclic matchings on face posets. In this talk we will give the necessary background and explain the 'main theorem'. Then we will compute some basic examples and see my favorite example from the wild.