BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Algebraic Harder-Narasimhan filtrations Treffinger, Hipolito


In this talk we introduce the notion of an indexed chain of torsion classes in an abelian length category $\mathcal{A}$ and we show that any such chain induce a Harder-Narasimhan (like) filtration for every object in $\mathcal{A}$. Later, building on this result, we compare the properties of indexed chains of torsion classes with the stability functions introduced by Rudakov. Finally, following ideas of Bridgeland, we show that the space of all chains of torsion classes induced by the interval $[0,1]$ form a topological space having a wall and chamber structure and we characterise its chambers.

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