Group actions and stability on elliptic surfaces

DIFFERENTIAL GEOMETRY

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April 20, 2021 9:00 pm - 10:00 pm
via Zoom Video Conferencing
Speaker:

Jason Lo - CSUN

There are two natural group actions on the Bridgeland stability manifold of a triangulated category: a left action by the group of autoequivalences, and a right action by the universal covering space of $\mathrm{GL}^+(2,\mathbb{R})$.  The left action is much harder to compute than the right action in general.  In this talk, we will discuss a method for recognising when a left action is equivalent to that of a right action, and apply it to a non-standard autoequivalence on elliptic surfaces.

This work is partly motivated by an attempt to understand equivalences of triangulated categories in representation theory and algebraic geometry at the same time.