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A Thurston compactification of the space of Bridgeland stability conditions

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Speaker: 
Naoki Koseki
Zugehörigkeit: 
Liverpool
Datum: 
Don, 02/02/2023 - 10:30 - 11:30
Location: 
MPIM Lecture Hall

Contact: Daniel Huybrechts.
 

Motivated by the homological mirror symmetry and the work of Bridgeland-Smith, we investigate an analogy between the theory of Bridgeland stability conditions and Teichmuller theory. Specifically, we construct a Thurston type compactification of the space of Bridgeland stability conditions on a smooth projective curve.

We give two applications in the case of an elliptic curve. Firstly, we compare our compactification with the classical construction for a torus via the homological mirror symmetry. Secondly, we give a Nielsen-Thurston type classification of autoequivalences.

This is based on a joint work with Kohei Kikuta (Osaka) and Genki Ouchi (Nagoya).

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