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).
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/node/5285