Title: Connected components of strata of k-differentials
Speaker: Quentin Gendron (CIMAT)
Date: 13 October 2021
Time: 9:00 pm
Venue: MS teams (team code hiq1jfr)
The k-differentials are sections of the tensorial product of the canonical bundle of a complex algebraic curves. Fixing a partition (m_1,…,m_n) of k(2g-2),
we can define the strata of k-differentials of type (m_1,…,m_n) to be the space of k-differentials on genus g curves with zeroes of orders m_i.
After checking that the strata or not empty, the first interesting topological question about these strata is the classification of their connected component.
In the case k=1, this was settled in an important paper of Kontsevich and Zorich. This result was extend to k=2 by Lanneau, with corrections of Chen-Möller.
The classification is unknown for k greater or equal to 3 as soon as g is greater or equal to 2. In this talk, I will present partial results on this
classification problem obtained together with Dawei Chen (arXiv:2101.01650) and in progress with Andrei Bogatyrev. In particular, I will highlight the way
Pell-Abel equation appears in this problem.