Painleve VI: the search for canonical representations

In 1902, Painleve introduced a collection of 6 differential equations yielding all second order equations with no movable singularities. It turns out that algebraic solutions to Painleve’s sixth equation correspond to canonical triples of 2 by 2 complex matrices. We will describe the history of what is known about these canonical tuples of matrices. These canonical tuples can also be viewed as canonical representations of fundamental groups of Riemann surfaces, and also as local systems on certain covers of the moduli space of curves. This talk includes joint work with Daniel Litt.

For more information, please see: https://people.math.harvard.edu/~ana/ons/