# Algebra/Number Theory Seminar

## Solutions of equations involving the modular j function.

Sebastian Herrero, Pontificia Universidad Católica de Valparaíso, Chile

Thursday, October 17th, 2019
11:00 AM - 12:00 PM
Hylan 1106A

Inspired on Zilber’s work on pseudo-exponentiation, in particular on his analysis of the complex exponential field, several authors have studied the existence of generic solutions of exponential-polynomial equations. Results on the existence of solutions in certain cases follow from the work of Katzberg (1983) and Brownawell-Masser (2016), among others. On the other hand, assuming Schanuel’s conjecture, Marker (2006), Mantova (2016) and D’Aquino-Fornasiero-Terzo (2018) have proved that generic solutions also exist (again, in certain cases). Since there are plenty of analogies between the exponential and the modular j function, it is natural to ask if the results mentioned above can be replicated for the j function. In this talk I will report on work in progress in collaboration with Sebastián Eterovic (University of California, Berkeley) where we prove that solutions of certain polynomial equations involving the j function exist. Moreover, assuming a modular analogue of Schanuel’s conjecture, we obtain results on the existence of generic solutions.

Event contact: dinesh dot thakur at rochester dot edu