In the first week of May 2018 I was invited to give a mini-course at the Universidad Autonoma de Yucatan for their Jornada de Algebra 2018. I had a great time in Merida, and I couldn’t have had a better time at the conference. Thanks again to the organizers for the invitation, and thanks to my host Alex Lara for his generous hospitality!
The conference was aimed at undergraduate and masters level students of UADY, and my course consisted of three talks where I gave a gentle introduction to the ring of polynomials over a finite fields, drawing similarities to the ring of integers. I went on to give a parallel picture of the Carlitz zeta values and the Riemann zeta values, following Euler’s approach. In the final talk of my course, we discovered Goss’ Eisenstein series in a similar way as Carlitz discovered the “Eulerian” Carlitz zeta values. The slides for my course are here (if you have any comments, questions, or suggestions feel free to email me at rudolph dot perkins at gmail): Fqtheta, EulerCarlitz, DrinfeldGossMFs
I also gave a course on some of my work with F. Pellarin on Drinfeld modules over Tate algebras, and described how they should lead to a full explicit description of Eisenstein series for Hecke congruence subgroups of prime power levels which are also Hecke eigenforms. The slides for my talk can be found here: VMFoverT