## Algebra

•  Zijian Yao, University of Chicago
•  The eigencurve over the boundary of the weight space
•  11/28/2022
•  3:00 PM - 4:00 PM
•  C304 Wells Hall
•  Preston Wake (wakepres@msu.edu)

The eigencurve is a rigid analytic curve that $p$-adically interpolates eigenforms of finite slope. The global geometry of the eigencurve is somewhat mysterious. However, over the boundary, it is predicted to behave rather nicely (by the so-called Halo conjecture). This conjecture has been studied by Liu--Wan--Xiao for definite quaternion algebras. In this talk, we will report on some work in progress on this conjecture in the case of $\rm{GL}(2)$. If time permits, we will discuss some generalizations towards groups beyond $\rm{GL}(2)$. This is partially joint with H. Diao.

## Contact

Department of Mathematics
Michigan State University