Department of Mathematics


  •  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 (

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.



Department of Mathematics
Michigan State University
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