The geometry of weight one forms — Kartik Prasanna (University of Michigan)

Weight one forms are rather mysterious since their associated motives do not appear in any simple way in the cohomology of Shimura varieties. However weight one forms do contribute to the coherent cohomology of modular curves. I will discuss a circle of ideas relating motivic cohomology (or equivalent, the theory of higher Chow groups) to the coherent cohomology of Shimura varieties, which helps us better understand the geometry of weight one forms and their higher rank analogs. One of the examples I will discuss is some upcoming work in the case of Siegel modular forms (joint with Alex Horawa).