We construct generalized Newton polytopes for Schubert subvarieties in the variety of complete flags in C^n . Every such “polytope” is a union of faces of a Gelfand–Zetlin polytope (the latter is a well-known Newton–Okounkov body for the flag variety). These unions of faces are responsible for Demazure characters of Schubert varieties and were originally used for Schubert calculus.
The aim of this Arbeitsgemeinschaft is to go over the proof of the higher Gross–Zagier formula established in the paper [YZ15]. The formula relates arbitrary order central derivative of the base change L-function of an unramifed automorphic representation of PGL2 over a function field to the self-intersection number of a certain algebraic cycle on the moduli stack of Shtukas.
We show that all elliptic orbifolds have the property of being modular. Namely, that there is a non--trivial Givental's action that leaves it unaffected.