Séminaire Algèbre et Arithmétique - Salle de conférences du CMLS - 14h00

11 juin. 2026

Le séminaire aura lieu le 11 juin à l'École polytechnique - Salle de conférences du CMLS

14h-15h – Minseong Kwon (Morningside Center of Mathematics - Chine)

«Homogeneous Legendrian subvarieties of adjoint varieties»

Abstract: Adjoint varieties are rational homogeneous spaces associated to simple Lie algebras. Every adjoint variety admits a natural complex contact structure, and it is well known that any homogeneous Legendrian subvarieties of the adjoint variety of type C can be realized as the so-called subadjoint varieties. In this talk, I will present a classification of homogeneous Legendrian subvarieties of arbitrary adjoint varieties. To this end, I will introduce Merkulov’s theory of Legendre moduli space, which plays an important role in the classification.

15h30-16h30 – Elie Studnia (Université de Leiden)

«Arithmetic intersections of Heegner divisors on the modular curve Xns+(p)»

Abstract:

In 1985, Gross and Zagier computed the arithmetic intersection of certain CM divisors on the modular curve X(1). In concrete terms, they computed the factorization of the norm of the algebraic integer j(s)-j(t), where s,t generate the rings of integers of two imaginary quadratic fields with coprime discriminants. They extended their work with Kohnen in order to determine the arithmetic intersection of Heegner divisors on the modular curve X_0(N), which led to the best-known Gross-Zagier formula (on the central derivative of an L-function). In this joint work with Jan Vonk and Jonathan Love, we determine the arithmetic intersection of similar Heegner divisors on the modular curve Xns+(p), where p is prime. One of the difficulties is that, unlike in Gross-Zagier, intersections may happen in the fibre at p (at which the curve has bad reduction); this is solved by finding a new modular interpretation for this fibre.