Séminaire Autour des Cycles Algébriques organisé par A. Cadoret - B.Kahn - A. Pirutka Février 2015, Place Jussieu, 75005 Paris 04/02/15 14h30-15h30 Jan Hendrik Bruinier (Technische Universität Darmstadt) Jussieu, salle Kudla’s modularity conjecture and formal Fourier-Jacobi series. 1516-4-13 A famous theorem of Gross, Kohnen, and Zagier states that the generating series of Heegner divisors on a modular curve is an elliptic modular form of weight 3/2 with values in the Picard group. This result can be viewed as an elegant description of the relations among Heegner divisors. More generally, Kudla conjectured that the generating series of codimension g special cycles on an orthogonal Shimura variety of dimension n is a Siegel modular form of genus g and weight 1+n/2 with coefficients in the Chow group of codimension g cycles. We report on joint work with Martin Raum on the modularity of formal FourierJacobi series, which, when combined with a result of Wei Zhang, leads to a proof of Kudla’s modularity conjecture. 04/02/15 16h-17h Christopher Daw (IHES) Jussieu, salle Heights of pre-special points of Shimura varieties. 1516-4-13 In this talk we discuss a bound for the height of the pre-image of a special point on a Shimura variety in a fundamental set of the associated Hermitian symmetric domain. This bound is polynomial in terms of standard invariants associated with the corresponding Mumford-Tate torus and constitutes the final ingredient needed to complete a new proof of the André-Oort conjecture assuming the Generalised Riemann Hypothesis, using a strategy of Pila and Zannier. This is joint work with Martin Orr (University College London).