Talks

11 October 2018, Heegner points on X0(67)+ by Matija. 18 October 2018, Positions of Heegner points in modular Jacobians by Jan. 25 October 2018, Gross-Zagier in genus 0 by Nils. 1 November 2018, Archimedean local heights by Tiago. 8 November 2018, Non-archimedean local heights I by Netan. 15 November 2018, Non-archimedean local heights II by Francesca. 22 November 2018, Derivatives of Rankin L-series by Alex. 29 November 2018, The adelic viewpoint (Gross - Heegner points and representation theory) by Federico.

Sources

The main source we intend to follow is the original paper (or papers) of Gross-Zagier:
Gross, Zagier - Heegner points and derivatives of L-series (1986)
(Prequel) Gross, Zagier - On singular moduli (1984)
(Sequel) Gross, Kohnen, Zagier - Heegner points and derivatives of L-series II (1987)

Other useful resources are:

Darmon, Zhang - Heegner points and Rankin L-series (Book)
Zagier - Modular points, modular curves, modular surfaces, and modular forms (1984)
Zagier - L-series and Green's functions of modular curves (1986)
A seminar at Michigan on the same topic: (click)

Some notes for the first two talks: here