We will begin with a discussion of an example in the paper "Lois de réciprocité supérieures et points rationnels" by Colliot-Thélène, Parimala and Suresh (arXiv:1302.2377).
Afterwards, we will discuss two recent manuscripts of David Harari and Tamas Szamuely (one also with Claus Scheiderer), available at
http://www.math.u-psud.fr/~harari/articles/pchp.pdf
http://www.math.u-psud.fr/~harari/articles/pcwa.pdf
Participants are encouraged to look at these papers beforehand.