The subject of my lecture this year is the arithmetic site, a Grothendieck topos with a structural bundle. The results were obtained in collaboration with C. Consani.
References
A. Connes, C. Consani, The Arithmetic Site, Comptes rendus mathématiques Ser. I 352 (2014), 971-975.
A. Connes, C. Consani, Geometry of the Arithmetic Site, Adv. Math, 291, 2016, 274-329.
A. Connes, C. Consani, Absolute algebra and Segal's Γ-sets, J. Number Theory, 162, 2016, 518-551