Zijian Yao (Harvard),  A crystalline perspective on Ainf-cohomologyAinf-cohomology theory is a cohomology theory constructed by Bhatt-Morrow-Scholze that interpolates various p-adic cohomology theories (notably etale, crystalline and de Rham cohomology). In this talk we review the (classical) construction of this theory, and provide a crystalline interpretation of Ainf-cohomology valued on certain "small" object. This allows us to connect Ainf-cohomology to the absolute crystalline cohomology valued in Fontaine's period ring Acris, and recover various p-adic comparison theorems. If time permits, we briefly mention the extension to the logarithmic setup.June 14th. Aula 1 AD 100, Dipartimento di Matematica "Tullio-Levi Civita".Website: https://events.math.unipd.it/indamlanglandsschool/