Advanced seminar on Gestalten theory

Harvard FAS

The interplay between geometry and algebra has been a guiding principle in modern mathematics. A central example is the theory of schemes, which geometrizes commutative rings; other examples include rigid geometry and spectral algebraic geometry. Another key idea is categorification.In this seminar, we will study the recent theory of Gestalten developed by Scholze and Stefanich, which pushes these ideas further by encoding very general geometric objects through ((\infty,\infty))-categories.…