Date/Time: 8 September 2023, 4:30pm ET Location: Elizabethtown College, Esbenshade 382 and Zoom Speaker: Naruki Masuda, Johns Hopkins University Title: The Tensor Product of Categorical Spectra: The First Step Towards Higher^2 Algebra Abstract: Abelian groups and their tensor product is the base on which all the algebraic geometry is built. Their homotopical analog, spectra, also admit a canonical tensor product. In fact, its robust implementation unlocked the highly successful development of the "brave new" algebraic geometry. Categorical spectra are spectra's higher categorical generalizations: we consider sequences of pointed $(\infty, \infty)$-categories, instead of pointed spaces, related by the loop operation. I will explain why this may be a reasonable thing to even think about. After that, I will explain why constructing a tensor product here is trickier, how I did it and what are the difficulties ahead.