Thursday 20 May 2021, 12:45-13:15 via zoom
Tommy Lundemo (RU)
What is higher algebra?
In the same way that algebra is rooted in the integers, "higher" algebra is rooted in a topological object called the "sphere spectrum". While the integers are obtained by adding negative numbers to the natural numbers, the sphere spectrum is obtained by adding "negative sets" to the collection of finite sets. I will briefly explain how one can make sense of the above construction. Then I will explain some analogies and differences between algebra over the integers and over the sphere spectrum. If time permits, I will say something about modules of differentials and related theories in both contexts, and give examples showing that higher algebra often gives the better behaved theory.