Title: Dirac geometryAbstract: Whatever it is that animates anima and breathes life into higher algebra, this something gives the homotopy groups of a commutative algebra in spectra the structure of a commutative algebra in the symmetric monoidal category of graded abelian groups. Being commutative, these algebras form the affine building blocks of a geometry, which […]
Title: Elliptic curves and modular forms.Abstract: If you’ve heard of Fermat’s last theorem, you might have heard that its proof involves some sophisticated geometric objects that seemingly have nothing to do with whether a^n + b^n = c^n for n > 2. The objects in question are elliptic curves and modular forms. I will attempt […]
Title: Condensed abelian groups IAbstract: We will talk about the categories of κ-condensed abelian groups with Grothendieck axioms and why they are the abelian category of the nicest possible sort.
Title: Relative trace formulae and progress on the mixed truncationAbstract: After a quick (re)introduction to relative trace formulae, we shall focus on the divergence issue in establishing them. We plan to survey known examples of the mixed truncation and discuss an ongoing work on trace formulae for infinitesimal symmetric spaces.