Nagoya University and University of Copenhagen
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 we call Dirac geometry. Informally, Dirac geometry constitutes a square root of equivariant geometry for the multiplicative group, and more concretely, the grading exhibits the hallmarks of spin in that it distinguishes symmetric and anti-symmetric behavior and provide the coherent cohomology of Dirac schemes and Dirac stacks with half-integer Serre twists. This is joint work with Piotr Pstragowski.