- Time: TuTh 9:00–10:20am
- Place: 380-380Y
A fundamental invariant of a linear endomorphism $f \colon V \to V$ of a finite dimensional vector space is its trace $\tr(f)$. The construction $f \mapsto \tr(f)$ can be performed in any symmetric monoidal (higher)-category. In recent years, people realize that several seemingly unrelated theorems/constructions, including but not limited to
- Grothendieck–Riemann–Roch formula
- Atiyah–Bott fixed point formula
- Lefschetz–Verdier formula
- Deligne–Lusztig theory
- V. Lafforgue’s construction of excursion algebras
can all be understood in the framework of such trace construction. This course aims to give an introduction of such ideas.