Home / Trace methods in algebraic geometry and representation theory

Trace methods in algebraic geometry and representation theory

  • 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.