V. Golyshev: “Quantum Motives: Linearizations, Realizations, Use, Detections”
Here are my notes from Golyshev’s talk in Bonn.
Summary:
- a historical analogy: the study of Fano varieties now versus algebraic number theory prior to the proof of the Weil Conjectures
- linearization and motives
- Tannakian categories
- the “quantum Tannakian category”
- realizations in algebraic number theory: one can detect algebraic varieties by detecting their motives (in practice by detecting their L-functions via Selberg-Stark)
- the “quantum Tate realization” and quantum detection
- the Satake correspondence and its quantum parallel