BV formalism in derived geometry

by Nikola Tomić

Tuesday May 5, 2026, 2:00 PM → 3:00 PM Europe/Paris

IMT 1R2 207 (Salle Pellos)

Batalin–Vilkoviski (BV) formalism in theoretical physics is a formalism meant to handle local gauge symmetries in the process of (geometric) quantization. Given a function f : U → 𝔸¹ on a smooth scheme U corresponding to an action functional, the usual object of study for physicists is the critical locus Crit(f). It can happens that a group of symmetries acts on U and left f invariant, in that case G is called a gauge groupe. But it can also happen that G doesn't exist, and symmetries arise only on the critical locus Crit(f) (those are called "local", "open", or "on shell" symmetries). In order to handles those symmetries Batalin and Vilkoviski (this is also used in BRST formalism) introduce the so called ghost variables. In this talk I will take inspiration from Grataloup's thesis and try to explain why the process of solving the Classical Master Equation (introducing those local symmetries) have a natural interpretation in derived geometry, especially in shifted symplectic geometry. If time permits, I will try to interpret the Quantum Master Equation in this setting; it is believed that this is related to shifted geometry quantization and Donaldson–Thomas theory.