49 citations · 267 across the 21 of their papers we have counts for
13 papers · 1 filter
Torsion volume forms
Florian Naef, Pavel Safronov
We introduce volume forms on mapping stacks in derived algebraic geometry using a parametrized version of the Reidemeister-Turaev torsion. In the case of derived loop stacks we des…
Shifted Coisotropic Correspondences
Rune Haugseng, Valerio Melani, Pavel Safronov
We define (iterated) coisotropic correspondences between derived Poisson stacks, and construct symmetric monoidal higher categories of derived Poisson stacks where the -morphism…
Lectures on shifted Poisson geometry
Pavel Safronov
These are expanded notes from lectures given at the États de la Recherche workshop on "Derived algebraic geometry and interactions". These notes serve as an introduction to the eme…
Poisson-Lie structures as shifted Poisson structures
Pavel Safronov
Classical limits of quantum groups give rise to multiplicative Poisson structures such as Poisson-Lie and quasi-Poisson structures. We relate them to the notion of a shifted Poisso…
Derived coisotropic structures II: stacks and quantization
Valerio Melani, Pavel Safronov
We extend results about -shifted coisotropic structures from part I of this work to the setting of derived Artin stacks. We show that an intersection of coisotropic morphisms ca…
Braces and Poisson additivity
Pavel Safronov
We relate the brace construction introduced by Calaque and Willwacher to an additivity functor. That is, we construct a functor from brace algebras associated to an operad to a…
Derived coisotropic structures I: affine case
Valerio Melani, Pavel Safronov
We define and study coisotropic structures on morphisms of commutative dg algebras in the context of shifted Poisson geometry, i.e. -algebras. Roughly speaking, a coisotropic…
Poisson reduction as a coisotropic intersection
Pavel Safronov
We give a definition of coisotropic morphisms of shifted Poisson (i.e. ) algebras which is a derived version of the classical notion of coisotropic submanifolds. Using this we…
A Lagrangian Neighbourhood Theorem for shifted symplectic derived schemes
Dominic Joyce, Pavel Safronov
Pantev, Toen, Vaquié and Vezzosi arXiv:1111.3209 defined -shifted symplectic derived schemes and stacks for , and Lagrangians ${\bf f}:{\bf L}\to{\bf X}…
Symplectic implosion and the Grothendieck-Springer resolution
Pavel Safronov
We prove that the Grothendieck-Springer simultaneous resolution viewed as a correspondence between the adjoint quotient of a Lie algebra and its maximal torus is Lagrangian in the…
Gerbal central extensions of reductive groups by
Pavel Safronov
We classify central extensions of a reductive group by and , the sheaf of third Quillen -theory groups and its classifying stack. These turn…
Quasi-Hamiltonian reduction via classical Chern-Simons theory
Pavel Safronov
This paper puts the theory of quasi-Hamiltonian reduction in the framework of shifted symplectic structures developed by Pantev, Toën, Vaquié and Vezzosi. We compute the symplectic…
Virasoro constraints in Drinfeld-Sokolov hierarchies
Pavel Safronov
We describe a geometric theory of Virasoro constraints in generalized Drinfeld-Sokolov hierarchies. Solutions of Drinfeld-Sokolov hierarchies are succinctly described by giving a p…