49 citations · 267 across the 21 of their papers we have counts for
25 papers
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…
Batalin--Vilkovisky quantization and supersymmetric twists
Pavel Safronov, Brian R. Williams
We show that a family of topological twists of a supersymmetric mechanics with a Kähler target exhibits a Batalin--Vilkovisky quantization. Using this observation we make a general…
Classical BV formalism for group actions
Marco Benini, Pavel Safronov, Alexander Schenkel
We study the derived critical locus of a function on the quotient stack of a smooth affine scheme by the action of a smooth affine group…
Shifted geometric quantization
Pavel Safronov
We introduce geometric quantization in the setting of shifted symplectic structures. We define Lagrangian fibrations and prequantizations of shifted symplectic stacks and their geo…
A categorical approach to dynamical quantum groups
Artem Kalmykov, Pavel Safronov
We present a categorical point of view on dynamical quantum groups in terms of categories of Harish-Chandra bimodules. We prove Tannaka duality theorems for forgetful functors into…
Invertible braided tensor categories
Adrien Brochier, David Jordan, Pavel Safronov +1
We prove that a finite braided tensor category A is invertible in the Morita 4-category BrTens of braided tensor categories if, and only if, it is non-degenerate. This includes the…
A Taxonomy of Twists of Supersymmetric Yang--Mills Theory
Chris Elliott, Pavel Safronov, Brian R. Williams
We give a complete classification of twists of supersymmetric Yang--Mills theories in dimensions . We formulate supersymmetric Yang--Mills theory classically using…
The finiteness conjecture for skein modules
Sam Gunningham, David Jordan, Pavel Safronov
We give a new, algebraically computable formula for skein modules of closed 3-manifolds via Heegaard splittings. As an application, we prove that skein modules of closed 3-manifold…
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…
The quantum Frobenius for character varieties and multiplicative quiver varieties
Iordan Ganev, David Jordan, Pavel Safronov
We prove that quantized multiplicative quiver varieties and quantum character varieties define sheaves of Azumaya algebras over the corresponding classical moduli spaces, and we pr…
A categorical approach to quantum moment maps
Pavel Safronov
We introduce quantum versions of Manin pairs and Manin triples and define quantum moment maps in this context. This provides a framework that incorporates quantum moment maps for a…
Topological twists of supersymmetric algebras of observables
Chris Elliott, Pavel Safronov
We explain how to perform topological twisting of supersymmetric field theories in the language of factorization algebras. Namely, given a supersymmetric factorization algebra with…
The categorified Grothendieck-Riemann-Roch theorem
Marc Hoyois, Pavel Safronov, Sarah Scherotzke +1
In this paper we prove a categorification of the Grothendieck-Riemann-Roch theorem. Our result implies in particular a Grothendieck-Riemann-Roch theorem for Toën and Vezzosi's seco…
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…
Shifted symplectic Lie algebroids
Brent Pym, Pavel Safronov
Shifted symplectic Lie and algebroids model formal neighbourhoods of manifolds in shifted symplectic stacks, and serve as target spaces for twisted variants of classical…
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…