smooth invariants; extended symplectic category; Poisson manifolds; deformation quantization; coisotropic submanifolds; symplectic reduction; superconnections; Chen`s iterated integrals; configuration spaces; BV quantization; BV algebras; topological quantum field theories; Lie and symplectic groupoids; BFV formalism
Cattaneo Alberto S., Moshayedi Nima, Wernli Konstantin (2020), On the Globalization of the Poisson Sigma Model in the BV-BFV Formalism, in Communications in Mathematical Physics
, 375(1), 41-103.
Mnev Pavel, Schiavina Michele, Wernli Konstantin (2020), Towards Holography in the BV-BFV Setting, in Annales Henri Poincaré
, 21(3), 993-1044.
Hou Yuhang, Kandel Santosh (2020), Asymptotic analysis of determinant of discrete Laplacian, in Letters in Mathematical Physics
, 110(2), 259-296.
Braunack-Mayer Vincent, Sati Hisham, Schreiber Urs (2019), Gauge Enhancement of Super M-Branes Via Parametrized Stable Homotopy Theory, in Communications in Mathematical Physics
, 371(1), 197-265.
Cattaneo Alberto S., Schiavina Michele (2019), The Reduced Phase Space of Palatini–Cartan–Holst Theory, in Annales Henri Poincaré
, 20(2), 445-480.
Cattaneo Alberto S., Moshayedi Nima, Wernli Konstantin (2019), Globalization for Perturbative Quantization of Nonlinear Split AKSZ Sigma Models on Manifolds with Boundary, in Communications in Mathematical Physics
, 372(1), 213-260.
Bonechi F., Cattaneo A. S., Iraso R., Zabzine M. (2019), Observables in the equivariant A-model, in Lett. Math. Phys.
Cattaneo A. S., Schiavina M., Selliah I. (2018), BV equivalence between triadic gravity and BF theory in three dimensions, in Letters in Mathematical Physics
, 108(8), 1873-1884.
Cattaneo Alberto S., Mnev Pavel, Reshetikhin Nicolai (2018), Poisson Sigma Model and Semiclassical Quantization of Integrable Systems, in Reviews in Mathematical Physics
, 30(06), 1840004-1840004.
Canepa Giovanni, Dappiaggi Claudio, Khavkine Igor (2018), IDEAL characterization of isometry classes of FLRW and inflationary spacetimes, in Classical and Quantum Gravity
, 35(3), 035013.
HerrmannChristian, LorandJonathan, WeinsteinAlan, (Co)isotropic triples and poset representations, in Rendiconti del Seminario Matematico della Università di Padova
CattaneoAlberto, ShimizuTatsuro, A Note on the Θ-Invariant of 3-Manifolds, in Quantum Topology
CattaneoAlberto, SchiavinaMichele, BV-BFV approach to General Relativity: Palatini-Cartan-Holst action, in Adv. Theor. Math. Phys.
CattaneoAlberto, MoshayediNima, Introduction to the BV-BFV formalism, in Rev. Math. Phys.
CattaneoAlberto, MnevPavel, WernliKonstantin, Theta invariants of lens spaces via the BV-BFV formalism, in Progress in Mathematics
This project mainly aims at studying perturbative Topological Quantum Field Theories (TQFT) using cut-and-paste techniques in the quantum BV-BFV formalism made available by our recent work. In particular, we plan to study the perturbative quantization of BF theories and their variants, to apply some of these ideas to general relativity, to develop the study of perturbative Chern-Simons theory on manifolds with boundary with the goal of comparing the results with the asymptotics of the Reshetikhin-Turaev invariant, and to study the Poisson sigma model on surfaces with boundary also with the goal of quantizing the relational symplectic groupoid. In addition to the above specific goals, this projects is an arena to start using the quantum BV-BFV formalism before moving on to non topological theories.