Project

Back to overview

TQFTs via Cut and Paste Techniques

English title TQFTs via Cut and Paste Techniques
Applicant Cattaneo Alberto Sergio
Number 172498
Funding scheme Project funding (Div. I-III)
Research institution Institut für Mathematik Universität Zürich
Institution of higher education University of Zurich - ZH
Main discipline Mathematics
Start/End 01.04.2017 - 31.03.2020
Approved amount 450'000.00
Show all

All Disciplines (2)

Discipline
Mathematics
Theoretical Physics

Keywords (14)

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

Lay Summary (Italian)

Lead
Questo progetto si propone di studiare teorie quantistiche di campo utilizzando moderne tecniche di taglia e incolla.
Lay summary
La teoria quantistica dei campi è la modellazione matematica dei sistemi di particelle elementari. La località, un'mportante proprietà fisica, suggerisce che si possa suddividere lo spazio-tempo in porzioni piccole e semplici, fare i calcoli localmente e quindi incollare i risultati assieme. Alcune teorie di campo sono già state formulate e calcolate in questo modo. Il progetto attuale mira a sviluppare e applicare tecniche generali per questi calcoli tenendo anche conto delle simmetrie del problema, le quali svolgono un ruolo fondamentale in tutta la fisica moderna. Poiché questo è un progetto matematico, ci concentriamo principalmente sulla struttura sottostante. Come terreno di prova ci proponiamo di studiare principalmente (ma non solo) teorie di campo che sono invarianti rispetto a riparametrizzazioni (teorie di campo topologiche). Il nostro formalismo ha anche una controparte classica che illumina fenomeni strutturali fondamentali nelle  teorie classiche. In questo contesto abbiamo anche in programma di ricavare risultati riguardanti la relatività generale.
Direct link to Lay Summary Last update: 01.04.2017

Responsible applicant and co-applicants

Employees

Publications

Publication
On the Globalization of the Poisson Sigma Model in the BV-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.
Towards Holography in the BV-BFV Setting
Mnev Pavel, Schiavina Michele, Wernli Konstantin (2020), Towards Holography in the BV-BFV Setting, in Annales Henri Poincaré, 21(3), 993-1044.
Asymptotic analysis of determinant of discrete Laplacian
Hou Yuhang, Kandel Santosh (2020), Asymptotic analysis of determinant of discrete Laplacian, in Letters in Mathematical Physics, 110(2), 259-296.
Gauge Enhancement of Super M-Branes Via Parametrized Stable Homotopy Theory
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.
The Reduced Phase Space of Palatini–Cartan–Holst Theory
Cattaneo Alberto S., Schiavina Michele (2019), The Reduced Phase Space of Palatini–Cartan–Holst Theory, in Annales Henri Poincaré, 20(2), 445-480.
Globalization for Perturbative Quantization of Nonlinear Split AKSZ Sigma Models on Manifolds with Boundary
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.
Observables in the equivariant A-model
Bonechi F., Cattaneo A. S., Iraso R., Zabzine M. (2019), Observables in the equivariant A-model, in Lett. Math. Phys., 1-17.
BV equivalence between triadic gravity and BF theory in three dimensions
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.
Poisson Sigma Model and Semiclassical Quantization of Integrable Systems
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.
IDEAL characterization of isometry classes of FLRW and inflationary spacetimes
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.
(Co)isotropic triples and poset representations
HerrmannChristian, LorandJonathan, WeinsteinAlan, (Co)isotropic triples and poset representations, in Rendiconti del Seminario Matematico della Università di Padova.
A Note on the Θ-Invariant of 3-Manifolds
CattaneoAlberto, ShimizuTatsuro, A Note on the Θ-Invariant of 3-Manifolds, in Quantum Topology.
BV-BFV approach to General Relativity: Palatini-Cartan-Holst action
CattaneoAlberto, SchiavinaMichele, BV-BFV approach to General Relativity: Palatini-Cartan-Holst action, in Adv. Theor. Math. Phys..
Introduction to the BV-BFV formalism
CattaneoAlberto, MoshayediNima, Introduction to the BV-BFV formalism, in Rev. Math. Phys..
Theta invariants of lens spaces via the BV-BFV formalism
CattaneoAlberto, MnevPavel, WernliKonstantin, Theta invariants of lens spaces via the BV-BFV formalism, in Progress in Mathematics.

Collaboration

Group / person Country
Types of collaboration
SISSA, Trieste Italy (Europe)
- Publication
University of Uppsala Sweden (Europe)
- Publication
INFN, Florence Italy (Europe)
- Publication
UC Berkeley United States of America (North America)
- Publication
University of Notre Dame United States of America (North America)
- Publication
RIMS, Kyoto Japan (Asia)
- Publication
Amherst College United States of America (North America)
- Publication

Scientific events

Active participation

Title Type of contribution Title of article or contribution Date Place Persons involved
Solvay Workshop on "Higher Spin Gauge Theories, Topological Field Theory and Deformation Quantization" Talk given at a conference The BV-BFV formalism 17.02.2020 ULB (Université Libre de Bruxelles), Belgium Cattaneo Alberto Sergio;
New Trends in Geometry and Mathematical Physics Talk given at a conference The Poisson sigma model and its applications 23.08.2019 CSF, Ascona, Switzerland Cattaneo Alberto Sergio;
Seminario Individual talk BV-BFV description of General Relativity in three dimensions 23.07.2019 Università degli Studi di Genova, Italy Canepa Giovanni;
Seminar Individual talk An Introduction to the BV-BFV Formalism 26.06.2019 Università del Piemonte Orientale, Alessandria, Italy Cattaneo Alberto Sergio;
Deformation theory and homotopy algebra Talk given at a conference An Introduction to the BV-BFV Formalism 09.05.2019 Emei campus of Southwest Jiaotong University, China Cattaneo Alberto Sergio;
KMPB – Lectures Individual talk Chern-Simons perturbation theory 06.05.2019 Humboldt Universität zu Berlin, Germany Wernli Konstantin;
Colloquium seminar Individual talk An Introduction to the BV-BFV Formalism 03.05.2019 Yau Mathematical Sciences Center, China Cattaneo Alberto Sergio;
Representation Theory and Mathematical Physics Seminar Individual talk Globalization of Split AKSZ Sigma Models in the BV-BFV Formalism 24.04.2019 UC Berkeley, United States of America Moshayedi Nima;
Topology Seminar Talk given at a conference An Introduction to the BV-BFV Formalism 09.04.2019 University of Notre Dame, United States of America Cattaneo Alberto Sergio;
Geometry/Physics Seminar Individual talk An Introduction to the BV-BFV Formalism 04.04.2019 Northwestern University, Chicago, United States of America Cattaneo Alberto Sergio;
Geometry/Physics Seminar Individual talk Poisson sigma model by cut and paste 04.04.2019 Northwestern University, Chicago, United States of America Cattaneo Alberto Sergio;
Deformation quantization, Batalin-Vilkovisky formalism and index Talk given at a conference Poisson sigma model by cut and paste, II 21.03.2019 Geneva, Switzerland Cattaneo Alberto Sergio;
Deformation quantization, Batalin-Vilkovisky formalism and index Talk given at a conference Poisson sigma model by cut and paste, I 20.03.2019 Geneva, Switzerland Cattaneo Alberto Sergio;
ΓΕΝΙΚΟ ΣΕΜΙΝΑΡΙΟ Individual talk An Introduction to the BV-BFV Formalism 14.03.2019 University of Athens, Greece Cattaneo Alberto Sergio;
Algebra and Geometry Seminar Individual talk Globalization of Nonlinear AKSZ Sigma Models in the BV-BFV Formalism 13.03.2019 Università di Roma I, "La Sapienza", Italy Moshayedi Nima;
Geometry Seminar Individual talk Poisson sigma model by cut and paste 12.03.2019 University of Atens, Greece Cattaneo Alberto Sergio;
Symplectic Geometry and Higher Structures Talk given at a conference Poisson sigma model by cut and paste 24.02.2019 Suzhou University, China Cattaneo Alberto Sergio;
Séminaire de géométrie et physique mathématique Individual talk The Casson Invariant and Feynman diagrams 23.11.2018 Université Paris Diderot - Paris 7, France Wernli Konstantin;
Séminaire de topologie Individual talk The Casson Invariant and Feynman diagrams 09.11.2018 Institut Fourier, Grenoble, France Wernli Konstantin;
Oberseminar Differentialgeometrie Individual talk The Casson Invariant and Feynman diagrams 29.10.2018 U. Freiburg, Germany Wernli Konstantin;
GRASP Seminar Individual talk General Relativity on manifolds with corners in the BV-BFV formalism 24.10.2018 UC Berkeley, United States of America Canepa Giovanni;
Seminars in geometry/topology Individual talk Introduction to Perturbative Quantum Gauge Theories 15.10.2018 NTNU, Trondheim, Norway Moshayedi Nima;
QGM seminar Individual talk Weights of Chern-Simons Feynman diagrams on handlebodies and lens spaces 10.10.2018 Centre for Quantum Geometry of Moduli Spaces, Aarhus, Denmark Wernli Konstantin;
Introductory seminar Individual talk Perturbative Quantization of Gauge Theories 09.10.2018 Centre for Quantum Geometry of Moduli Spaces, Aarhus, Denmark Wernli Konstantin;
Séminaire Physique mathématique Individual talk Perturbative quantization of nonlinear AKSZ sigma models on manifolds with boundary 05.10.2018 U. of Lyon, France Moshayedi Nima;
Geometry and Physics Seminar Individual talk An introduction to the BV-BFV formalism 03.10.2018 U. of Uppsala, Sweden Cattaneo Alberto Sergio;
2018 QSPACE Training SchooL Talk given at a conference Four lectures on the BV-BFV formalism 25.09.2018 Centro de Ciencias de Benasque Pedro Pascual, Spain Cattaneo Alberto Sergio;
Poisson Geometry and Higher Structures Talk given at a conference Poisson sigma model by cut and paste 14.09.2018 INDAM, Rome, Italy Cattaneo Alberto Sergio;
5th SwissMAP General Meeting Talk given at a conference General Relativity on manifolds with corners in the BV-BFV formalism 11.09.2018 Grindelwald, Switzerland Canepa Giovanni;
London Mathematical Society Durham Symposium: Higher structures in M-theory Talk given at a conference Parametrised homotopy theory and gauge enhancement 15.08.2018 Durham, Great Britain and Northern Ireland Braunack-Mayer Vincent;
Seminar at the Academy of Mathematics and Systems Science Individual talk Rational parametrised stable homotopy theory 22.06.2018 Chinese Academy of Sciences, Beijing, China Braunack-Mayer Vincent;
Topology Seminar Individual talk Rational Parametrised Stable Homotopy Theory 12.06.2018 EPFL, Switzerland Braunack-Mayer Vincent;
Estate Quantistica 2018 Talk given at a conference Geometrical construction of reduced phase spaces 11.06.2018 Scalea, Italy Cattaneo Alberto Sergio;
Seminar at University of Naples Individual talk An Introduction to the BV-BFV Formalism 08.06.2018 University of Naples, Italy Cattaneo Alberto Sergio;
Representation Theory, Mathematical Physics and Integrable Systems Talk given at a conference An introduction to the BV-BFV formalism 04.06.2018 CIRM, Marseille, France Cattaneo Alberto Sergio;
Fundamental interaction seminar Individual talk Geometrical construction of reduced phase spaces 01.06.2018 University of Marseille, France Cattaneo Alberto Sergio;
Interfaces between Geometric Analysis and Mathematical Physics Talk given at a conference An introduction to the BV-BFV formalism 07.05.2018 Institut Mittag-Leffler, Djursholm, Sweden Cattaneo Alberto Sergio;
Topology Seminar Individual talk The globalization of the Poisson sigma model in the BV-BFV formalism 24.04.2018 University of Notre Dame, United States of America Moshayedi Nima;
Symplectic and Poisson Geometry Seminar Individual talk The globalization of the Poisson sigma model in the BV-BFV formalism 16.04.2018 University of Illinois at Urbana-Champaign, United States of America Moshayedi Nima;
Matematické metody kvantové teorie pole Individual talk Geometrical construction of reduced phase spaces 05.04.2018 Charles University, Prague, Czech Republic Cattaneo Alberto Sergio;
Higher Differential Geometry Seminar Individual talk Perturbative Chern-Simons invariants on lens spaces via BV-BFV quantization 04.04.2018 Max Planck Institute, Bonn, Germany Wernli Konstantin;
Higher Structures II Talk given at a conference BFV and Poisson 06.03.2018 University of Pennsylvania, Philadelphia, United States of America Cattaneo Alberto Sergio;
Topology Seminar Individual talk Perturbative Chern-Simons invariants from BV-BFV formalism 26.01.2018 University of Notre Dame, United States of America Wernli Konstantin;
Methusalem Colloquium Individual talk Geometrical construction of reduced phase spaces 30.11.2017 U. Leuven , Belgium Cattaneo Alberto Sergio;
Séminaire de géométrie et physique mathématique Individual talk Geometrical construction of reduced phase spaces 24.11.2017 U. Paris VII, France Cattaneo Alberto Sergio;
Representation Theory and Mathematical Physics seminar Individual talk Perturbative Chern-Simons invariants from quantum BV-BFV formalism 09.11.2017 UC Berkeley, United States of America Wernli Konstantin;
Talk Individual talk Geometrical construction of reduced phase spaces 09.11.2017 Politecnico di Torino, Italy Cattaneo Alberto Sergio;
Theoretical Astrophysics Seminar Individual talk Geometrical construction of reduced phase spaces and its application to GR in four dimensions 03.11.2017 University of Zurich, Switzerland Cattaneo Alberto Sergio;
A Lie Day in Bologna, 2017 Talk given at a conference Geometrical construction of reduced phase spaces 13.10.2017 Università di Bologna, Italy Cattaneo Alberto Sergio;
Algebraic Topology of Manifolds Talk given at a conference Relational Symplectic Groupoid Quantization and the Globalization of the Poisson Sigma Model in the BV-BFV Formalism 11.09.2017 Oxford, Great Britain and Northern Ireland Moshayedi Nima;
100e rencontre entre mathématiciens et physiciens théoriciens : Géométrie, dynamique et physique Talk given at a conference Geometrical construction of reduced phase spaces 07.09.2017 University of Strasbourg, France Cattaneo Alberto Sergio;
Modern mathematics of Quantum Theory Talk given at a conference Geometrical construction of reduced phase spaces 05.09.2017 University of York, Great Britain and Northern Ireland Cattaneo Alberto Sergio;
Field Theories and Higher Structures in Mathematics and Physics Talk given at a conference Relational Symplectic Groupoid Quantization for Constant Poisson Structures 04.06.2017 BIRS- CMO, Oaxaca, Mexico Moshayedi Nima;
Field Theories and Higher Structures in Mathematics and Physics Talk given at a conference An introduction to the BV-BFV formalism 04.06.2017 BIRS-CMO, Oaxaca, Mexico Cattaneo Alberto Sergio;
Geometric Structures Laboratory Individual talk Some applications of the BV-BFV formalism for field theories on manifolds with boundary 15.05.2017 Fields Institute, Canada Cattaneo Alberto Sergio;
Quantum Field Theory on Manifolds with Boundary and the BV Formalism Talk given at a conference Perturbative BV-BFV theories on manifolds with boundary 08.05.2017 Perimeter Institute, Canada Cattaneo Alberto Sergio;
Gone Fishing Talk given at a conference An overview of the Poisson sigma model 04.05.2017 Notre Dame, United States of America Cattaneo Alberto Sergio;
Joint Math-Physics and Symplectic-Poisson Geometry Seminar Individual talk Some applications of the BV-BFV formalism for field theories on manifolds with boundary 14.04.2017 University of Illinois at Urbana–Champaign, United States of America Cattaneo Alberto Sergio;
Current Problems in Theoretical Physics Talk given at a conference Some applications of the BV-BFV formalism for field theories on manifolds with boundary 07.04.2017 Vietri sul Mare, Italy Cattaneo Alberto Sergio;


Self-organised

Title Date Place
Winter School in Mathematical Physics - 2020 02.02.2020 Les Diablerets , Switzerland
Winter School in Mathematical Physics - 2019 06.01.2019 Les Diablerets, Switzerland
Winter School in Mathematical Physics - 2018 07.01.2018 Les Diablerets, Switzerland

Associated projects

Number Title Start Funding scheme
192080 TQFTs via Cut and Paste Techniques 01.04.2020 Project funding (Div. I-III)
149150 Integral invariants of knots and manifolds. Loop and path spaces and topological BF theories. Deformation quantization and Poisson sigma models 01.10.2013 Project funding (Div. I-III)

Abstract

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.
-