Institut für Mathematik


Prof. Dr. Anna Beliakova

Institut für Mathematik
Universität Zürich
Winterthurerstrasse 190
CH-8057 Zürich

Fax: +41 44 635 57 06
Büro: Y27J18
Niedrigdimensionale Topologie
Shang-Chi Hsiao

+41 44 635 58 51



  • University Basel, Mathematics, Habilitation, Title: Quantum invariants of 3-manifolds, 2003
  • FU Berlin, Ph.D. Physics, Advisor: Prof. R. Schrader, Thesis: Topological quantum field theories and invariants of graphs, 1994
  • Belorussian State University, M.S. in Physics with distinction, 1990


  • I-MATH, University of Zurich, Professor, 2010-present
  • I-MATH, University of Zurich, SNF-Professor, 2004-2010
  • Mathematical Institute, University of Basel, 1998-2004
  • Mathematical Institute, University of Bern, 1996-1998
  • IMRA Strasbourg, DFG Fellowship, 1995-1996

Lecture & Seminar

Analysis II für Physikstudierende


A. Beliakova, M. Hogancamp, K. Putyra, S. Wehrli
On unification of colored annular sl(2) knot homology
arXiv:2305.02977 PDF  

A. Beliakova, I. Bobtcheva, M. De Renzi, R. Piergallini
On Algebraization in Low-Dimensional Topology
arXiv:2312.15986 PDF  

A. Beliakova, Ch. Blanchet
Abelian TQFTS and Schrödinger local systems
arXiv:2306.10725 PDF  

A. Beliakova, K. Putyra, L.-H. Robert, E. Wagner
A proof of Dunfield-Gukov-Rasmussen Conjecture
arXiv:2210.00878 PDF  

A. Beliakova, M. De Renzi
Refined Bobtcheva-Messia Invariants of 4-Dimensional 2-Handlebodies
In Essays in Geometry - Dedicated to Norbert A’Campo, EMS Publishing House Berlin (2023) ISBN: 978-3-98547-024-2 PDF  

A. Beliakova, M. De Renzi
Kerler-Lyubashenko Functors on 4-Dimensional 2-Handlebodies
Intern. Math. Research Notices PDF

A. Beliakova, M. Hogancamp, K. Putyra, S. Wehrli
On the functoriality of sl(2) tangle homology
PDF Algebraic & Geometric Topology 23 (2023) 1303–1361

A. Beliakova, E. Gorsky
Cyclotomic expansions for glN knot invariants via interpolation Macdonald polynomials
arXiv:2101.08243 PDF  

A. Beliakova, K. Hikami
Non-semisimple invariants and Habiro series
Topology & Geometry: Special Issue Dedicated to Vladimir G. Turaev, EMS Publishing House, Berlin (2021) PDF  

A. Beliakova, Ch. Blanchet, A. Gainutdinov
Modified trace is a symmetrised integral (2021)
Selecta Mathematica, Vol. 27, pp. 1-51 PDF  

A. Beliakova, K. Habiro
A categorification of the ribbon element in quantum sl(2)
Acta Math. Vietnamica, Vol. 46 pp. 225–264 PDF  

A. Beliakova, K. Putyra, S. Wehrli
Quantum Link Homology via Trace Functor I
Inventiones mathematicae, Vol. 215, Issue 2 pp. 383–492 PDF  

A. Beliakova, Ch. Blanchet, N. Geer
Logarithmic Hennings invariants for restricted quantum SL(2)
Algebraic & Geometric Topology, Vol. 18 (2018) pp. 4329-4358 PDF  

A. Beliakova, B. Cooper
Steenrod Structures on Categorified Quantum Groups
Fund. Math., Vol. 241 (2018) pp. 179-207 PDF  

A. Beliakova, K. Habiro, A. Lauda, B. Webster
Current algebras and categorified quantum groups
J. Lond. Math. Soc. (2), Vol. 95 (2017) no. 1, pp. 1-29 PDF  

A. Beliakova, K. Habiro, A. Lauda, B. Webster
Cyclicity for categorified quantum groups
Journal of Algebra, Vol. 452 (2016) pp. 118-132 PDF  

A. Beliakova, K. Habiro, A. Lauda, M. Zivkovic
Trace decategorification of categorified quantum sl(2)
Math. Annalen, Vol. 367, no. 1-2 (2016) pp. 1-44 PDF  

A. Beliakova, Q. Chen, T. Le
On the integrality of Witten-Reshetikhin-Turaev 3-manifold invariants
Quantum Topology, Vol. 5, Issue 1 (2014) pp. 99–141 PDF  

A. Beliakova, A. Lauda
Categorified quantum sl(2) is an inverse limit of flag 2-categories
Transformation Groups, Vol. 19, Issue 1 (2014) pp. 1-26 PDF  

A. Beliakova, M. Khovanov, A. Lauda
A categorification of the Casimir of quantum sl(2)
Advances in Mathematics, Vol. 230, Issue 3 (2012) pp. 1442-1501 PDF  

A. Beliakova, I. Bühler, T. Le
Unified SO(3) quantum invariant for rational homology 3-Spheres
Inventiones, Vol. 185, Issue 1 (2011) pp. 121-174 PDF  

A. Beliakova, Z. Guliyev, K. Habiro, A. Lauda
Trace as an alternative decategorification functor
Acta Math. Vietnamica, Vol. 39, Issue 4 (2014) pp. 425-480 PDF  

A. Beliakova, T. Le
On the unification of quantum 3-manifold invariants
Introductory Lectures on Knot Theory (L. H. Kauffman, S. Lambropoulou, S. Jablan, J. H. Przytycki, eds.), World Scientific, Vol.46, (2012) pp. 1-21 PDF  

A. Beliakova, Ch. Blanchet, T. Le
Unified quantum invariants and their refinements for homology 3-spheres with 2-torsion
Fund. Math., Vol. 201 (2008) pp. 217-239 PDF  

A. Beliakova, E. Wagner
On link homology theories from extended cobordisms
Quantum Topology., Vol. 1 (2010) pp. 379–398 PDF  

A. Beliakova
On simplification of combinatorial link Floer homology
Journal of Knot Theory Ram., Oberwolfach Proceedings, Vol. 3 (2010) pp. 1-19 PDF  

A. Beliakova, Ch. Blanchet, E. G. Contreras
Spin Modular Categories
Quantum Topology, Vol. 8, Issue 3 (2017) pp. 459–504 PDF  

A. Beliakova, S. Wehrli
Categorification of the colored Jones polynomial and Rasmussen invariant of links
Canad. J. Math., Vol. 60 (2008) pp. 1240-1266 PDF  

A. Beliakova, T. Q. Le
Integrality of quantum 3-manifold invariants and rational surgery formula
Compositio Mathematica, Vol. 143, Issue 06 (2007) pp. 1593-1612 PDF  

A. Beliakova
Geometric construction of spinors in orthogonal modular categories
Alg. & Geom. Topology, Vol. 3 (2003) pp. 969-992 PDF  

A. Beliakova, Ch. Blanchet
Modular categories of types B, C and D
Comment. Math. Helvetica, Vol. 76 (2001) pp. 467-500 PDF  

A. Beliakova, Ch. Blanchet
Skein construction of idempotents in Birman-Murakami-Wenzl algebras
Math. Annalen, Vol. 321 (2001) pp. 347-373 PDF  

A. Beliakova, N. Habegger
The Casson-Walker-Lescop invariant as a quantum 3-manifold invariant
J. of Knot Theory and its Ramifications, Vol. 9 (2000), pp. 459-470 PDF  

A. Beliakova, A. Schumakovich
Aufloesung mathematischer Knoten,
Uni Nova, Vol. 87 (2000) pp. 45-50 PDF  

A. Beliakova
Refined invariants and TQFT's from Homfly skein theory
J. of Knot Theory and Its Ramifications, Vol. 8 (1999) pp. 569-587 PDF  

A. Beliakova
Spin topological quantum field theories
Int. J. of Math., Vol. 9 (1998) pp. 129-152 PDF  

A. Beliakova, B. Durhuus
On the relation between two quantum group invariants of 3-cobordisms
J. Geom. Phys., Vol. 20 (1996) pp. 305-317 PDF  

A. Beliakova, B. Durhuus
Topological quantum field theory and invariants of graphs for quantum groups
Comm. Math. Phys., Vol. 167 (1995) pp. 395-429 PDF  


PD Dr. Matthieu Faitg, Institut de Mathématiques de Toulouse, Université Toulouse III Paul Sabatier (Toulouse)
10.06.24 - 13.06.24Beliakova, Anna
Dr. Marco De Renzi, Université de Montpellier (Montpellier)
23.01.24 - 26.01.24Beliakova, Anna
Dr. Azat Gainutdinov, Institut Denis-Poisson, CNRS, Université de Tours, Tours, France (Tours)
23.01.24 - 25.01.24Beliakova, Anna


Future events

Colloquium in Regensburg, Germany, December 13, 2022

Conferences organised

Quantum symmetries: Tensor categories, Topological quantum field theories, Vertex algebras, CRM Montréal, Québec, Canada - October 10 - November 4, 2022

SwissMAP Conference: From Subfactors to Quantum Topology, Conference in memory on Vaughan Jones, Geneva, Switzerland, June 27-July 1, 2022

Braids, Institute for Computational and Experimental Research in Mathematics (ICERM), Brown University, Rhode Island, USA,  February 1 - May 6, 2022

Braids in Representation Theory and Algebraic Combinatorics, Institute for Computational and Experimental Research in Mathematics (ICERM), Brown University, Rhode Island, USA, February 14 – 18, 2022

Recent development in link homology, SRS Les Diablerets, Switzerland, January 30 – February 4, 2022

SwissMAP Conference Algebraic Structures in Topology and Geometry, Riederalp, Switzerland, January 14-19, 2018

Women in Topology and Geometry , together with Anton Alekseev and Maria Podkopaeva, Zurich, Switzerland, June 14-16, 2017

SwissMAP conference Geometry and Topology , Engelberg, Switzerland, January 24-29, 2016

SwissMAP Summer school 2015, Engelberg, Switzerland, September 2-4, 2015

Second SwissMAP Geometry & Topology conference, Les Diablerets, Switzerland, June 22-26, 2015

Conference on Categorification in Algebra, Geometry and Physics, Cargèse, Corsica, May 4-8, 2015

SwissMAP Geometry & Topology conference, Engelberg, Switzerland, January 18-23, 2015

International Conference Quantum Topology and Hyperbolic Geometry, Nha Trang, Vietnam, May 13-17, 2013

International Conference Swiss Knots 2011, Gwatt, Switzerland, May 22-27, 2011

Joint Meeting of the American Mathematical Society, Deutsche Mathematische Vereinigung and Oesterreichische Mathematische Gesellschaft, Special Session on "Quantum Knots Invariants", Mainz, Germany, June 16-19, 2005