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

Übungen Analysis II für Physikstudierende Gr3
Übungen Analysis II für Physikstudierende Gr 1
Übungen Analysis II für Physikstudierende Gr2
Introduction to Algebraic Topology

Exercises Introduction to Algebraic Topology


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