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Conformal Invariance, Discrete Holomorphicity and Integrability

Scientific advisory committee


Registration form

Time and place

June 10-16 2012
University of Helsinki
Main building, address Fabianinkatu 33
Lecture hall 1 (exception: on Wednesday in lecture hall 13)


The general scope of the meeting is modern methods of random geometry, integrability and conformal invariance applied to statistical mechanics.

Many important lattice models of statistical mechanics are exactly solvable or integrable. At the critical point of a continuous phase transition these models are expected to have conformally invariant scaling limits. The physics research of these systems has been very active since 1980’s: conformal field theory is used to describe the scaling limit and exact solution of the lattice model is often based on the integrable structure in the form of commuting transfer matrices obtained from solutions to the Yang-Baxter equations.

Promising new mathematical ideas include conformally invariant random geometry, especially the random curves known as Schramm-Loewner Evolutions (SLE). A key advance is the use of discrete harmonic or discrete holomorphic observables of the lattice models for proving existence and conformal invariance of scaling limits. The purpose of this meeting is to bring together mathematical physicists with expertise in probability theory, analysis, integrable systems, combinatorics and representation theory, in order to advance further the discrete holomorphicity method, its relation to integrability and conformal field theory and related topics.


Many participants are staying in Hotel Cumulus Kaisaniemi or in Töölö Towers. We can no longer take new hotel reservation requests.

Approximate timetable


Mon 11.6.

Tue 12.6.

Wed 13.6.

Thu 14.6.

Fri 15.6.

Sat 16.6.










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Denis Bernard: A detour into wave function collapses from Brownian motions
Jérémie Bouttier: The nested loop approach to the O(n) model on random maps
Luigi Cantini: A one-parameter refinement of the Razumov-Stroganov correspondence
John Cardy: Holomorphic parafermions on the lattice and in conformal field theory
Dmitry Chelkak: Conformal invariance of spin correlations in the planar Ising model
Béatrice de Tilière: Mappings of the 2-dimensionl Ising model
Hugo Duminil-Copin: Crossing probabilities in the study of critical lattice models
Bertrand Duplantier: SLE, KPZ and Liouville Quantum Gravity
Paul Fendley: Discrete holomorphicity from topology
Emmanuel Guitter: Distance statistics in random maps
Anthony Guttmann: A generalised identity for self-avoiding walks on the honeycomb lattice
Christian Hagendorf: Spin chains and dynamical lattice supersymmetry
Clément Hongler: Conformal Invariance of Ising Interfaces
Yacine Ikhlef: Discretely holomorphic parafermions and integrable boundary conditions
Konstantin Izyurov: Ising interfaces and SLE(3) in multiply connected domains
Jesper Jacobsen: Exact critical manifolds from graph polynomials
Kurt Johansson: Continuum scaling limits in random tilings
Richard Kenyon: Conformal Invariance of double-dimer paths
Ivan Kostov: O(n) loops in complex magnetic field. File 1, file 2
Gregory Lawler: Recent Results on SLE
Zhongyang Li: Critical Temperature of Periodic Ising Models
Ioan Manolescu: Bond Percolation on Isoradial Graphs
Pekka Nieminen: Gaussian free field and Hadamard's variational formula
Bernard Nienhuis: Elliptic Bethe Ansatz for itinerant fermions on a chain
Eero Saksman: An application of stochastic games to PDE:s
Hubert Saleur: Edge states in the spin quantum Hall effect
Jacob Simmons: Six-point CFT correlation functions with applications to critical loop models
Christian Webb: An overview of recent results concerning low temperature Gibbs measures for logartihmically correlated Gaussian fields
Paul Zinn-Justin: Exact ground states of spin chains from quantum Knizhnik–Zamolodchikov equation

The abstracts of the presentations are in this file.

Registered participants

Nikolai Antonov,  Saint Petersburg State University (Russia)
Murray Batchelor,  Australian National University (Australia)
Michel Bauer,  CEA Saclay (France)
Denis Bernard,  ENS and CNRS (France)
Agnese Bissi,  Niels Bohr Insitiute (Denmark)
Jérémie Bouttier,  CEA Saclay (France)
Steven Brett,  IOP Publishing (UK)
Luigi Cantini,  Université Cergy-Pontoise (France)
John Cardy,  University of Oxford (UK)
Dmitry Chelkak,  Steklov Institute (Russia)
Jeremy Clark,  University of Helsinki (Finland)
Béatrice de Tilière,  University Pierre et Marie Curie (France)
Hugo Duminil-Copin,  University of Geneva (Switzerland)
Bertrand Duplantier,  CEA Saclay (France)
Bergfinnur Durhuus,  University of Copenhagen (Denmark)
Kari Eloranta,  Aalto University (Finland)
Chun Fang,  University of Helsinki (Finland)
Paul Fendley,  University of Virginia (USA)
Azat Gainutdinov,  CEA Saclay (France)
Dario Gasbarra,  University of Helsinki (Finland)
Alexander Glazman,  University of Geneva and St. Petersburg State University (Russia)
Emmanuel Guitter,  CEA Saclay (France)
Anthony Guttmann,  University of Melbourne (Australia)
Christian Hagendorf,  University of Geneva (Switzerland)
Antti Haimi,  KTH Royal Institute of Technology (Sweden)
Alan Hammond,  University of Oxford (UK)
Håkan Hedenmalm,  KTH Royal Institute of Technology (Sweden)
Clément Hongler,  Columbia University (USA)
Mariusz Hynek,  KTH Royal Institute of Technology (Sweden)
Yacine Ikhlef,  University of Geneva (Switzerland)
Konstantin Izyurov,  St. Petersburg State University (Russia)
Nissinen Jaakko,  University of Oslo (Norway)
Jesper Jacobsen,  Ecole Normale Supérieure (France)
Kurt Johansson,  KTH Royal Institute of Technology (Sweden)
Niko Jokela,  Universidade de Santiago de Compostela (Spain)
Thordur Jonsson,  University of Iceland (Iceland)
Antti Kemppainen,  University of Helsinki (Finland)
Richard Kenyon,  Brown University (USA)
Mikhail Khristoforov,  St. Petersburg State University (Russia)
Ivan Kostov,  CEA Saclay (France)
Michael Kozdron,  University of Regina (Canada)
Antti Kupiainen,  University of Helsinki (Finland)
Kalle Kytölä,  University of Helsinki (Finland)
Gregory Lawler,  University of Chicago (USA)
Eunghyun Lee,  University of Helsinki (Finland)
Zhongyang Li,  University of Cambridge (UK)
Juha Loikkanen,  University of Helsinki (Finland)
Jani Lukkarinen,  University of Helsinki (Finland)
Ioan Manolescu,  University of Cambridge (UK)
Anthony Mays,  University of Melbourne (Australia)
Peng Mei,  University of Helsinki (Finland)
Claus Montonen,  Helsinki Institute of Physics (Finland)
Pavel Mozolyako,  St. Petersburg State University (Russia)
Paolo Muratore-Ginanneschi,  University of Helsinki (Finland)
Hoa Ngo,  University of Helsinki (Finland)
Pekka Nieminen,  University of Helsinki (Finland)
Bernard Nienhuis,  University of Amsterdam (Netherlands)
Miika Nikula,  University of Helsinki (Finland)
Pierre Nolin,  ETH Zürich (Switzerland)
Anna Pachol,  University of Iceland (Iceland)
Mikko Pakkanen,  Aarhus University (Denmark)
Eveliina Peltola,  University of Helsinki (Finland)
Anita Ponsaing,  University of Geneva (Switzerland)
Istvan Prause,  University of Helsinki (Finland)
Tri Quach,  Aalto University (Finland)
Mohammad Ali Rajabpour,  SISSA (Italy)
Eero Saksman,  University of Helsinki (Finland)
Hubert Saleur,  CEA Saclay (France)
Jacob Simmons,  Maine Maritime Academy (USA)
Ville Suomala,  University of Oulu (Finland)
Nikolay Tropin,  St. Petersburg State University (Russia)
Petri Tuisku,  University of Helsinki (Finland)
Hans-Olav Tylli,  University of Helsinki (Finland)
Thomas Vallier,  University of Helsinki (Finland)
Romain Vasseur,  CEA Saclay (France)
Eric Vernier,  ENS and CEA Saclay (France)
Samuel Watson,  Massachusetts Institute of Technology (USA)
Christian Webb,  University of Helsinki (Finland)
Hao Wu,  Université Paris-Sud (France)
Seyedali Zahabi,  University of Helsinki (Finland)
Paul Zinn-Justin,  Université Pierre et Marie Curie (France)

  • European Science Foundation, “Random Geometry of Large Interacting Systems and Statistical Physics”
  • NordForsk, “Random geometry” network
  • University of Helsinki, Department of Mathematics and Statistics
  • Academy of Finland, The Finnish Centre of Excellence in Analysis and Dynamics Research
  • The Magnus Ehrnrooth foundation
  • Finnish Academy of Science and Letters

Photo (c) Niko Jokela

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