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Anyons from Small to Large Scales

July 14 - July 18, 2025

In nature, most particles fall into two categories based on their exchange statistics: bosons, with symmetric wave functions, and fermions, with antisymmetric ones. However, quantum mechanics also allows for more exotic particles, known as anyons, whose exchange statistics lie between these two extremes. Initially considered only a mathematical possibility, the physical existence of anyons was predicted in the 1980s in the context of the quantum Hall effect and has since been strongly supported by recent experiments. Nevertheless, a precise understanding of anyons remains a challenge for both physicists and mathematicians, as it involves the topological braiding and knotting of particle trajectories in space and time, often leading to nonlinear and nonlocal effective models. 

This conference focuses on the mathematical theory of anyons, aiming to foster collaboration and dialogue among researchers approaching the subject from different perspectives. The workshop will concentrate on three areas where the mathematical theory of anyons is being actively developed: quantum lattice systems, topological quantum field theory (TQFT), and statistical mechanics. 

Recorded seminars:

Seminars Scroll to the next upcoming seminar

  • Yasuyuki Kawahigashi: Anyons, tensor networks and operator algebras July 14 10:15 - 11:05

    Yasuyuki Kawahigashi: Anyons, tensor networks and operator algebras

  • Davide Fermi: Zero-range interactions for anyonic and Aharonov-Bohm Hamiltonians July 14 11:25 - 12:15

    Davide Fermi: Zero-range interactions for anyonic and Aharonov-Bohm Hamiltonians

  • Théotime Girardot: Upper bound for the almost-bosonic anyon gas in term of the stationary Chern-Simons-Schrödinger eq… July 14 14:00 - 14:25

    Théotime Girardot: Upper bound for the almost-bosonic anyon gas in term of the stationary Chern-Simons-Schrödinger eq…

  • Alireza Ataei: Stability of many body anyons July 14 14:25 - 14:50

    Alireza Ataei: Stability of many body anyons

  • Maria Stella Adamo: The construction of full 2D CFTs: the case of the Heisenberg conformal net July 14 15:20 - 16:10

    Maria Stella Adamo: The construction of full 2D CFTs: the case of the Heisenberg conformal net

  • Gerald Goldin: Anyonic Structures Predicted from Representations of a Universal Kinematical Group July 14 16:20 - 17:10

    Gerald Goldin: Anyonic Structures Predicted from Representations of a Universal Kinematical Group

  • Zhenghan Wang: Topology of the space of quantum interactions and anyon models July 15 10:00 - 10:50

    Zhenghan Wang: Topology of the space of quantum interactions and anyon models

  • Eric Rowell: The Condensed Fiber Product and Zesting of Anyon Models July 15 11:20 - 12:10

    Eric Rowell: The Condensed Fiber Product and Zesting of Anyon Models

  • Domenico Cafiero: Homogenization regime for several Aharonov-Bohm fluxes July 15 14:00 - 14:25

    Domenico Cafiero: Homogenization regime for several Aharonov-Bohm fluxes

  • Qiyun Yang: Dimensional reduction for a system of 2D anyons July 15 14:25 - 14:50

    Qiyun Yang: Dimensional reduction for a system of 2D anyons

  • Shawn Cui: On some problems in topological quantum computing July 15 15:20 - 16:10

    Shawn Cui: On some problems in topological quantum computing

  • Colleen Delaney: On complexity-theoretic hierarchies of anyon models July 15 16:20 - 17:10

    Colleen Delaney: On complexity-theoretic hierarchies of anyon models

  • Alex Bols: Sector theory for quantum double & Levin-Wen models July 16 10:00 - 10:50

    Alex Bols: Sector theory for quantum double & Levin-Wen models

  • Nicolas Rougerie: What do we mean by “anyons”? July 16 11:20 - 12:10

    Nicolas Rougerie: What do we mean by “anyons”?

  • François Visconti: Average-field approximation for very dilute almost-bosonic anyon gases July 16 14:00 - 14:25

    François Visconti: Average-field approximation for very dilute almost-bosonic anyon gases

  • Jinyeop Lee: Derivation of the Chern–Simons–Schrödinger equation from the dynamics of an almost-bosonic-anyon gas July 16 14:25 - 14:50

    Jinyeop Lee: Derivation of the Chern–Simons–Schrödinger equation from the dynamics of an almost-bosonic-anyon gas

  • Daria Rudneva: On the unitarity and modularity of ribbon tensor categories associated with affine Lie algebras July 16 15:20 - 15:45

    Daria Rudneva: On the unitarity and modularity of ribbon tensor categories associated with affine Lie algebras

  • Israel Michael Sigal: On Chern-Simons-Ginzburg-Landau equations July 16 15:50 - 16:40

    Israel Michael Sigal: On Chern-Simons-Ginzburg-Landau equations

  • Alberto Ruiz-de-Alarcón: One-Dimensional Mixed-State Phases, Matrix Product Density Operators, and Parent Lindbladians July 17 10:00 - 10:50

    Alberto Ruiz-de-Alarcón: One-Dimensional Mixed-State Phases, Matrix Product Density Operators, and Parent Lindbladians

  • David Perez Garcia: Haag duality for 2D quantum spin systems July 17 11:20 - 12:10

    David Perez Garcia: Haag duality for 2D quantum spin systems

  • Ask Ellingsen & Filippa Getzner: Non-linear Landau levels: Ground state energy approximation and Berry phases July 17 14:00 - 14:25

    Ask Ellingsen & Filippa Getzner: Non-linear Landau levels: Ground state energy approximation and Berry phases

  • Daniel Wallick: An operator algebraic approach to symmetry-enriched topological orders July 17 14:25 - 14:50

    Daniel Wallick: An operator algebraic approach to symmetry-enriched topological orders

  • Angelo Lucia: Thermalization of 2D topologically ordered spin models July 17 15:20 - 16:10

    Angelo Lucia: Thermalization of 2D topologically ordered spin models

  • Christoph Schweigert: Tensor network states: a topological field theory perspective July 17 16:20 - 17:10

    Christoph Schweigert: Tensor network states: a topological field theory perspective

  • Free discussion July 18 11:20 - 12:10

    Free discussion

  • Lunch July 18 12:10 - 13:10

    Lunch

Recordings

Participants

Name University Country Arrival and Departure
Maria Stella
Adamo
University: University of Erlangen–Nuremberg Country: Germany Arrival and Departure:
Eddy
Ardonne (Online)
University: Stockholm University Country: Sweden Arrival and Departure:
Alireza
Ataei
University: Uppsala University Country: Sweden Arrival and Departure:
Sven
Bachmann
University: The University of British Columbia Country: Canada Arrival and Departure:
Alex
Bols
University: Eidgenössische Technische Hochschule Zürich Country: Switzerland Arrival and Departure:
Nicolas
Bridges (Online)
University: Purdue University Country: United States Arrival and Departure:
Morris
Brooks (Online)
University: University of Zurich Country: Switzerland Arrival and Departure:
Domenico
Cafiero
University: Politecnico di Milano Country: Italy Arrival and Departure:
Matthew
Corbelli (Online)
University: University of California, Davis Country: United States Arrival and Departure:
Michele
Correggi
University: Politecnico di Milano Country: Italy Arrival and Departure:
Shawn
Cui
University: Purdue University Country: United States Arrival and Departure:
Michele
Del Zotto
University: Uppsala University Country: Sweden Arrival and Departure:
Colleen
Delaney
University: Purdue University Country: United States Arrival and Departure:
Ask
Ellingsen
University: Uppsala University Country: Sweden Arrival and Departure:
Davide
Fermi
University: Politecnico di Milano Country: Italy Arrival and Departure:
Martin
Fraas (Online)
University: UC Davis Country: United States Arrival and Departure:
Jürg
Fröhlich (Online)
University: Eidgenössische Technische Hochschule Zürich Country: Switzerland Arrival and Departure:
Alan
Getz (Online)
University: University of British Columbia Country: Canada Arrival and Departure:
Filippa
Getzner
University: Uppsala University Country: Sweden Arrival and Departure:
Theotime
Girardot
University: Gran Sasso Science Institute Country: Italy Arrival and Departure:
Gerald
Goldin
University: Rutgers University Country: United States Arrival and Departure:
Corey
Jones (Online)
University: North Carolina State University Country: United States Arrival and Departure:
Kohtaro
Kato
University: Nagoya University Country: Japan Arrival and Departure:
Yasuyuki
Kawahigashi
University: the University of Tokyo Country: Japan Arrival and Departure:
Kan
Kitamura (Online)
University: RIKEN Country: Japan Arrival and Departure:
Boris
Kjaer
University: Copenhagen University Country: Denmark Arrival and Departure:
Gaultier
Lambert (Online)
University: KTH Royal Institute of Technology Country: Sweden Arrival and Departure:
Edwin
Langmann
University: KTH Royal Institute of Technology Country: Sweden Arrival and Departure:
Jinyeop
Lee
University: The University of British Columbia Country: Canada Arrival and Departure:
Angelo
Lucia
University: Politecnico di Milano Country: Italy Arrival and Departure:
Douglas
Lundholm
University: Uppsala University Country: Sweden Arrival and Departure:
Per
Moosavi (Online)
University: Stockholm University Country: Sweden Arrival and Departure:
Dinh-Thi
Nguyen (Online)
University: University of Science, Vietnam National University Ho Chi Minh City Country: Vietnam Arrival and Departure:
Yoshiko
Ogata
University: Kyoto University Country: Japan Arrival and Departure:
David
Perez-Garcia
University: Universidad Complutense de Madrid Country: Spain Arrival and Departure:
Daniel
Ranard (Online)
University: California Institute of Technology Country: United States Arrival and Departure:
Nicolas
Rougerie
University: Centre national de la recherche scientifique & École normale supérieure de Lyon Country: France Arrival and Departure:
Eric
Rowell
University: Texas A&M University Country: United States Arrival and Departure:
Darya
Rudneva
University: Stockholm University Country: Sweden Arrival and Departure:
Alberto
Ruiz-de-Alarcón
University: CUNEF University Country: Spain Arrival and Departure:
Christoph
Schweigert
University: Hamburg University Country: Germany Arrival and Departure:
Michael
Sigal
University: University of Toronto Country: Canada Arrival and Departure:
Jan Philip
Solovej (Online)
University: University of Copenhagen Country: Denmark Arrival and Departure:
Wulf
Staubach (Online)
University: Uppsala University Country: Sweden Arrival and Departure:
Yoh
Tanimoto (Online)
University: University of Rome Country: Italy Arrival and Departure:
Nat
Tantivasadakarn (Online)
University: California Institute of Technology Country: United States Arrival and Departure:
Francois
Visconti
University: LMU Munich Country: Germany Arrival and Departure:
Daniel
Wallick
University: The Ohio State University Country: United States Arrival and Departure:
Zhenghan
Wang
University: University of California, Santa Barbara Country: United States Arrival and Departure:
Qiyun
Yang
University: École normale supérieure de Lyon Country: France Arrival and Departure:
Qing
Zhang
University: University of California, Santa Barbara Country: United States Arrival and Departure:
Pengming
Zhang (Online)
University: Sun Yat-sen University Country: China Arrival and Departure: