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
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Yasuyuki Kawahigashi: Anyons, tensor networks and operator algebras July 14 10:15 - 11:05 -
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
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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…
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Alireza Ataei: Stability of many body anyons July 14 14:25 - 14:50 Alireza Ataei: Stability of many body anyons
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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
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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
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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
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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
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Domenico Cafiero: Homogenization regime for several Aharonov-Bohm fluxes July 15 14:00 - 14:25 Domenico Cafiero: Homogenization regime for several Aharonov-Bohm fluxes
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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
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Shawn Cui: On some problems in topological quantum computing July 15 15:20 - 16:10 Shawn Cui: On some problems in topological quantum computing
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Colleen Delaney: On complexity-theoretic hierarchies of anyon models July 15 16:20 - 17:10 Colleen Delaney: On complexity-theoretic hierarchies of anyon models
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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
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Nicolas Rougerie: What do we mean by “anyons”? July 16 11:20 - 12:10 Nicolas Rougerie: What do we mean by “anyons”?
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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
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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
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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
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Israel Michael Sigal: On Chern-Simons-Ginzburg-Landau equations July 16 15:50 - 16:40 Israel Michael Sigal: On Chern-Simons-Ginzburg-Landau equations
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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
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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
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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
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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
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Angelo Lucia: Thermalization of 2D topologically ordered spin models July 17 15:20 - 16:10 Angelo Lucia: Thermalization of 2D topologically ordered spin models
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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
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: |