Cluster algebras and representation theory
CAR
6 September 2021 to 17 December 2021
Programme theme
The theory of cluster algebras is one of the most active research areas in Mathematics over the last 18 years. Introduced by Fomin and Zelevinsky in 2002 in the context of Lie theory and total positivity, cluster algebras quickly developed deep connections to different disciplines such as representation theory, combinatorics, algebraic, hyperbolic and symplectic geometry, dynamical systems, topology and string theory. Among the major applications of cluster algebras are the construction of part of Lusztig's dual semicanonical basis in Lie theory, the discovery of generalized associahedra in combinatorics, the development of cluster-tilting theory in the representation theory of finite dimensional algebras, the proof of Zamolodchikov's periodicity conjecture in conformal field theory, the development of a new approach to Teichmüller theory and the discovery of a fundamental relationship with Donaldson-Thomas invariants and wall-crossing in algebraic geometry. Much work on cluster algebras has centred around applications to the representation theory of finite dimensional algebras. These grew from categorical models for cluster algebras. In particular, the cluster-tilted algebras arising from cluster categories have given new insights into classical tilting theory. The interaction is in both directions, with the representation-theoretic models also being used to answer fundamental questions about cluster algebras. This programme will focus on interactions between cluster algebras and representation theory as well as interdisciplinary applications of cluster algebras.
Click here to download the programme's final scientific report
CAR programme: interview w/Karin Baur, Bethany Marsh, Ralf Schiffler & Sibylle Schroll
Preprints
| Title | Year | Programme | |
|---|---|---|---|
Quiver combinatorics for higher-dimensional triangulationsAuthors: Nicholas Williams |
2021 | CAR | 20 October 2022 |
DERIVED CATEGORIES OF SKEW-GENTLE ALGEBRAS AND ORBIFOLDSAuthors: Daniel Labardini Fragoso, Sibylle Schroll, Yadira Valdivieso-Diaz |
2021 | CAR | 20 October 2022 |
CORRIGENDUM TO “ON TWO CONJECTURES CONCERNING CONVEX CURVES”, BY V. SEDYKH AND B. SHAPIROAuthors: Boris Shapiro, Michael Shapiro |
2021 | CAR | 7 February 2022 |
RSK tableaux and box-ball systemsAuthors: Ben Drucker, Rose Silver, Emily Gunawan, Eli Garcia, Aubrey Rumbolt |
2021 | CAR | 14 December 2021 |
PERFECT MATCHING MODULES, DIMER PARTITION FUNCTIONS AND CLUSTER CHARACTERSAuthors: Ilke Canakci, Alastair King, Matthew Pressland |
2021 | CAR | 14 December 2021 |
FRIEZES FOR A PAIR OF PANTSAuthors: Anna Felikson, Ilke Canakci, Ana Garcia Elsener, Pavel Tumarkin |
2021 | CAR | 26 November 2021 |
THE ROLE OF GENTLE ALGEBRAS IN HIGHER HOMOLOGICAL ALGEBRAAuthors: Sibylle Schroll, Karin M. Jacobsen, Johanne Haugland |
2021 | CAR | 15 November 2021 |
A geometric model for syzygies over 2-Calabi-Yau tilted algebras IIAuthors: Ralf Schiffler, Khrystyna Serhiyenko |
2021 | CAR | 15 November 2021 |
Knot Theory and Cluster AlgebrasAuthors: Véronique Bazier-Matte, Ralf Schiffler |
2021 | CAR | 15 November 2021 |
A geometric model for syzygies over 2-Calabi-Yau tilted algebrasAuthors: Khrystyna Serhiyenko, Ralf Schiffler |
2021 | CAR | 15 November 2021 |
DEFORMATION THEORY FOR FINITE CLUSTER COMPLEXESAuthors: NATHAN ILTEN, Hipolito Treffinger, ALFREDO N ́AJERA CH ́AVEZ |
2021 | CAR | 8 November 2021 |
Workshops
New developments in representation theory arising from cluster algebras research school
13 September 2021 to 17 September 2021
New developments in representation theory arising from cluster algebras
20 September 2021 to 24 September 2021
Interdisciplinary applications of cluster algebras
8 November 2021 to 12 November 2021
The Organisers would like to thank the following sponsors for their generous support of the event:
Seminars
| Tuesday 28th September 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Emily Gunawan University of Oklahoma |
Room 2 | |
| Monday 4th October 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Bernhard Keller Université Paris 7 - Denis-Diderot |
Room 1 | 
|
| Tuesday 5th October 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Bethany Marsh University of Leeds |
Room 1 |
|
| Wednesday 6th October 2021 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Bernhard Keller Université Paris 7 - Denis-Diderot |
Room 1 |
|
| Tuesday 12th October 2021 | |||
|---|---|---|---|
| 16:00 to 17:30 |
Michael Shapiro Michigan State University; Higher School of Economics, Moscow |
Room 1 |
|
| Wednesday 13th October 2021 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Bernhard Keller Université Paris 7 - Denis-Diderot |
Room 1 |
|
| Tuesday 19th October 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Pavel Tumarkin Durham University |
Room 1 |
|
| Wednesday 20th October 2021 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Bernhard Keller Université Paris 7 - Denis-Diderot |
Room 1 |
|
| Friday 22nd October 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Amihay Hanany Imperial College London |
Room 1 |
|
| Tuesday 26th October 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Hipolito Treffinger Rheinische Friedrich-Wilhelms-Universität Bonn |
Room 1 |
|
| Friday 29th October 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Francesca Fedele Università degli Studi di Verona; Università degli Studi di Padova |
Room 1 |
|
| Monday 1st November 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Gordana Todorov Northeastern University |
Room 1 |
|
| Tuesday 2nd November 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Gregg Musiker University of Minnesota |
Room 2 |
|
| Friday 5th November 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Nathan Reading North Carolina State University |
Room 2 |
|
| Tuesday 16th November 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Aslak Bakke Buan Norwegian University of Science and Technology |
Room 2 |
|
| Wednesday 17th November 2021 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Gordana Todorov Northeastern University |
Room 2 |
|
| Thursday 18th November 2021 | |||
|---|---|---|---|
| 15:30 to 16:30 |
Drew Duffield Durham University |
Room 2 | |
| Friday 19th November 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Ekaterina Shemyakova University of Toledo |
Room 2 |
|
| Monday 22nd November 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Elie Casbi Max-Planck-Institut für Mathematik, Bonn |
Room 2 |
|
| Tuesday 23rd November 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Raquel Coelho Simoes Lancaster University - Mathematics and Statistic Dept. |
Room 2 |
|
| Wednesday 24th November 2021 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Gordana Todorov Northeastern University |
Room 2 |
|
| Thursday 25th November 2021 | |||
|---|---|---|---|
| 15:30 to 16:30 |
Oleg Karpenkov University of Liverpool |
Room 1 |
|
| Friday 26th November 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Yilin Wu Université Paris 7 - Denis-Diderot; East China Normal University |
Room 1 |
|
| Tuesday 30th November 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Lang Mou University of Cambridge |
Room 2 |
|
| Wednesday 1st December 2021 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Gordana Todorov Northeastern University |
Room 2 |
|
| Friday 3rd December 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Marco Armenta Université de Sherbrooke |
Room 1 |
|
| Tuesday 7th December 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Sibylle Schroll University of Cologne |
Room 1 |
|
| Friday 10th December 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Véronique Bazier-Matte University of Connecticut |
Room 2 | |
| Tuesday 14th December 2021 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Dixy Msapato University of Leeds |
Room 1 |
|
Organisers
- Karin Baur University of Leeds; Karl-Franzens-Universität Graz
- Bethany Marsh University of Leeds
- Ralf Schiffler University of Connecticut
- Sibylle Schroll University of Cologne
Speakers
- Marco Armenta Université de Sherbrooke
- Véronique Bazier-Matte University of Connecticut
- Aslak Bakke Buan Norwegian University of Science and Technology
- Elie Casbi Max-Planck-Institut für Mathematik, Bonn
- Raquel Coelho Simoes Lancaster University - Mathematics and Statistic Dept.
- Drew Duffield Durham University
- Francesca Fedele Università degli Studi di Padova; Università degli Studi di Verona
- Emily Gunawan University of Oklahoma
- Amihay Hanany Imperial College London
- Oleg Karpenkov University of Liverpool
- Bernhard Keller Université Paris 7 - Denis-Diderot
- Bethany Marsh University of Leeds
- Lang Mou University of Cambridge
- Dixy Msapato University of Leeds
- Gregg Musiker University of Minnesota
- Nathan Reading North Carolina State University
- Sibylle Schroll University of Cologne
- Michael Shapiro Michigan State University; Higher School of Economics, Moscow
- Ekaterina Shemyakova University of Toledo
- Gordana Todorov Northeastern University
- Hipolito Treffinger Université Paris 7 - Denis-Diderot
- Pavel Tumarkin Durham University
- Yilin Wu Université Paris 7 - Denis-Diderot; East China Normal University
Participants
- Ibrahim Assem None / Other; Université de Sherbrooke
- Karin Baur University of Leeds; Karl-Franzens-Universität Graz
- Véronique Bazier-Matte University of Connecticut
- Thomas Brüstle Bishop's University; Université de Sherbrooke
- Aslak Bakke Buan Norwegian University of Science and Technology
- Ilke Canakci Vrije Universiteit Amsterdam
- Elie Casbi Max-Planck-Institut für Mathematik, Bonn
- Wen Chang Shaanxi Normal University
- Man Wai Cheung Harvard University
- Joel Costa University of Leeds
- Drew Duffield Durham University
- Eleonore Faber University of Leeds
- Anna Felikson Durham University
- Sergey Fomin University of Michigan
- Chris Fraser Michigan State University
- Ana Garcia Elsener University of Glasgow
- Misha Gekhtman University of Notre Dame
- Jan Grabowski Lancaster University
- Sira Gratz University of Glasgow
- Victoria Guazelli Universidad Nacional de Mar del Plata
- Emily Gunawan University of Oklahoma
- Amihay Hanany Imperial College London
- Rei Inoue Chiba University
- Haibo Jin University of Cologne
- Oleg Karpenkov University of Liverpool
- Bernhard Keller Université Paris 7 - Denis-Diderot
- Alastair King University of Bath
- Daniel Labardini-Fragoso Universidad Nacional Autonoma de Mexico (UNAM)
- Bernard Leclerc CNRS - Université de Caen Basse-Normandie
- Kyungyong Lee University of Alabama at Tuscaloosa
- Li Li Oakland University
- Bethany Marsh University of Leeds
- Sophie Morier-Genoud Sorbonne Université
- Lang Mou University of Cambridge
- Dixy Msapato University of Leeds
- Gregg Musiker University of Minnesota
- Tomoki Nakanishi Nagoya University
- Pierre-Guy Plamondon Université de Versailles Saint-Quentin-en-Yvelines
- Matthew Pressland University of Leeds
- Fan Qin Shanghai Jiao Tong University
- Yu Qiu Tsinghua University
- Nathan Reading North Carolina State University
- Ralf Schiffler University of Connecticut
- Sibylle Schroll University of Cologne
- Jan Schröer Universität Bonn
- Khrystyna Serhiyenko University of Kentucky
- Michael Shapiro Michigan State University; Higher School of Economics, Moscow
- Ekaterina Shemyakova University of Toledo
- Hugh Thomas Université du Québec à Montréal
- Gordana Todorov Northeastern University
- Hipolito Treffinger Université Paris 7 - Denis-Diderot
- Michail Tsironis Vrije Universiteit Amsterdam
- Pavel Tumarkin Durham University
- Alek Vainshtein University of Haifa
- Yadira Valdivieso-Diaz University of Leicester
- Daping Weng Michigan State University
- Lauren Williams Harvard University
- Nicholas Williams University of Cologne
- Emine Yildirim Isaac Newton Institute; University of Cambridge
Supported By
