New developments in representation theory arising from cluster algebras

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Workshop theme

Cluster algebras were defined by Fomin and Zelevinsky as a combinatorial tool to understand Luztig's dual canonical bases and total positivity. It was quickly noticed that cluster algebras could be successfully categorified using the representation theory of finite dimensional algebras. Furthermore, the categorification of cluster algebras introduced many novel innovative ideas to representation theory, giving rise to new areas of study that today are central to the theory such as higher homological algebra, Calabi-Yau categories and τ-tilting theory. The aim of this workshop is to share the latest developments in these cluster-inspired areas of research and discuss their future development.

Due to the ongoing COVID-19 pandemic, all non-UK based applicants should attend this event virtually.

Fees

Registration Only

Registration Package: £TBC
Student Registration Package: £TBC

The Registration Package includes admission to all seminars, lunches and refreshments on the days that lectures take place (Monday - Friday), wine reception and formal dinner, but does not include other meals or accommodation.

Formal Dinner Only

Formal Dinner: £50

Participants on the Accommodation Package or Registration Package, including organisers and speakers, are automatically included in this event. For all remaining participants who would like to attend, such as programme participants, the above charge will apply.

Accommodation

Unfortunately we do not have any accommodation to offer so all successful applicants will need to source their own accommodation.

Please see the Hotels Combined website for a list of local hotels and guesthouses

Meals

Lunch Lunch timings and location will be confirmed with timetable.

Evening Meal Participants are free to make their own arrangements for dinner.

Formal Dinner The Formal Dinner location and date is to be confirmed.

Participants on the Accommodation Package or Registration Package, including organisers and speakers, are automatically included in this event.

Photo Gallery

Timetable

Monday 20th September 2021
12:00 to 12:20	Registration	No Room Required
12:20 to 12:50	Lunch	No Room Required
12:50 to 13:00	Christie Marr Isaac Newton Institute Welcome Talk	Room 1
13:00 to 13:30	Ralf Schiffler University of Connecticut Chair: Bethany Marsh Knot Theory and Cluster Algebras	Room 1
13:30 to 13:45	Break	No Room Required
13:45 to 14:15	Karin Marie Jacobsen Norwegian University of Science and Technology Chair: Bethany Marsh On the Role of Gentle Algebras in Higher Homological Algebra	Room 1
14:15 to 14:45	Afternoon Tea	No Room Required
14:45 to 15:15	Pierre-Guy Plamondon Université de Versailles Saint-Quentin-en-Yvelines Chair: Bethany Marsh On g-vectors and Grothendieck Groups of Extriangulated Categories	Room 1
15:15 to 15:30	Break	No Room Required
15:30 to 16:00	Thomas Brüstle Bishop's University; Université de Sherbrooke Chair: Bethany Marsh Labelling Chains of Torsion Classes	Room 1
16:00 to 17:00	Welcome Wine Reception at INI	No Room Required

Tuesday 21st September 2021
12:00 to 13:00	Lunch	No Room Required
13:00 to 13:30	Sira Gratz University of Glasgow Chair: Claire Amiot When Aisles Meet	No Room Required
13:30 to 13:45	Break	No Room Required
13:45 to 14:15	Yu Zhou Tsinghua University Chair: Claire Amiot Connectedness of the Support Tau-Tilting Graph of a Gentle Algebra	No Room Required
14:15 to 14:45	Afternoon Tea	No Room Required
14:45 to 15:15	Chris Fraser Michigan State University Chair: Claire Amiot Cluster Combinatorics of SLk Skein Algebras in the Presence of Punctures	Room 2
15:15 to 15:30	Break	No Room Required
15:30 to 16:00	Emine Yildirim Isaac Newton Institute; University of Cambridge Chair: Claire Amiot Cluster Structures	Room 2

Wednesday 22nd September 2021
12:00 to 13:00	Lunch	No Room Required
13:00 to 13:30	Peter Jorgensen Aarhus Universitet Chair: Aslak Buan n-exact Subcategories of (n+2)-Angulated Categories (After Klapproth)	Room 2
13:30 to 13:45	Break	No Room Required
13:45 to 14:15	Khrystyna Serhiyenko University of Kentucky Chair: Aslak Buan Geometric model for syzygies over 2-Calabi-Yau tilted algebras	Room 2
14:15 to 14:45	Afternoon Tea	No Room Required
14:45 to 15:15	Jenny August Max Planck Institute for Mathematics Chair: Aslak Buan Silting and tilting for weakly symmetric algebras	Room 2
19:30 to 22:00	Formal Dinner	No Room Required

Thursday 23rd September 2021
12:00 to 13:00	Lunch	No Room Required
13:00 to 13:30	Claire Amiot Université Grenoble Alpes Chair: Sonia Trepode Indecomposable Objects in the Derived Category of Skew-Gentle Algebra.	Room 2
13:30 to 13:45	Break	No Room Required
13:45 to 14:15	Alireza Nasr-Isfahani University of Isfahan; IPM - Institute for Research In Fundamental Sciences Chair: Sonia Trepode Cluster algebras generated by projective cluster variables	Room 2
14:15 to 14:45	Afternoon Tea	No Room Required
14:45 to 15:15	Matthew Pressland University of Leeds Chair: Sonia Trepode A cluster character for y-variables	Room 2
15:15 to 15:30	Break	No Room Required
15:30 to 16:00	Daniel Labardini-Fragoso Universidad Nacional Autonoma de Mexico (UNAM) Chair: Sonia Trepode Generalized cluster algebras as Caldero-Chapoton algebras of gentle algebras	Room 2

Friday 24th September 2021
12:00 to 13:00	Lunch	No Room Required
13:00 to 13:30	Michael Wemyss University of Glasgow Chair: Ralf Schiffler Noncommutative Singularity Theory	Room 1
13:30 to 13:45	Break	No Room Required
13:45 to 14:15	Yu Qiu Tsinghua University Chair: Ralf Schiffler Geometric Models for Graded Skew-Gentle Algebras	Room 1
14:15 to 14:45	Afternoon Tea	No Room Required
14:45 to 15:15	Yadira Valdivieso-Diaz University of Leicester Chair: Ralf Schiffler Geometric model of the derived category of Skew-gentle algebras	Room 1

Cluster algebras and representation theory

Organisers

Karin Baur University of Leeds; Karl-Franzens-Universität Graz
Ana Garcia Elsener University of Glasgow
Sibylle Schroll University of Cologne
Hipolito Treffinger Rheinische Friedrich-Wilhelms-Universität Bonn

Speakers

Claire Amiot Université Grenoble Alpes
Jenny August Max Planck Institute for Mathematics
Thomas Brüstle Bishop's University; Université de Sherbrooke
Chris Fraser Michigan State University
Sira Gratz University of Glasgow
Karin Marie Jacobsen Norwegian University of Science and Technology
Peter Jorgensen Aarhus Universitet
Daniel Labardini-Fragoso Universidad Nacional Autonoma de Mexico (UNAM)
Alireza Nasr-Isfahani University of Isfahan; IPM - Institute for Research In Fundamental Sciences
Pierre-Guy Plamondon Université de Versailles Saint-Quentin-en-Yvelines
Matthew Pressland University of Leeds
Yu Qiu Tsinghua University
Ralf Schiffler University of Connecticut
Khrystyna Serhiyenko University of Kentucky
Yadira Valdivieso-Diaz University of Leicester
Michael Wemyss University of Glasgow
Emine Yildirim Isaac Newton Institute; University of Cambridge
Yu Zhou Tsinghua University

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Participants

Claire Amiot Université Grenoble Alpes
Ibrahim Assem None / Other; Université de Sherbrooke
Jenny August Max Planck Institute for Mathematics
Esther Banaian University of Minnesota
Karin Baur University of Leeds; Karl-Franzens-Universität Graz
Charlie Beil Independent Consultant/Independent Researcher
James Beyer University of Oklahoma
Sandipan Bhattacherjee None / Other
Léa Bittmann University of Edinburgh
Matheus Brito Universidade Federal do Paraná
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
Agustín Cañadas Universidad Nacional de Colombia
Aaron Kay Yam Chan Nagoya University
Wen Chang Shaanxi Normal University
Cristian Chaparro Universidad de Buenos Aires
Rajarshi Chatterjee Kazi Nazrul University
Xueqing Chen None / Other
Man Wai Cheung Harvard University
Merlin Christ Universität Hamburg
Praveen Kumar Dhankar Rashtrasant Tukadoji Maharaj Nagpur University
Drew Duffield Durham University
Nicholas Early Max-Planck-Institut für Physik, München
Eleonore Faber University of Leeds
Anna Felikson Durham University
Pedro Fernando Fernández Espinosa Universidad Nacional de Colombia
Monica Garcia Université Paris-Saclay; Université de Versailles Saint-Quentin-en-Yvelines
Ana Garcia Elsener University of Glasgow
Misha Gekhtman University of Notre Dame
Jan Grabowski Lancaster University
Sira Gratz University of Glasgow
Emily Gunawan University of Oklahoma
Mohamad Haerizadeh University of Tehran
Amihay Hanany Imperial College London
Zezhuang Hao University of Southampton
Johanne Haugland NTNU
Lauren Hindmarch Lancaster University
Rei Inoue Chiba University
Karin Marie Jacobsen Norwegian University of Science and Technology
Haibo Jin University of Cologne
Bernhard Keller Université Paris 7 - Denis-Diderot
Elizabeth Kelley University of Illinois at Urbana-Champaign
Alastair King University of Bath
Viktória Klász Universität Bonn
Daniel Labardini-Fragoso Universidad Nacional Autonoma de Mexico (UNAM)
Li Li Oakland University
Saikat Maity University of Calcutta; Indian Institute of Technology
Juan Pablo Maldonado None / Other
Bethany Marsh University of Leeds
Astrid Carolina Melo lopez Universidad Nacional de Colombia
Lang Mou University of Cambridge
Dixy Msapato University of Leeds
Gregg Musiker University of Minnesota
Tomoki Nakanishi Nagoya University
Alireza Nasr-Isfahani University of Isfahan; IPM - Institute for Research In Fundamental Sciences
David Nkansah Universität Bonn
Yann Palu Université de Picardie Jules Verne
David Pauksztello Lancaster University
Pierre-Guy Plamondon Université de Versailles Saint-Quentin-en-Yvelines
Matthew Pressland University of Leeds
Tomasz Przezdziecki University of Edinburgh
Fan Qin Shanghai Jiao Tong University
Yu Qiu Tsinghua University
Jhon Alexander Ramirez Bermudez University of Antioquia
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
Daniel Soskin University of Notre Dame
Ashish Srivastava Saint Louis University
Håvard Terland Norwegian University of Science and Technology
Gordana Todorov Northeastern University
Hipolito Treffinger Rheinische Friedrich-Wilhelms-Universität Bonn
Sonia Elisabet Trepode Universidad Nacional de Mar del Plata
Michail Tsironis Vrije Universiteit Amsterdam
Pavel Tumarkin Durham University
Alek Vainshtein University of Haifa
Juan Daniel Valdivia Fuentes Universidad Nacional de Ingeniería
Yadira Valdivieso-Diaz University of Leicester
Dmitriy Voloshyn University of Notre Dame
Peter Webb University of Minnesota
Michael Wemyss University of Glasgow
Emine Yildirim Isaac Newton Institute; University of Cambridge
Haiyan Yu Chongqing University
Yu Zhou Tsinghua University