Cluster Algebras Portal

This is a collection of links on cluster algebras and related topics.

Papers

• arXiv math
• arXiv physics
• arXiv full text search (math)
• Google Scholar
• MathSciNet (requires subscription)
• Lecture notes and surveys
• Special issues: PNAS, J. Physics A.

Conferences, Summer Schools, and Lecture Series

• Cluster algebras at the Sophus Lie Conference Center, Nordfjordeid, 2003.
• Lecture notes for the conference Current Developments in Mathematics, Cambridge, MA, 2003.
• Root systems and generalized associahedra, Park City Mathematics Institute, 2004.
• Braid Groups, Clusters and Free Probability, Palo Alto, 2005.
• Cluster algebras, master class at CIRM, Luminy, 2005.
• Representations of Algebras and Related Topics, Boston, 2005.
• Representation Theory and Related Topics, Trieste, 2006.
• Teichmüller Theory and Cluster Algebras, Leicester, 2006.
• Cluster Algebras and Cluster Tilted Algebras, Bielefeld, 2006.
• Cluster Algebras and Applications (NSF/CBMS), Raleigh, 2006.
• Perspectives on rings and algebras, Murcia, 2006.
• Microlocal and Geometric Methods in Representation Theory, Schloss Reisensburg, 2006.
• Perspectives in Representation Theory, Bad Honnef, 2006.
• Symmetries and Integrability of Difference Equations, Melbourne, 2006.
• XIX Escola de Algebra, Belo Horizonte, 2006.
• Quantum Moduli Spaces and TQFT, Aarhus, 2006.
• Cluster algebras mini-course at University of Lisbon, 2006.
• Cluster algebras at CMS Meeting, Toronto, 2006.
• Groupes, géometrie et représentations, Amiens, 2007.
• Perspectives in Auslander-Reiten Theory, Trondheim, 2007.
• ICRA XII, Torun, 2007.
• Categorification, Quantization and Clusters, Beijing, 2007.
• Maurice Auslander Lectures, Boston, 2007.
• Representation Theory and Related Topics, Boston, 2007.
• LieGrits Workshop, Oxford, 2008.
• Lie Theory, MSRI, 2008.
• Topics in Combinatorial Representation Theory, MSRI, 2008.
• Higher Teichmüller Theory, Clusters and Quantization, Jerusalem, 2008.
• Combinatorics of moduli spaces, Hurwitz numbers, and cluster algebras, Moscow, 2008.
• Representation Theory of Algebras, Tehran, 2008.
• Algebraic Structures in Geometry and Physics, Leicester, 2008.
• ICRA XIII, Sao Paulo, 2008.
• Interactions Between Noncommutative Algebra and Algebraic Geometry, Banff, 2008.
• Cluster Algebras and Related Topics, Morelia and Mexico City, 2008.
• Representations of Algebras and Related Topics, Woods Hole, 2009.
• Felix Klein Lectures, Bonn, 2009.
• Homological and geometric methods in algebra, Trondheim, 2009.
• Representation Theory and Combinatorics, Beijing, 2009.
• Séminaire Bourbaki, Paris, 2009.
• Combinatorics and Representation Theory, Coimbra, 2010.
• Dean Jacqueline B. Lewis Memorial Lectures, New Brunswick, NJ, 2010.
• Homological and Geometrical Methods in Representation Theory, Trieste, 2010.
• Combinatorics of Moduli Spaces, Cluster Algebras, and Symplectic Invariants, Moscow, 2010.
• Cluster algebras and representation theory, Leeds, 2010.
• Teichmüller Theory and its Interactions in Mathematics and Physics, Bellaterra, 2010.
• Cluster algebras and quiver representations, Tehran, 2010.
• ICRA XIV, Tokyo, 2010.
• Colloque sur les surfaces et les représentations, Sherbrooke, 2010.
• Algebraic and geometric aspects of discrete integrable systems -- Integrable systems and cluster algebras, Tokyo, 2010.
• Cluster Algebras and Lusztig's Semicanonical Basis, Eugene, OR, 2011.
• Abel Symposium: Algebras, Quivers, and Representations, Balestrand, Norway, 2011.
• Cluster Algebras and Cluster Combinatorics, Summer Graduate Workshop, MSRI, 2011.
• Twenty-five years of representation theory of quantum groups, Banff, 2011.
• Cluster algebras and statistical physics, ICERM, Providence, 2011.
• Cluster algebras, representation theory, and Poisson geometry, Banff, 2011.
• Wall crossing, Bures-sur-Yvette, 2011.
• Quantum cluster algebras and related topics, Osaka, 2011.
• Noncommutative Birational Geometry and Cluster Algebras, Boston, 2012.
• Cluster Categories and Cluster Tilting, Trondheim, 2012.
• Cluster Algebras and Combinatorics, Graz, 2012.
• Tropical geometry and cluster algebras, Paris, 2012.
• Geometry, representation theory and clusters, Leicester, 2012.
• Combinatorics of moduli spaces, cluster algebras, knots, and topological recursion, Moscow, 2012.
• Cluster Algebras and Related Topics, Regina, 2012.
• ICRA XV, Bielefeld, 2012.
• Connections for Women, Cluster Algebras and Commutative Algebra programs, MSRI, 2012.
• Introductory Workshop, Cluster Algebras and Commutative Algebra programs, MSRI, 2012.
• Mathematics and Physics of Moduli Spaces, Heidelberg, 2012.
• Cluster Algebras in Combinatorics, Algebra, and Geometry, MSRI, 2012.
• Triangulations and Mutations, Newcastle, 2013.
• Cluster Algebras and Related Combinatorics, AMS Special Session, Boulder, CO, 2013.
• Maurice Auslander Lectures and Conference, Woods Hole, MA, 2013.
• Algebra, Combinatorics and Representation Theory (Zelevinsky Fest), Boston, 2013.
• Cluster Algebras and Tropical Geometry, Strasbourg, 2013.
• Mirror Symmetry and Cluster Algebras, Leeds, 2013.
• Cluster Algebras and Representation Theory, Oberwolfach, 2013.
• Cluster Algebras and Related Topics, Oberwolfach, 2013.
• Cluster Algebras and Combinatorics, Münster, 2014.
• Hall and Cluster Algebras, Montreal, 2014.
• Cluster Algebras, Snowbird, UT, 2014.
• Non-crossing partitions in representation theory, Bielefeld, 2014.
• Combinatorics of Moduli Spaces, Cluster Algebras and Topological Recursion, Moscow, 2014.
• Integrability and Cluster Algebras: Geometry and Combinatorics, ICERM, Providence, 2014.
• Cluster Algebras in Mathematical Physics, Summer School, Nagoya, 2014.
• Cluster algebras and preprojective algebras, Cardiff, 2014.
• Cluster algebras and representation theory, Seoul, 2014.
• Cluster algebras in combinatorics and topology, Seoul, 2014.
• Strings, quivers and cluster algebras in mathematical physics, Seoul, 2014.
• Cluster Algebras and Dynamical Systems, Münster, 2015.
• Cluster algebras and integrable systems, Durham, 2015.
• SAGE Days 64.5: Cluster Algebras, Minneapolis, 2015.
• Cluster algebras and finite dimensional algebras, Leicester, 2015.
• Algebraic Interfaces of Integrability, Leeds, 2015.
• Positive Grassmannians, Montreal, 2015.
• Total positivity: a bridge between representation theory and physics, Canterbury, 2016.
• Homological Methods, Representation Theory and Cluster Algebras, Mar del Plata, 2016.
• Cluster Algebras and Geometry, Münster, 2016.
• Hot Topics: Cluster algebras and wall-crossing, MSRI, Berkeley, 2016.
• Quivers and bipartite graphs, London, 2016.
• Combinatorics of Moduli Spaces, Hurwitz numbers, and cohomological field theories, Moscow, 2016.
• Symmetries and Integrability of Difference Equations, Sainte-Adèle, QC, 2016.
• ICRA 2016, Syracuse, 2016.
• Lie theory and cluster algebras, Rome, 2016.
• Quivers, cluster algebra and mathematical physics, Hong Kong, 2016.
• Stability conditions, Donaldson-Thomas invariants and cluster varieties, Sheffield, 2017.
• Cluster algebras and log Gromov-Witten invariants in the Gross-Siebert program, KIAS, Seoul, 2017.
• New trends in representation theory: The impact of cluster theory in representation theory, Leicester, 2017.
• Quiver Grassmannians and their applications, Wuppertal, 2017.
• Cluster algebras in mathematical physics, Mainz, 2017.
• Cluster algebras, Storrs, CT, 2017.
• Cluster algebras and related topics, Tianjin, 2017.
• Cluster algebras: Twenty years on, Luminy, March 2018.
• Cluster algebras and mathematical physics, East Lansing, May 2018.
• R-matrices, cluster algebras, and integrable systems, Nagoya, May 2018.
• Combinatorics of moduli spaces, cluster algebras and topological recursion, Moscow, June 2018.
• Interactions of quantum affine algebras with cluster algebras, current algebras and categorification, June 2018.
• Non-commutative structures, cluster algebras and applications (Retakh Fest), Angers, June 2018.
• Cluster algebras and algebraic geometry, Nottingham, July 2018.
• Stability conditions and representation theory of finite-dimensional algebras, Banff, October-November 2018.
• Combinatorics and beyond, Ann Arbor, November 2018.
• Cluster algebras, Bangalore, December 2018.
• Cluster structures in geometry, physics, combinatorics and representation theory, Jerusalem, December 2018.
• Faces of integrability, Montreal, April-May 2019.
• Interactions between representation theory and homological mirror symmetry, Leicester, May 2019.
• Mirror Symmetry and Cluster Algebras, Cambridge, UK, July 2019.
• Quiver varieties and representation theory, Montreal, August 2019.
• Mutations: mirror symmetry, deformations, and combinatorics, Banff, August 2019.
• Algebraic Representation Theory and Related Topics, Sanya, October 2019.
• Cluster Algebras, Representation Theory, and Geometry, Osaka, March 2020.
• Cluster Algebras and the Geometry of Scattering Amplitudes, Edinburgh, March 2020.
• Bridges between representation theory and algebraic geometry: Singularities, friezes and cluster categories, Leeds, May 2020.
• Combinatorics of moduli spaces, cluster algebras and topological recursion, Moscow, June 2020.
• ICRA 2020, Trieste, July 2020.
• Bases for Cluster Algebras, Oaxaca, September-October 2020.

Seminars and working groups

• Université Lyon 1, 2004.
• Institut de Mathématiques de Jussieu, 2004-2010.
• Université de Picardie, 2004.
• UNAM, Mexico, 2004, 2007.
• University of Leicester, 2005.
• Fields Institute, 2005-06.
• University of Bielefeld, 2005-06.
• University of Manchester, 2006-07.
• University of Leeds, 2007.
• ETH Zürich, 2006-07, 2009, 2010.
• University of Paderborn, 2008-10.
• University of Hannover, 2009.
• University of Sherbrooke, 2010.
• M.I.T.-Northeastern, 2011.
• University of California at Berkeley, 2011.
• University of Bonn, 2012.
• University of Connecticut, 2013-present.
• University of California at Berkeley, 2013.
• Nagoya University, 2013-2015.
• University of Michigan, 2014.
• University of Notre Dame, 2016.
• Université de Strasbourg, 2016.
• Michigan State University, 2017.

Courses

• University of Leeds, 2008 (by Robert Marsh)
• UNAM, 2008 (by Michael Barot and Christof Geiss)
• Harvard University, 2008 (by Lauren Williams)
• University of Oregon, 2009 (by Arkady Berenstein)
• Northeastern University, 2009 (by Andrei Zelevinsky)
• University of Bielefeld, 2010
• University of Hannover, 2010 (by Thorsten Holm)
• Louisiana State University, 2010 and 2011 (by Milen Yakimov)
• University of Aarhus, 2010 (by Sergey Fomin)
• University of California at Berkeley, 2011 (by Lauren Williams)
• University of Kent, 2011 (by Andy Hone and Stephane Launois)
• University of Minnesota, 2011, 2015, and 2016 (by Gregg Musiker)
• Stony Brook University, 2011 (by Michael Movshev)
• University of Bath, 2012 (by Alastair King)
• Nagoya University, 2013 and 2014 (by Laurent Demonet)
• University of Michigan, 2014 (by Sergey Fomin)
• Institut Henri Poincaré, 2014 (by Lauren Williams)
• North Carolina State University, 2015 (by Salvatore Stella)
• CRM, 2015 (by Michael Gekhtman)
• University of Illinois, 2015 (by Philippe Di Francesco)
• Stockholm University, 2015 (by Michael Shapiro)
• Erwin Schrödinger Institute, 2015 (by Andrew Hone)
• UQAM, 2016 (by Hugh Thomas)
• Columbia University, 2016 (by Lauren Williams)
• Mar Del Plata, 2016 (by Ralf Schiffler, Ibrahim Assem, and Pierre-Guy Plamondon)
• Tsinghua University, 2016 (by Linhui Shen)
• University of Nebraska, 2017 (by Kyungyong Lee)
• University of California at Berkeley, 2017 (by Lauren Williams)
• University of Michigan, 2018 (by Sergey Fomin)
• ETH Zürich, 2018 (by Ran Tessler)
• University of Connecticut, 2018 (by Ralf Schiffler)
• M.I.T., 2018 (by Alexander Postnikov)
• Harvard University, 2018 (by Man-Wai Cheung)
• Hong Kong University of Science and Technology, 2019 (by Ivan Ip)

Software and data

• Mutations in Maple and Mupad by Frédéric Chapoton
• Java applets for quiver mutations and clusters/exchange graphs by Bernhard Keller
• Quiver Mutation Explorer by Grégoire Dupont and Matthieu Pérotin
• Integer sequences (by OEIS)
• Cluster algebra and quiver package in Sage (by Gregg Musiker and Christian Stump)
• Wolfram Demonstrations Project (by Bernhard Keller, Christian Korff, and Lauren Williams)
• Plabic tilings (by Pavel Galashin)

Thematic programs

• Combinatorial Representation Theory, MSRI, 2008.
• Algebraic Lie Theory and Discrete Integrable Systems, Isaac Newton Institute, 2009.
• Tropical geometry and cluster algebras, Paris/Strasbourg, 2009-2013.
• Interaction of Representation Theory with Geometry and Combinatorics, Hausdorff Institute, 2011.
• Cluster Algebras, Mathematical Sciences Research Institute (MSRI), 2012.
• Cluster algebras in mathematics and physics, KIAS, Seoul, 2014.
• Cluster Algebras, Research Institute for Mathematical Sciences (RIMS), 2019.
• Quiver varieties and representation theory, CRM, Montreal, 2019.

Publicity and awards

• Interviews with Andrei Zelevinsky at in-cites.com (2006) and the Northeastern Voice (2007)
• Interview (Thomson Scientific, 2007) with the authors of Tilting theory and cluster combinatorics
• ICRA Award (2007), MSJ Algebra Prize (2008), and MSJ Spring Prize (2010) to Osamu Iyama
• December 2007 issue of Notices of the AMS: What is... a cluster algebra?
• Interview with Bernhard Keller and Idun Reiten in Science Watch, 2008.
• Whitehead Prize 2009 to Robert Marsh
• ICRA Award (2010) to Claire Amiot
• Emmy Noether Lecture at ICM 2010 by Idun Reiten
• University Distinguished Professorship awarded posthumously to Andrei Zelevinsky (2013)
• Profile of Ralf Schiffler in UConn Today (2013).
• Prix Sophie Germain to Bernhard Keller (2014)
• AWM-Microsoft Research Prize to Lauren Williams (2016)
• Steele Prize to Sergey Fomin and Andrei Zelevinsky (2018)

Andrei Zelevinsky, 1953-2013

• Zelevinsky's blog
• Andrei Zelevinsky on Wikipedia
• memorial page at Northeastern University
• memorial conference (April 24-28, 2013)
• extended obituary in Transformation Groups
• eulogy in Journal of Algebraic Combinatorics
• remembrances in Troitskiy Variant (in Russian)
• preface to the special volume of Advances in Mathematics
• Andrei Zelevinsky Research Instructorship

Other

• Cluster algebras (13F60) in the 2010 Mathematics Subject Classification.
• Cluster algebra entry on Wikipedia

This page is maintained by Sergey Fomin.