Research
Relevant Document
Collaborations
Ongoing projects are listed approximately in the order in which they started. Projects in the very early stages are not yet listed.
Continuous gentle quivers; with Karin M. Jacobsen
Representations of poset quivers; with Charles Paquette and Emine Yıldırım
Continuous d-cluster tilting subcategories; with Karin M. Jacobsen
Semilinear representations and persistence modules, with Raphael Bennett-Tennenhaus
I have also worked with Eric J. Hanson, Kiyoshi Igusa, Maitreyee C. Kulkarni, Jacob P. Matherne, Fatemeh Mohammadi, Kaveh Mousavand, Gordana Todorov, Francesca Zaffalon, and Shijie Zhu.
Papers
Peer Reviewed
(With S. Zhu) Continuous Nakayama Representations. Applied Categorical Structures (2023).
(With E. J. Hanson) Composition series of arbitrary cardinality in modular lattices and abelian categories. Advances in Mathematics (2023).
(With Fatemeh Mohammadi and Francesca Zaffalon) Progress on Infinite Cluster Categories Related to Triangulations of the (Punctured) Disk. Accepted to Journal of Algebra and its Applications special issue on "Cluster Algebras and Related Topics."
Preprint: arXiv:2209.15513
(With E. J. Hanson) Decomposition of Pointwise Finite-Dimensional S^1 Persistence Modules. Journal of Algebra and its Applications (2022).
Continuous Quivers of Type A (IV) Continuous Mutation and Geometric Models of E-clusters. Algebras and Representation Theory (2022).
(With K. Igusa and G. Todorov) Continuous Quivers of Type A (III) Embeddings of Cluster Theories. Nagoya Mathematical Journal (2022),
(With K. Igusa and G.Todorov) Continuous Quivers of Type A (I) Foundations. Rendiconti del Circolo Matematico di Palermo Series 2 (2022),
Submitted for Peer Review
(with Kiyoshi Igusa) Continuous Stability Conditions of Type A and Measured Laminations of the Hyperbolic Plane, arXiv:2302.14792, 2023
(with Karin M. Jacobsen) Admissible ideals for k-linear categories, arXiv:2209.13944, 2022
(With M. C. Kulkarni, J. P. Matherne, and K. Mousavand) A Continuous Associahedron of Type A, arxiv:2108.12927, 2021
Continuous Quivers of Type A (II) The Auslander—Reiten space, arXiv:1910.04140, 2019.
Further Preprints
Cluster Theories and Cluster Structures of Type A, arXiv:2112.14795, uploaded 2021, announced 2022
Conference Organization
I co-organized the following conferences.
Functor Categories, Model Theory, and Constructive Category Theory - 3—7 July 2023
Conference website [link]
Universidad de Málaga
Algebraic Analysis, Functor Categories and Constructive Methods - 7—10 March 2023
Conference website [link]
Universiteit Gent
Functor Categories, Model Theory, and Constructive Category Theory 2022 - 11—15 July 2022
Conference website [link]
Universidad de Almería
Peer Review
I have peer reviewed for the following journals.
Journal of Algebraic Combinatorics
Presentations
Invited Talks
Composition Series of Arbitrary Cardinality in Modular Lattices - 12 July 2023
SIAM Conference on Applied Algebraic Geometry (AG23)
Mini symposium on Recent Developments in Multi Parameter Persistence
Eindhoven Univeristy of Technology (TU/e) in Eindhoven, Netherlands
Progress on Continuous (Representations of) Quivers - 13 June 2023
Advances in Representation Theory of Algebras (ARTA) IX
Queen's University in Kingston, Canada
Composition Series of Arbitrary Cardinality via Modular Lattices - 29 March 2023
Combinatorial Aspects of Representation Theory
Centre of Advanced Study (CAS) at the Norwegian Academy of Sciences and Letters in Oslo, Norway
Composition Series of Arbitrary Cardinality in Abelian Categories - 11 May 2022
Symposium on Koszul Algebras and Abelian Categories [link]
Aarhus Universitet
Composition Series of Arbitrary Cardinality (in Abelian Categories) - 4 January 2022
Flash Talks in Representation Theory
Norges Teknisk-Naturvitenskapelige Universitet (NTNU) [Virtual]
A Continuous Associahedron - 9 October 2021
AMS Sectional Meeting
Quiver representations: bridging theory and application
[Virtual, originally at Creighton University]
Composition Series of Arbitrary Cardinality (in abelian categories) - 11 June 2021
Seminar Representation Theory of Algebras
Universität Bielefeld [Virtual]
"Continuous" Representation Theory - 18 May 2021
Algebra Seminar
Norges Teknisk-Naturvitenskapelige Universitet (NTNU) [Virtual]
Decomposition of Pointwise Finite-Dimensional Representations of the Circle - 13 January 2021
Théorie de Représentations et ses Applications et Connections
Université de Sherbrooke [Virtual]
Continuous Generalized Associahedra of Type A - 16 November 2020
Ghent Algebra and Geometry Seminars
Universiteit Gent [Virtual]
Decomposing Pointwise Finite-dimensional Representations of the Circle - 2 October 2020
Representation Theory and Related Topics Seminar
Northeastern University [Virtual]
Cluster Theories and Continuous Mutation - 29 April 2020
Séminaire D’algèbre
Université de Sherbrooke [Virtual]
The Auslander-Reiten Space - 8 November 2019
Representation Theory and Related Topics Seminar
Northeastern University
New Continuous Cluster Category - 17 August 2019
Homological Methods and Tilting Theory of Finite Dimensional Algebras
In Honor of Gordana Todorov's 70th Birthday
University of Iowa
Continuous Representations - 16 July 2019
Functor Categories, Model Theory, and Constructive Category Theory
University of Tartu, Pärnu College
Continuous Representations: What goes right and what goes wrong? Part II - 6 May 2019
Representation Theory and Related Topics Seminar
Northeastern University
Continuous Representations: What goes right and what goes wrong? Part I - 3 May 2019
Representation Theory and Related Topics Seminar
Northeastern University
Additional Talks
"Continuification" of quivers and representations - 7 March 2023
.Algebraic Analysis, Functor Categories, and Constructive Methods
Universiteit Gent in Ghent, Belgium
A Continuous Associahedron - 22 March 2023
Categories, clusters, and completions
Aarhus Universitet in Aarhus, Denmark
Continuous Stability Conditions of Type A [slides] - 9 August 2022
ICRA 2022 (Conference) [link]
Universidad de Buenos Aires
Continuous Nakayama Representations - 12 July 2022
Functor Categories, Model Theory, and Constructive Category Theory [link]
Universidad de Almería
Presentation at the request of the other organizers
Some Continuous Algebra - 5 Dececmber 2020
Trans Math Day 2020
Virtual Conference
Continuous Cluster Categories - 7 September 2019
XXXIème Rencontre de Théorie des Représentations des Algèbres
Université de Sherbrooke
Continuous Clusters and Continuous Mutation - 28 April 2019
Maurice Auslander Distinguished Lectures and International Conference
Woods Hole Oceanographic Institution
Continuous Representations - 7 September 2018
XXXème Rencontre de Théorie des Représentations des Algèbres
Université de Sherbrooke
Poster Presentations
Cluster Theories and Examples in Type A [PDF Version]- 9-25 November 2020
Workshop and International Conference on Representations of Algebras (ICRA) [Virtual]
Decomposing Pointwise Finite-dimensional Representations of the Circle [Poster] - 25-26 September 2020
Rencontre de Théorie des Représentations des Algèbres - Édition Corona [Virtual]