Quantum Mathematics is a regional work group in Ireland which comprises researchers from Mary Immaculate College (MIC), Munster Technological University (MTU) and University College Cork (UCC).
Claus Koestler, UCC Boole Center for Research in Informatics, UCC School of Mathematical Sciences
Arundhathi Krishnan, MIC Department of Mathematics and Computer Studies
J.P. McCarthy, MTU Department of Mathematics
Stephen Wills, UCC School of Mathematical Sciences
All meetings take place in Room 156 of Western Gateway Building, University College Cork, unless announced differently.
Upcoming Discussions/Talks
Monday 13. January 2024, 13:00 - 15:00
Topic/Title: T.B.C.
Discussion/Speaker: N.N.
Past Discussions/Talks 2025
Monday 6. January 2024, 13:00 - 15:00
(cancelled)
All meetings take place in Room 156 of Western Gateway Building, University College Cork, unless announced differently.
Past Discussions/Talks 2024
Monday 23. December 2024, 13:00 - 15:00
(cancelled)
Monday 16. December 2024, 13:00 - 15:00
Discussion
Monday 9. December 2024, 13:00 - 15:00
Title: Introduction to noncommutative Ito integration
Discussion/Speaker: Claus Koestler, University College Cork
Monday 2. December 2024, 13:00 - 15:00
(cancelled)
Monday, 25. November 2024, 13:00 - 15:00
Title: Distributional invariance principles for the CAR algebra
Speaker: Stephen Wills, University College Cork
Monday, 18. November 2024, 13:00 - 15:00
Title: Idempotent states on quantum permutation groups II (slides)
Speaker: J.P. McCarthy, Munster Technological University
Monday, 11. November 2024, 13:00 - 15:00
Discussion: Universal algebras
Monday, 4. November 2024, 13:00 - 15:00
(cancelled)
Monday, 28. October 2024, 13:00 - 15:00
(No Meeting - Bank Holiday)
Monday, 21. October 2024, 13:00 - 15:00
Title: Idempotent states on quantum permutation groups I (slides)
Speaker: J.P. McCarthy, Munster Technological University
Monday 14. October 2024, 13:00 - 15:00
Title: Central Limit Theorems for Coxeter systems and Artin systems of extra large type, Part II
Speaker: Arundhathi Krishnan, Mary Immaculate College
Monday, 7. October 2024, 13:00 - 15:00
Title: Central Limit Theorems for Coxeter systems and Artin systems of extra large type, Part I
Speaker: Arundhathi Krishnan, Mary Immaculate College
Monday, 30. September 2024, 13:00 - 15:00
Title: Some problems on Temperley-Lieb algebras, Part II
Speaker: Claus Koestler, University College Cork
Monday, 23. September 2024, 13:00 - 15:00
Title: A note on group algebras
Speaker: J.P. McCarthy, Munster Technological University
Monday, 16. September 2024, 13:00 - 14:30
Title: Some problems on Temperley-Lieb algebras, Part I
Speaker: Claus Koestler, University College Cork
(Summer Break)
Tuesday, 4. June 2024, 13:15 - 14:15
Venue: Western Gateway Building, Room G.13
Title: A quantum Frucht theorem?
Speaker: J.P. McCarthy, Munster Technological University
Abstract: The first part of the talk will give a post hoc motivation for Banica’s 2005 definition of the quantum automorphism group of a finite graph, and in doing so attempt to build a good intuition for quantum automorphism. Frucht in 1939 showed that every finite group is the automorphism group of a finite graph, and a natural pursuit in the theory of quantum automorphism groups is to establish quantum analogues of this result.
Based on a joint work with Banica, the second part of the talk will address this question. Slides.
Tuesday, 4. June 2024, 15:00 - 16:00
Venue: Western Gateway Building, Room G.13
Title: Entrywise preservers for matrices with positivity, negativity and inertia constraints
Speaker: Alexander Belton, University of Plymouth
Abstract: We all know how to multiply matrices, but it is also possible to treat them simply as arrays of numbers and perform algebraic operations entry by entry. For multiplication, this is called the Hadamard product. A notable feature of the Hadamard product is that it preserves the collection of matrices that are positive semidefinite: real symmetric matrices with non-negative eigenvalues. It follows immediately that applying any absolutely monotonic function entrywise also preserves this form of positivity. (A function is absolutely monotonic if its Maclaurin series has non-negative coefficients.) Rather more work is required to show that the converse is true: a function that preserves positive semidefiniteness when applied entrywise to matrices of arbitrary size is necessarily absolutely monotonic. The situation is more complex for matrices of a fixed size, or when the class of matrices being studied has some other form of positivity constraint, or possesses additional structure, such as Hankel or Toeplitz matrices. Recently some results have been obtained for entrywise inertia preservers and entrywise transforms of matrices with eigenvalues satisfying negativity constraints.
This is joint work with Dominique Guillot (University of Delaware), Apoorva Khare (Indian Institute of Science, Bangalore) and Mihai Putinar (University of California at Santa Barbara and Newcastle University).
Tuesday, 28. May 2024, 13:00 - 14:30
Venue: Western Gateway Building, Room G.13
Title: Ergodic theorem for random walks on finite quantum groups II (based on this paper, preprint here)
Speaker: J.P. McCarthy, Munster Technological University
Tuesday, 21. May 2024
(cancelled)
Tuesday, 14. May 2024, 13:00 - 14:30
Venue: Western Gateway Building, Room G.13
Title: Ergodic theorem for random walks on finite quantum groups I (based on this paper, preprint here)
Speaker: J.P. McCarthy, Munster Technological University
Tuesday, 7. May 2024, 10:30 -12:00
Venue: Western Gateway Building, Room G.13
Title: Introduction to CAR algebras III
Speaker: Stephen Wills, University College Cork
Wednesday, 1. May 2024
(cancelled)
Wednesday, 24. April 2024, 14:00 - 15:30
Title: Introduction to CAR algebras II
Speaker: Stephen Wills, University College Cork
Wednesday, 17. April 2024, 14:00 - 15:30
Title: Introduction to CAR algebras I
Speaker: Stephen Wills, University College Cork
Wednesday, 10. April, 14:00 - 15:30
(Cancelled)
Wednesday, 3. April, 14:00 - 15:30
(No Meeting - Easter Break)
Wednesday, 27. March 2024, 14:00 - 15:30
(No meeting - Easter Break)
Wednesday, 20. March 2024, 14:00 - 15:30
Title: Temperley-Lieb algebras from the viewpoint of noncommutative probability
Speaker: Claus Koestler, University College Cork
Wednesday, 13. March 2024, 15:00 - 16:00
Venue: Western Gateway Building, Room G.09
Title: New hyperfinite subfactors with small Jones index
Speaker: Dietmar Bisch, Vanderbilt University
Abstract: Since Vaughan Jones introduced the theory of subfactors in 1983, it has been an open problem to determine the set of Jones indices of irreducible, hyperfinite subfactors. Unfortunately, not much is known about this set. My student Julio Caceres and I could recently show that certain indices between 4 and 5 are realized by new hyperfinite subfactors with Temperley-Lieb-Jones standard invariant. This leads to a conjecture regarding Jones' problem. Our construction involves commuting squares, a graph planar algebra embedding theorem, and a few tricks that allow us to avoid solving large systems of linear equations to compute invariants of our subfactors. If there is time, I will explain a criterion that detects when a hyperfinite subfactor is not a commuting square subfactor.
Wednesday, 6. March 2024, 14:00 - 15:30
Title: Spreadability as a distributional invariance principle
Speaker: Claus Koestler, University College Cork
Wednesday, 28. February 2024, 14:00 - 15:30
Title: A central limit theorem in the framework of the Thompson group F (Part 2)
Speaker: Arundhathi Krishnan, Mary Immaculate College
Wednesday, 21. February 2024, 14:00 - 15:30
Title: A central limit theorem in the framework of the Thompson group F (Part 1)
Speaker: Arundhathi Krishnan, Mary Immaculate College
Wednesday, 14. February 2024, 14:00 - 15:30
Topic: An introduction to abstract reduction systems
Speaker: Arundhathi Krishnan, Mary Immaculate College
Wednesday, 7. February 2024, 14:00 - 15:30
Title: Tracing the orbitals of the quantum permutation group (notes)
Speaker: J.P. McCarthy, Munster Technological University
Wednesday, 31. January 2024, 14:00 - 15:30
Title: An introduction to the orbitals of quantum permutation groups (notes)
Speaker: J.P. McCarthy, Munster Technological University
Wednesday, 24. January 2024, 14:00 - 15:30
Title: An introduction to algebraic central limit theorems
Speaker: Claus Koestler, University College Cork
Wednesday, 17. January 2024, 14:00 - 15:30
Title: An introduction to distributional invariance principles
Speaker: Claus Koestler, University College Cork
Roland 65 - Free Probability
Saarbrücken (Germany), 9 June - 13 June 2025
Hamilton 220 Years Anniversary Celebration
Dublin (Ireland) , 13 March - 14 March 2025
Conference on Operator Algebras and Related Topics
Bombay (India), 24 February - 28 February 2025
Quantum Graphs
Saarbrücken (Germany), 17 February - 21 February 2025
Quantum Information, Quantum Groups and Operator Algebras
Cambridge (UK), 4 November - 6 December 2024
35th International Workshop on Operator Theory and its Applications
Canterbury (UK), 12 - 16 August 2024
Celebration of Albert Schwarz’s 70 Years in Science
Bois-Marie (France), 14-16 June 2024
UK Operator Algebras Conference
Newcastle (UK), 12 - 14 June 2024
Noncommutative Analysis on Groups and Quantum Groups (ANCG)
Besançon (France), 18 - 21 December 2023
BCRI Mini-Symposium: Logic, Semantics and Complexity in Computer Science
Cork (Ireland), 17 October 2023
Thematic Program on Operator Algebras and Applications
Toronto (Canada), 1 July - 31 December 2023
Operator Algebras: Subfactors and Applications
Cambridge (UK), 26 - 30 June 2023
Women in Operator Algebras III
Banff (Canada), 25 - 30 June 2023
BCRI Mini-Symposium: Noncommutative Probability & Quantum Information
Cork (Ireland), 10 October 2022
Noncommutative probability, noncommutative harmonic analysis and related topics, with applications
Będlewo (Poland), 31 July - 6 August 2022.
Operator Algebras: Subfactors, K-theory, Conformal Field Theory (David Evans 70)
Gregynog (UK), 27 July - 2 August 2022
Wales Mathematics Colloquium
Gregynog (UK), 23-25 May 2022
Women in Operator Algebras II
Banff (Canada), 5 - 10 December 2021
Women in Operator Algebras I
Banff (Canada), 4 - 9 November 2018
BCRI Mini-Symposium: Markovianity and Symmetry
Cork (Ireland), 10 September 2018
Structure of Operator Algebras: Subfactors and Fusion Categories
Cambridge (UK), 23 - 27 January 2017
George Boole Mathematical Sciences Conference
Cork (Ireland), 17 - 28 August 2015