Integrable models and deformations of vertex algebras via symmetric functions
Lead Research Organisation:
University of Glasgow
Department Name: School of Mathematics & Statistics
Abstract
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People |
ORCID iD |
| Christian Korff (Principal Investigator) |
| Description | Deformed Virasoro algebras and shifted quantum groups |
| Organisation | University of Tokyo |
| Country | Japan |
| Sector | Academic/University |
| PI Contribution | Expertise in describing deformed vertex operator algebras using lattice models from statistical mechanics. |
| Collaborator Contribution | Definition of a deformed Virasoro algebra related to Macdonald functions. |
| Impact | Research visit by Prof Junichi Shiraishi and workshop at the School of Mathematics and Statistics |
| Start Year | 2023 |
| Description | Exactly solvable lattice models and symmetric functions |
| Organisation | University of Amsterdam |
| Country | Netherlands |
| Sector | Academic/University |
| PI Contribution | Expertise on exactly solvable lattice models. Invited Dr Valentin Buciumas from the University of Amsterdam to a research visit and workshop to the UK. |
| Collaborator Contribution | Expertise in representation and number theory. |
| Impact | Workshop on integrable systems and symmetric functions. |
| Start Year | 2022 |
| Description | Ind Cluster Algebras and the Sato-Segal-Wilson Grassmannian |
| Organisation | Aarhus University |
| Country | Denmark |
| Sector | Academic/University |
| PI Contribution | Expertise on the Kadomstev-Petiashvili equation and its solution. Combinatorial description of solutions of the KP hierarchy via Postnikov diagrams. |
| Collaborator Contribution | Expertise on infinite rank cluster algebras. |
| Impact | Preprint in preparation; anticipated submission May 2025. |
| Start Year | 2023 |
| Description | Quantum Knizhnik-Zamolodchikov Equations |
| Organisation | University of Amsterdam |
| Country | Netherlands |
| Sector | Academic/University |
| PI Contribution | Expertise on integrable lattice models |
| Collaborator Contribution | Representation theory of double affine Hecke algebras (Prof. Jasper Stokman) |
| Impact | Visit to the Korteweg-de-Vries Institute in October 2022 (host Prof. Jasper Stokman) and seminar on cylindric Hecke characters |
| Start Year | 2022 |
| Description | Schur's Q functions and lattice models |
| Organisation | University of Illinois at Urbana-Champaign |
| Country | United States |
| Sector | Academic/University |
| PI Contribution | Expertise on exactly solvable lattice models and symmetric functions. |
| Collaborator Contribution | Combinatorial aspects of lattice models. |
| Impact | Multidisciplinary. Number theory, representation theory and mathematical physics. Output in preparation, planned submission summer 2025. |
| Start Year | 2023 |
| Description | Schur's Q functions and lattice models |
| Organisation | University of Minnesota |
| Country | United States |
| Sector | Academic/University |
| PI Contribution | Expertise on exactly solvable lattice models and symmetric functions. |
| Collaborator Contribution | Combinatorial aspects of lattice models. |
| Impact | Multidisciplinary. Number theory, representation theory and mathematical physics. Output in preparation, planned submission summer 2025. |
| Start Year | 2023 |
| Description | 3 month visiting Professorship at RIMS, Kyoto University |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | I was invited to a 3 month visiting professorship at the Research Institute for Mathematics Sciences at Kyoto University (similar to the Isaas Newton Institute in the UK). While there I spoke with many Japanese mathematicians thereby communicating the research generated by this award to a wide international audience. |
| Year(s) Of Engagement Activity | 2024 |
| Description | LMS Workshop on Integrable Systems and Symmetric Functions |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Postgraduate students |
| Results and Impact | Workshop bringing together researchers working at the interface of integrable systems and symmetric functions and representation theory. The workshop was run in hybrid format, with in person and online speakers from Australia, Europe, Japan and the U.S. Two preseminars were given to make the research talks accessible to postgraduate students and all talks were recorded as an important learning resource for postgraduate students. |
| Year(s) Of Engagement Activity | 2023 |
| URL | https://sites.google.com/view/lmsuog2023/home |
| Description | Opening talk at international conference on solvable lattice models |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | International conference on exactly solvable lattice model, representation theory and number theory with world leading experts as well as many PhD students in the audience. The meeting helped to build new contacts and bridges between different mathematical research communities. |
| Year(s) Of Engagement Activity | 2024 |
| URL | https://sites.google.com/bc.edu/solomon-friedberg/dublin2024 |
| Description | Research visit and seminar to Cardiff University |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | Regional |
| Primary Audience | Professional Practitioners |
| Results and Impact | 1 week research visit to Cardiff University and discussion of exactly solvable lattice models in connection with Zamolodchikov's presentation of the Virasoro algebra with Simon Wood and Roman Gonin (team members). Mathematical Physics seminar at the end of the visit disseminating the research project to a wider audience of mathematicians. |
| Year(s) Of Engagement Activity | 2023 |
| Description | Seminar Presentation and Queen Mary University London |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | Regional |
| Primary Audience | Professional Practitioners |
| Results and Impact | Explaining the research programme and recent results. Target included researchers working in theoretical physics. |
| Year(s) Of Engagement Activity | 2024 |
| Description | Talk and discussions at the University of Warwick |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | Regional |
| Primary Audience | Professional Practitioners |
| Results and Impact | Explaining the research programme and main outcomes so far on the project funded by the grant. Target included researchers working in algebraic combinatorics and statistics. |
| Year(s) Of Engagement Activity | 2023 |
| Description | Visit by Roman Gonin to the University of Glasgow |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | Local |
| Primary Audience | Professional Practitioners |
| Results and Impact | A brief visit by Roman Gonin in February reported on progress on understanding the representation theory behind the energy-momentum tensor of Zamolodchikov from the view of vertex operator algebras. This might help to understand more deeply the concept of vertex operator algebras which do not satisfy the usual axioms and have been discussed previously by Anguelova in the context of "twisted vertex operator algebras" and Date et. al in the connection with integrable hierarchies, the so-called BKP hierarchy. |
| Year(s) Of Engagement Activity | 2024 |