Vertex algebras and the rich structures enjoyed by their categories of modules
September, 2026, Braiding new ground: Vertex algebras meet the Yang-Baxter equation, Maynooth UniversityMaynooth, Ireland
Slides
Talks and presentations
See a map of all the places I've given a talk!
2026
Maynooth, Ireland
SlidesTorus \(1\)-point functions for the \(\mathfrak{sl}(2)\) WZW models and their modular properties
February, 2026, Integrable Systems and Mathematical Physics Seminar, University of Glasgow
Glasgow, UK
Slides
2025
Monoidal categories from vertex operator algebras – beyond rigidity
July, 2025, Recent Developments in Logarithmic Conformal Field Theory, Banff International Research Station
Banff, Canada
Slides | RecordingTorus \(1\)-point functions for the \(\mathfrak{su}(2)\) WZW model and their modular properties
May, 2025, Mathematical physics seminar, University of Edinburgh and Heriot-Watt University
Edinburgh, UK
SlidesThe rigidity of admissible \(\mathfrak{sl}(2)\) and \(\mathcal{N}=2\) vertex super algebras
April, 2025, Shenzhen Thematic Program "Representation Theory"
Shenzhen, China
2024
Admissible \(\mathfrak{sl}(2)\) and \(\mathcal{N}=2\), and their fusion product
December, 2024, Research on finite groups, algebraic combinatorics, and vertex algebras, RIMS
Kyoto, Japan
SlidesGrothendieck-Verdier duality as a generalisation of rigidity
December, 2024, Kyoto Representation Theory Seminar, RIMS
Kyoto, JapanDuality beyond rigidity
November, 2024, Tensor Categories, Quantum Symmetries, and Mathematical Physics, MATRIX
Creswick, Australia
SlidesDuality structures in tensor categories beyond rigidity
November, 2024, Vertex algebra seminar, Tokyo Woman's Christian University
Tokyo, Japan
2023
Duality structures on tensor categories coming from vertex operator algebras
June, 2023, Representation Theory XVIII
Dubrovnik, CroatiaDuality structures on tensor categories coming from vertex operator algebras
June, 2023, Groups, Rings and the Yang-Baxter equation 2023
Blankenberge, Belgium
SlidesSymmetric function combinatorics and conformal field theory
January, 2023, Pure Mathematics Colloquium, Hamburg University
Hamburg, Germany
2022
Representation categories of vertex algebras
December, 2022, ZMP Seminar, Hamburg University
Hamburg, Germany
SlidesThe classification of simple (semi)relaxed admissible affine \(\mathfrak{sl}(3)\) modules and their modular properties at level \(−\frac{3}{2}\)
October, 2022, Representation Theory XVII
Dubrovnik, Croatia
SlidesModular properties for well chosen non-rational vertex operator algebras
July, 2022, Modular Forms and Representation Theory
Manigod, FranceLie theory beyond category O in conformal field theory and vertex operator algebras
July, 2022, Mathematics Seminar, Friedrich-Alexander-Universität Erlangen-Nürnberg
Erlangen, GermanyTensor structures out in the wild
May, 2022, Hamburg research seminar in algebra and mathematical physics, Hamburg University
Hamburg, Germany
2021
Grothendieck-Verdier duality in categories of VOA modules with examples
November, 2021, Quantum Field Theories and Quantum Topology Beyond Semisimplicity, Banff International Research Station
Banff, Canada (online)
RecordingClassifying representations in conformal field theory via the combinatorics of symmetric functions
October, 2021, Virtual Integrable Systems Seminars, International Centre for Mathematical Sciences
Edinburgh, UK (online)There is always more that can be learnt from the free boson
March, 2021, Rocky Mountain Representation Theory Seminar, University of Colorado Boulder
Boulder, Colorado, USA (online)From vertex operator algebras to tensor products
January, 2021, Algebra and Mathematical Physics Seminar, Hamburg University
Hamburg, Germany (online)
2020
Vertex algebras with nice structure despite failing all conventional niceness criteria
February, 2020, Algebra Seminar, University of Aberdeen
Aberdeen, UK
Slides
2019
Logarithmic vs rational conformal field theory – Who really wants to be rational anyway?
December, 2019, School of Physics and Astronomy, Queen Mary University
London, UK
SlidesI ain’t afraid of no ghost
June, 2019, The Mathematical Foundations of Conformal Field Theory and Related Topics - A conference in honor of Yi-Zhi Huang, Chern Institute, Nankai University
Tianjin, China
2018
\(\beta\gamma\) ghost algebras and the Verlinde formula
December, 2018, Algebra and Mathematical Physics Seminar, Hamburg University
Hamburg, Germany
SlidesNon-rational conformal field theory with \mathfrak{sl}(3)$$ symmetry
December, 2018, Mathematical Physics Seminar, Glasgow University
Glasgow, UK
SlidesPresentations of Zhu algebras from free field realisations
November, 2018, Workshop on vertex algebras and infinite-dimensional Lie algebras, University of Split
Split, CroatiaLogarithmic Conformal Field Theory and the Verlinde Formula
October, 2018, 11th Seminar on Conformal Field Theory, Friedrich-Alexander-Universität Erlangen-Nürnberg
Erlangen, GermanyThe standard module formalism and affine \(\mathfrak{sl}(3)\) at level \(−\frac{3}{2}\)
July, 2018, RIMS Workshop: Vertex Operator Algebras and Symmetries, RIMS Kyoto University
Kyoto, Japan
Slides\(\mathcal{N} = 2\) minimal models at unitary and beyond
June, 2018, International conference on Vertex Operator Algebras, Number Theory and Related Topics, A celebration of Geoff Mason's 70th Birthday, Sacramento State University
Sacramento, California, USAAdmissible level \(\mathfrak{osp}(1\vert 2)\) minimal models and their relaxed highest weight modules
May, 2018, Vertex algebras and related topics, University of Zagreb
Zagreb, CroatiaClassifying simple positive energy modules over vertex operator superalgebras
May, 2018, Mathematics Seminar, University of Melbourne
Melbourne, AustraliaYang-Baxter equations and symmetric groups
May, 2018, Mathematics - String Theory seminar, Kavli IPMU, University of Tokyo
Tokyo, JapanModule classification through free fields and symmetric functions
April, 2018, Conformal field theories and categorical structures beyond rationality, Woudschoten, Utrecht University
Zeist, NetherlandsConformal field theory from affine Lie algebras at fractional levels
February, 2018, Quantum Field Theory Seminar, University of Oxford
Oxford, UK
2017
Vertex algebra module theory made easy-ish
November, 2017, University of Glasgow
Glasgow, UKRepresentation theory in conformal field theories
November, 2017, Durham University
Durham, UK
SlidesClassifying positive energy modules in conformal field theory
September, 2017, Shanks Workshop: Subfactors and Applications, Vanderbilt University
Nashville, Tennessee, USA
SlidesAffine vertex operator superalgebras at admissible levels
June, 2017, Representation Theory XV
Dubrovnik, Croatia
SlidesWhat to expect from logarithmic conformal field theory
June, 2017, Operator algebras: subfactors and their applications, Isaac Newton Institute
Cambridge, UK
Slides | RecordingFusion by hand: The NGK algorithm
June, 2017, Tensor Categories and Field Theory
Melbourne, AustraliaYang-Baxter equations and the symmetric groups
May, 2017, University of Melbourne
Melbourne, Australia
SlidesModule classification in conformal field theory through symmetric polynomials
May, 2017, King's College London
London, UK
SlidesWhat to expect from logarithmic conformal field theory
April, 2017, Quantum Field Theory: Concepts, Constructions & Curved Spacetimes
York, UK
Slides
2016
Universal vertex algebras and free field realisations
March, 2016, MS Seminar (Mathematics - String Theory), Kavli IPMU, University of Tokyo
Tokyo, Japan
SlidesSymmetric functions and their relation to free field vertex algebras
March, 2016, AMS Sectional Meeting
Stony Brook, New York, USA
SlidesThe rationality of the \(\mathcal{N}=1\) minimal model vertex algebra and its connection to symmetric functions
March, 2016, Mathematics Seminar, Rutgers University
New Brunswick, New Jersey, USAUniversal vertex algebras and free field realisations
March, 2016, Mathematics Seminar, Notre Dame University
South Bend, Indiana, USA
SlidesThe rationality of N=1 minimal models through symmetric polynomials
February, 2016, BIRS Workshop: Vertex Algebras and Quantum Groups
Banff, Canada
RecordingSymmetric functions and their relation to free field vertex algebras
February, 2016, Mathematics Seminar, University of Alberta
Edmonton, Canada
2015
Minimal models from free fields
December, 2015, ANZAMP Meeting 2015, University of Newcastle
Newcastle, Australia
SlidesClassifying simple modules at minimal model central charges through symmetric polynomials
November, 2015, University of Queensland
Brisbane, Australia
SlidesThe Verlinde formula in logarithmic conformal field theory
September, 2015, MS Seminar (Mathematics - String Theory), Kavli IPMU, University of Tokyo
Tokyo, Japan
SlidesSymmetric polynomials and modules over affine \(\mathfrak{sl}(2)\) at admissible level
August, 2015, Conference in Honor of J. Lepowsy and R. Wilson on Lie Algebras, Vertex Operator Algebras, and Related Topics, University of Notre Dame
South Bend, Indiana, USA
SlidesTwo-dimensional conformal field theory with affine Lie algebra symmetry
April, 2015, Symmetries and Spinors Interactions between Geometry and Physics, University of Adelaide
Adelaide, Australia
SlidesSymmetric polynomials and their relation to conformal field theory
March, 2015, Australian National University
Canberra, Australia
Slides
2014
From free field theory to symmetric polynomials
December, 2014, Australia New Zealand Mathematics Convention 2014, University of Melbourne
Melbourne, Australia
SlidesJack symmetric polynomials and their connection to the Lie algebra of infinitesimal conformal transformations
October, 2014, Mathematics seminar, University of Queensland
Brisbane, Australia
SlidesConformal symmetry in physics
October, 2014, Colloquium, University of Queensland
Brisbane, AustraliaFrom free field theory to symmetric polynomials
June, 2014, String-Math 2014, University of Alberta
Edmonton, Canada
SlidesSymmetric polynomials in free field theories
June, 2014, Theoretical physics seminar, Laval University
Quebec City, Canada
SlidesSymmetric polynomials in free field VOAs
June, 2014, University of Montreal
Montreal, Canada
SlidesSymmetric polynomials in free field VOAs
May, 2014, Mathematics seminar, Rutgers University
New Brunswick, New Jersey, USAConformal symmetry in physics
May, 2014, Colloquium, California State University, Chico
Chico, California, USA
SlidesA working Verlinde formula for logarithmic CFT
April, 2014, MS Seminar (Mathematics - String Theory), Kavli IPMU, University of Tokyo
Tokyo, JapanRational logarithmic extensions of the minimal models and their simple modules
March, 2014, Modern Trends in TQFT, Erwin Schrödinger Institute
Vienna, Austria
SlidesA working Verlinde formula for logarithmic CFT
March, 2014, Technical University of Vienna
Vienna, Austria
Slides
2013
On the extended \(W\)-algebra of type \(\mathfrak{sl}(2)\) at positive rational level
October, 2013, Mathematics Seminar, Simons Center for Geometry and Physics, Stony Brook
Stony Brook, New York, USAOn the extended \(W\)-algebra of type \(\mathfrak{sl}(2)\) at positive rational level
October, 2013, Mathematics Seminar, University at Albany, SUNY
Albany, New York, USAOn the extended \(W\)-algebra of type \(\mathfrak{sl}(2)\) at positive rational level
October, 2013, Mathematics Seminar, The University of Alberta
Edmonton, Canada
SlidesOn the extended \(W\)-algebra of type \(\mathfrak{sl}(2)\) at positive rational level, II
August, 2013, String theory, integrable systems and representation theory, RIMS Symposium, The University of Kyoto
Kyoto, Japan
SlidesOn the extended \(W\)-algebra of type \(\mathfrak{sl}(2)\) at positive rational level
March, 2013, Infinite Analysis Seminar, The University of Tokyo
Tokyo, Japan
2012
\(M_{p_+,p_-}\) the extended \(W\)-algebra of \(\mathfrak{sl}(2)\) type at rational level
December, 2012, Conformal Field Theory and Moonshine Trimester, Hausdorff Research Institute for Mathematics, Bonn
Bonn, GermanyUnderstanding logarithmic CFT
July, 2012, String Math 20212, Hausdorff Center for Mathematics, Bonn
Bonn, GermanyLogarithmic versus non-logarithmic CFT
March, 2012, Australian National University, Department of Theoretical Physics
Canberra, Australia
2011
Vertex operator algebras for logarithmic CFT
December, 2011, Academia Sinica, Taipei
Taipei, Taiwan
Slides