Andrew Kels

School of Mathematics

The University of New South Wales, Sydney

NSW 2052, Australia

a.kels@unsw.edu.au

I am currently a research fellow working with Wolfgang Schief at the University of New South Wales, Sydney, Australia. I previously worked at SISSA, Italy, The University of Tokyo, Japan, and The Technical University of Berlin, Germany.

My research interests are in the area of integrable systems, including lattice models of statistical mechanics, nonlinear difference and differential equations and their solutions, dynamical maps, special functions, and applications to quantum field theories.

My list of publications and preprints are included below. Preprints of all of my papers are also available on arXiv.

In Term 1 2025 I am lecturer for 1st year course MATH1031 Mathematics for Life Sciences.

Last year I organised a joint seminar series between UNSW and USYD on the topic of elliptic difference equations with Pieter Roffelsen. More details can be found at the seminar website. The seminars will continue this year, more details will be available shortly.

Preprints

Quasi-classical expansion of a hyperbolic solution to the star-star relation and multicomponent 5-point difference equations, arXiv:2412.21096 (2024)
The QV equation: Algorithmic derivation of Bäcklund transformations for lattice equations via decomposability, submitted (2024) (co-author: W.K. Schief)
Integrable systems on hexagonal lattices and consistency on polytopes with quadrilateral and hexagonal faces, arXiv:2205.02720 (2022)

Publications

Algebraic entropy for hex systems, Nonlinearity 37 125007 (2024) (co-authors: G. Gubbiotti and C-M. Viallet)
Two-component Yang-Baxter maps and star-triangle relations, Physica D 448 (2023) 133723
Discrete integrable equations on face-centered cubics: consistency and Lax pairs of corner equations, Proc. R. Soc. A 478: 20210892 (2022)
Algebraic entropy for face-centered quad equations, J. Phys. A: Math. Theor.: 54 (2021) 455201 (co-author: G.Gubbiotti)
Lax matrices for lattice equations which satisfy consistency-around-a-face-centered-cube, Nonlinearity 34 7064 (2021)
Entanglement of Two Disjoint Intervals in Conformal Field Theory and the 2D Coulomb Gas on a Lattice, Phys. Rev. Lett. 127 141605 (2021) (co-authors: T. Grava and E. Tonni)
Interaction-round-a-face and consistency-around-a-face-centered-cube, J. Math. Phys. 62(3): 033509 (2021)
Integrable quad equations derived from the quantum Yang-Baxter equation, Lett. Math. Phys. 110, 1477-1557 (2020)
Extended Z-invariance for integrable vector and face models and multi-component integrable quad equations, J. Stat. Phys. 176, 1375–1408 (2019)
Lens generalisation of tau-functions for the elliptic discrete Painlevé equation, Int. Mat. Res. Not. 2021, 754-765 (2019) (co-author: M. Yamazaki)
Lens elliptic gamma function solution of the Yang-Baxter equation at roots of unity, J. Stat. Mech. (2018) 023108 (co-author: M. Yamazaki)
Elliptic hypergeometric sum/integral transformations and supersymmetric lens index, SIGMA 14, (2018) 013 (co-author: M. Yamazaki)
Exactly solved models on planar graphs with vertices in Z3, J. Phys. A: Math. Theor.:50 (2017) 495202
The star-triangle relation, lens partition function, and hypergeometric sum/integrals, J. High Energ. Phys. (2017) 2017:40 (co-author: I. Gahramanov)
Quasi-classical expansion of the star-triangle relation and integrable systems on quad-graphs, J. Phys. A: Math. Theor.:49 (2016) 464001 (co-authors: V.V. Bazhanov and S.M. Sergeev)
New solutions of the star-triangle relation with discrete and continuous spin variables, J. Phys. A: Math. Theor.:48 (2015) 435201
A new solution of the star-triangle relation, J. Phys. A: Math. Theor.:47 (2014) 055203
Comment on star-star relations in statistical mechanics and elliptic gamma-function identities, J. Phys. A: Math. Theor.:46 (2013) 152001 (co-authors: V.V. Bazhanov and S.M. Sergeev)
The second epoch Molonglo Galactic Plane Survey: compact source catalogue, MNRAS: 382, 382-392 (2007) (co-authors: T. Murphy, T. Mauch, A. Green, R.W. Hunstead, B. Piestrzynska, P. Sztajer)

Workshop and conference presentations

Yang-Baxter equation and discrete integrable systems in the honeycomb lattice, The 11th Australian and New Zealand Association of Mathematical Physics (ANZAMP) meeting, Katoomba, Australia 2024. (slides)

Integrable lattice models of statistical mechanics and Lagrangian multiform theory, Lagrangian Multiform Theory and Pluri-Lagrangian Systems, Banff International Research Station, Hangzhou, China, Oct 2023. (slides)

Two-component Yang-Baxter maps, ISLAND VI, Isle of Skye, Scotland, June 2023. (slides)

Consistency for 5-point lattice equations, SIDE 14.2, University of Warsaw, Poland, June 2023. (slides)

Integrable models on lattices and dualities of supersymmetric indices, Dynamics of SCFTs and Special Functions, Simons Center for Geometry and Physics, Stony Brook, USA, April 2022. (slides)

16 new Yang-Baxter maps, The 65th Annual Meeting of the Australian Mathematical Society, University of Newcastle, Australia, December 2021. (slides)

New discrete integrable systems from Lagrangian functions, Integrable Systems Workshop 2020, The University of Sydney, Australia, December 2020. (slides)

New developments for integrability and the star-triangle relations, Baxter 2020: Frontiers in Integrability, The Australian National University, February 2020. (slides)

Yang-Baxter maps associated to discrete soliton equations and hypergeometric functions, The 8th Australian and New Zealand Association of Mathematical Physics (ANZAMP) meeting, Tweed Heads, Australia, February 2020. (slides)

A generalisation of tau-functions for the elliptic difference Painlevé equation of type E8, The 9th International Congress on Industrial and Applied Mathematics (ICIAM), Valencia, Spain, July 2019. (slides)

Discrete integrability from hypergeometric integrals, Elliptic Integrable Systems, Special Functions and Quantum Field Theory Workshop, Nordita, Sweden, June 2019. (slides)

Hypergeometric integrals, Yang-Baxter equations, and 3D-consistent equations, The 13th Symmetries and Integrability of Difference Equations (SIDE) Conference, Fukuoka, Japan, November 2018. (slides)

Yang-Baxter/3D-consistency correspondence, Asymptotic, Algebraic and Geometric Aspects of Integrable Systems Workshop, Tsinghua Sanya International Mathematics Forum, Sanya, China, April 2018. (slides)

Google Sites

Report abuse