# Home page

I’m a research fellow in mathematical physics at the University of Melbourne. I work on **quantum integrability** somewhere in between theoretical physics and mathematics. For me this means combining motivation, interpretation and intuition from the former with the powerful analytical techniques, deep structural understanding and elegance from the latter in order to push the boundaries of both.

On this website you can read about my research interests, publications, past and upcoming presentations, teaching and supervision and more.

You can **reach me** at jules⊗l⊕unimelb⊗edu⊗au or

School of Mathematics and Statistics

University of Melbourne, VIC 3010

Australia

I am the co-supervisor of Paul Zinn-Justin’s PhD student Ajeeth Gunna. Before moving down under, I was a postdoc in the group of Hjalmar Rosengren at the department of mathematics of Chalmers and the University of Gothenburg. I am also the co-supervisor of Linnea Hietala, see also here.

Prior to that, I was a PhD candidate at the Institute for Theoretical Physics of Utrecht University, supervised by Gleb Arutyunov and informally cosupervised by André Henriques.

See also my profiles on **StackExchange** and **Google scholar** or my **CV**.

Last update: 1 Oct ’20

My research focusses on **quantum integrability **in the contexts of

- Quantum
**spin chains**with**long-range**interactions (Heisenberg, Inozemtsev, Haldane–Shastry), **Quantum many-body systems**(Calogero–Sutherland, Ruijsenaars),- Classical statistical-mechanical
**lattice models**(six-vertex, elliptic solid-on-solid),

as well as the associated

**Quantum algebra**(quantum groups, affine Hecke algebras),**Diagrammatic methods**(a picture is worth a thousand words), and**Orthogonal polynomials**(Jack, Macdonald).

More broadly I am interested in **mathematical physics**: the interplay between mathematics and theoretical physics. This includes quantum field theory, both ordinary and supersymmetric (I like *N*=2); in fact, that is where my interest in quantum integrability started: see my MSc thesis for theoretical physics.

See also the **events** that I have participated in or check out my questions and answers on **MathOverflow**, **Mathematica.SE** and other StackExchange sites.

Last update: 18 Oct ’20

Below you can find an overview of my publications. See also my profiles at **arXiv**, **Google scholar**, INSPIRE and ORCID.

As you can see, so far I have joint publications with Gerard Barkema, Rembert Duine, Wellington Galleas, Rick Keesman (2x), Rob Klabbers, Yuan Miao, Vincent Pasquier (2x) and Didina Serban.

### 2020

- Y Miao, JL and V Pasquier,
*On the Q operator and the spectrum of the XXZ model at root of unity*, arXiv:2012.10224 - R Klabbers and JL,
*How coordinate Bethe ansatz works for Inozemtsev model*, arXiv:2009.14513 - JL, V Pasquier and D Serban,
*Spin-Ruijsenaars, q-deformed Haldane-Shastry and Macdonald polynomials*, arXiv:2004.13210

### 2018

- JL,
*The functional method for the domain-wall partition function*, SIGMA**14**(2018) 064, arXiv:1801.09635 - JL,
*Resurrecting the partially isotropic Haldane–Shastry model*, Phys Rev B**97**(2018) 214416, arXiv:1801.05728

### 2017

- R Keesman and JL,
*A numerical study of the F-model with domain-wall boundaries*, Phys Rev E**95**(2017) 052117, arXiv:1702.05474

### 2016

- JL,
*On elliptic quantum integrability: vertex models, solid-on-solid models and spin chains*, PhD thesis (2016) - R Keesman, JL, R A Duine and G T Barkema,
*Finite-size scaling at infinite-order phase transitions*, J Stat Mech: Theor Exp**2016**(2016) 093201, arXiv:1605.08876

### 2015

- JL,
*Integral formula for elliptic SOS models with domain walls and a reflecting end*, Nucl Phys B**901**(2015) 556, arXiv:1510.00342

### 2014

- JL,
*A pedagogical introduction to quantum integrability, with a view towards theoretical high-energy physics*, PoS**Modave2014**(2014) 001, arXiv:1501.06805 - W Galleas and JL,
*Reflection algebra and functional equations*, Nucl Phys B**886**(2014) 1003, arXiv:1405.4281

### Earlier

My BSc and MSc theses can be found at CV.

Last update: 1 Apr ’21

Below you can find an overview of my upcoming and past presentations, in antichronological order. See also my pedagogical experience, other activities I have been involved with, and a list with all events that I have participated in.

### Upcoming

*Recent advances for integrable long-range spin chains*

Pure math seminar, U NSW (14 Jun ’21) [zoom]

Mathematical physics seminar, U Melbourne (18 May ’21)*Schur*(~ Section 12.3 of Chari*–*Weyl duality for Yangians and quantum affine algebras*–*Pressley)

Quantum algebra reading group, Nordita (weekly, 24 March – … ’21) [zoom]

### Recent

*Recent advances for integrable long-range spin chains*Student workshop on integrability, online (26 Apr ’21) [zoom, slides]

Condensed matter theory seminar, U of Amsterdam (6 Apr ’21) [zoom, slides]

Pure mathematics seminar, U Queensland (17 Feb ’21) [slides]

Mathematical physics session, AustMS (9 Dec ’20) [zoom, slides]*Macdonald operators*(~ Section VI.3 of Macdonald)

Macdonald reading group, U Melbourne (weekly, Feb 8–15 ’21) [zoom, notes part one part two]*An invitation to spin chains and quantum integrability*

Three W’s seminar, KIAS, Korea (9 Nov ’20) [zoom, slides]*How coordinate Bethe ansatz works for Inozemtsev model*

New Connections in Integrable Systems, U Queensland (30 Sep ’20) [zoom, slides, video]*Spin-Ruijsenaars, q-deformed Haldane*Nordita integrability journal club (16 and 23 June ’20) [zoom, slides]*–*Shastry and Macdonald polynomials

Analysis and Probability seminar, Chalmers (19 May ’20) [zoom]

Seminar of the Edinburgh mathematical physics group (13 May ’20) [zoom]*A fresh look at Inozemtsev’s elliptic spin chain*

Baxter 2020: Frontiers in Integrability, Australian National U, Canberra (12 Feb ’20) [slides]*The q-deformed Haldane*New trends in integrable systems, Osaka City U, Japan (18 Sep ’19) [slides]*–*Shastry spin chain: from the affine Hecke algebra, via ‘freezing’, to exact eigenvectors

Integrable systems seminar, U Leeds, UK (13 Sep ’19)

Elliptic integrable systems, special functions and quantum field theory, Nordita, Stockholm (16 June ’19)

Joint pure maths and mathematical physics seminar, UQ Brisbane (17 May ’19)

Math phys seminar, U Melbourne (30 Apr ’19)

### Longer ago

*An exactly solvable long-range spin chain: the q-deformed Haldane*Virginia Integrable Probability Summer School 2019, U Virginia, Charlottesville VA (7 June ’19)*–Shastry model*

ANZAMP Annual Meeting 2019, Merimbula, NSW (5 Feb ’19) [slides]*An update on the q-deformed Haldane–Shastry model*Mathematical physics seminar, IPhT CEA Saclay (17 Sep ’18) [video]

*The q-analogue of the Haldane–Shastry spin chain*

Theoretical physics seminar, Trinity College Dublin (10 July ’18)

Correlation functions in exactly solvable models, Nordita, Stockholm (5 June ’18)*Quantum spin chains: the quantum-integrable perspective*

and*What is a quantum group (and why care)?*

Workshop on probabilistic approaches to quantum spin systems, Gothenburg (17 and 20 Apr ’18)*Resurrecting the q-analogue of the Haldane–Shastry spin chain*

Mathematical physics seminar, U Melbourne (27 Mar ’18) [slides]

Strings, integrability and beyond, IPhT CEA Saclay (14 Feb ’18)

String theory seminar, DESY Hamburg (30 Jan ’18)

Poster session, Young Researchers Integrability School and Workshop, Monte Verità, Ascona (7 Jan ’18) [poster], awarded a honourable mention for poster contribution*Resurrecting the partially isotropic Haldane–Shastry model*

Condensed matter theory seminar, U of Amsterdam (20 Dec ’17)

Group of Prof Essler, Condensed matter theory, Oxford U (7 Dec ’17)

Strings, cft & integrability seminar, ETH Zürich (14 Nov ’17)*The structure of the temperate region of the F-model with domain-wall boundaries*

Student session, Exact methods in low dimensional statistical physics, Cargèse (29 July ’17) [slides]

Geometry, physics and probability seminar, U C Louvain, Louvain-la-Neuve (20 Apr ’17) [blackboard + slides]

KTH/Nordita/SU seminar in theoretical physics, Stockholm (8 Feb ’17)*The constructive method for the elliptic solid-on-solid model with domain walls and a reflecting end*

Poster session, Elliptic hypergeometric functions in combinatorics, integrable systems and physics, ESI Vienna (20 Mar ’17) [poster]*Constructive method for the domain-wall partition function*

Analysis and probability seminar, Chalmers, Gothenburg (13 Dec ’16)

Student session, Les Houches Summer School on Integrability, Les Houches (22 June ’16) [video]*On elliptic quantum integrability: vertex models, solid-on-solid models and spin chains*

PhD defense, Utrecht U (1 June ’16)

PhD thesis talk, Institute for Theoretical Physics, Utrecht (30 May ’16) [slides]*Functional equations for elliptic SOS models with domain walls and a reflecting end*

Analysis and probablility seminar, Chalmers, Gothenburg (12 Nov ’15) [slides]

Representation theory seminar, U of Amsterdam (16 Oct ’15)

DESY Theory Workshop, DESY Hamburg (30 Sep ’15) [slides]*Differential approach to on-shell scalar products*

Poster session, IGST, Imperial College London, UK (July ’15)*Ice: an introduction to the six-vertex model*

Student seminar, NIKHEF theory meeting, Amsterdam (26 June ’15)

PLaneT seminar, Institute for Theoretical Physics, Utrecht U (23 June ’15)*Functional equations from the reflection algebra*

Poster session, Trends in theory, Dalfsen (29 May ’15)

Poster session, IGST, DESY Hamburg, and Summer school on quantum groups and integrability, U Hamburg (July ’14) [poster]*Kramers–Wannier duality for a two-dimensional square lattice*

Advanced graduate seminar, Utrecht U (7 and 31 Mar ’14)*Algebraic aspects of the Berezinian*

MSc thesis talk, Mathematical Institute, Utrecht U (14 Sep ’12)*The Bethe/gauge correspondence: a mysterious link between quantum integrability and supersymmetric gauge theories*

MSc thesis talk, Institute for Theoretical Physics, Utrecht U (26 June ’12)

Last update: 27 Apr ’21

Here is a description of my pedagogical experience. See also these other activities that I have been involved in.

### Melbourne

For simplicity I keep using the seasons of the Northern hemisphere.

- Spring 2020–present: co-supervising Paul Zinn-Justin’s PhD student Ajeeth Gunna
- Fall 2019: assisting the MSc course
*Exactly Solvable Models*taught by Paul Zinn-Justin - Spring 2019: teaching assistant for
*Schur functions and Schur processes*, taught by Ole Warnaar, and*Quantum integrability and symmetric polynomials*taught by Paul Zinn-Justin at the Virginia Integrable Probability Summer School 2019

### Chalmers

- Fall 2016–present: co-supervising Hjalmar Rosengren’s PhD student
**Linnea Hietala**, see also here - Spring 2017:
**Quantum and classical particle systems**, together with Jakob Björnberg

### Utrecht U

As a PhD candidate

- Spring 2014–winter 2015:
**Seminar on mathematical aspects of QFT**, organised together with PhD candidates from the Mathematical Institute at Utrecht U - Summer 2014:
**Introduction to quantum integrability**at the Modave summer school in mathematical physics, Modave (summer 2014) [**lecture notes**] - Spring 2014:
**Introduction to higher-spin gauge theory**, taught by Kramers Professor Mikhail Vasiliev from the Lebedev Physical Institute [**lecture notes**] - Spring 2014:
**Advanced graduate seminar**, organised by Marcos Crichigno, on dualities and emergent gauge symmetry in condensed matter - Fall 2012–Fall 2014: assisted Gleb Arutyunov in supervising MSc thesis in theoretical physics:

R Klabbers,*Inozemtsev’s elliptic spin chains: asymptotic Bethe ansatz and thermodynamics*(2014)

R J Rodger,*A pedagogical introduction to the AGT conjecture*(2013) - Fall 2013:
**Seminar on quantum-integrable models**[mirror], organised together with André Henriques and Gleb Arutyunov [comparison of notations in our references] - Spring 2013:
**Field theory in particle physics**, taught by Bernard de Wit and Eric Laenen

During my master’s studies I assisted various Bachelor courses in physics and mathematics. I also taught at SSL in Leiden, preparing high-school students for their final exams in mathematics.

Last update: 1 Oct ’20