# 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, combining motivation and intuition from the former with powerful analytical tools from the latter to get a better understanding of both.

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

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

School of Mathematics and Statistics

University of Melbourne, VIC 3010

Australia

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 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 unofficially by André Henriques.

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

Last update: 5 Feb ’19

My work revolves around the following topics:

**Quantum integrability**, in particular in the contexts of- Exactly solvable
**long-range**quantum**spin chains**, and - Classical statistical-mechanical
**lattice models**; **Quantum algebra**, especially the*q*-deformed and (Felder’s) elliptic cases;**Diagrammatic methods**in algebra;**Orthogonal polynomials**, which have recently started to appear in my work;- Physics in
**two dimensions**, where “two” may be written as 1+1 or 2+0.

More broadly I am interested in **mathematical physics**: the interplay between mathematics and theoretical physics, for example in quantum field theory, both ordinary and (especially *N*=2) supersymmetric. In fact, my interest in quantum integrability originates in the work of Nekrasov and Shatashvili: once upon a time I thought I was a high-energy theorist, see also my education, and especially my master’s 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: 5 Feb ’19

Below you can find an overview of my publications.

As you can see, so far I have published work together with Gerard Barkema, Rembert Duine, Wellington Galleas and Rick Keesman.

See also my profiles at **arXiv**, **Google scholar**, INSPIRE and ORCID.

## 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 - W Galleas and JL,
*Differential approach to on-shell scalar products in six-vertex models*, arXiv:1505.06870

## 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 my CV.

Last update: 15 Nov ’18

Here is an overview of my upcoming and past presentations.

See also my pedagogical experience, other activities I have been involved with, and a list with all events that I have participated in.

## Upcoming

- Talk at
*Elliptic integrable systems, special functions and quantum field theory*, Nordita, Stockholm (1620 June ’19)*–* - Talk at
*Virginia Integrable Probability Summer School 2019*, Charlottesville VA (7 June ’19)

## Recent

*The q-deformed Haldane*Joint pure maths and maths physics seminar, UQ Brisbane (17 May ’19)*–*Shastry spin chain: from the affine Hecke algebra, via ‘freezing’, to exact eigenvectors

Math phys seminar, U Melbourne (30 Apr ’19)*An exactly solvable long-range spin chain: the q-deformed Haldane*ANZAMP Annual Meeting 2019, Merimbula, NSW (5 Feb ’19) [slides]*–Shastry model*

## Longer ago

*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*

Math phys & stat mech 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]

GPP 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 probablility 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]*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: 20 May ’19

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

## At Chalmers (as a postdoc)

- Fall 2016–present: co-supervising
**Linnea Hietala**, see also here. - Spring 2017:
**Quantum and classical particle systems**, together with Jakob Björnberg

## At 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 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

## At Utrecht U (as a student)

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: 15 Nov ’18