Jesper Jacobsen is a Professor of Theoretical Physics at École Normale Supérieure and Université Pierre et Marie Curie, Paris. He works in statistical physics and conformal field theory and was awarded the Société Française de Physique Paul Langevin Prize in 2016.

He was also a winner of the Journal of Physics A: Mathematical and Theoretical Best Paper prize in 2016 and we are very pleased that he has joined the Editorial Board of the journal for 2017. We take the opportunity to find out more about his career, motivations and expectations for the future.

**Could you provide us with a brief summary of your career so far? **

Having undertaken my undergraduate studies in physics and mathematics at Aarhus University (Denmark), I embarked on a Ph.D. with Hans Fogedby at the same place. However, I soon became interested in conformal field theory (CFT) and was fortunate to get the opportunity to study under the guidance of John Cardy at Oxford University for the last two years of my Ph.D. This gave rise to a detailed study of the effects of quenched bond disorder on first-order phase transitions. I also spent three months at a workshop at the Kavli Institute (UCSB) where I started a collaboration with Jané Kondev, then a young postdoc, on the CFT of fully packed loop models. This set of subjects has remained an active part of my research in the following years.

I subsequently spent a short (one-year) postdoc period at the Ecole Normale in Paris, working with Bernard Derrida on a problem of non-Hermitean quantum mechanics. I also started independent collaborations with a number of other people, including Jean Vannimenus and Vladimir Dotsenko.

I was then appointed an assistant professor at the Université Paris-Sud in Orsay where I remained for more than eight years, until I was promoted to full professor and returned to the Laboratory of Theoretical Physics at the Ecole Normale. Those were exciting years during which I broadened my research interests to include integrability and graph polynomials, in collaborations with Paul Zinn-Justin and Alan Sokal.

However, the most fruitful encounter was with Hubert Saleur at a summer school at Les Houches. He gradually became my closest collaborator, and until now we have written some forty joint publications and supervised half a dozen Ph.D. students. In the course of this extended collaboration my focus on CFT and integrable models shifted towards subtle boundary effects, and logarithmic and non-compact features.

**You have done a degree of work on exactly solvable models. What other research areas are of interest to you and what led you to this area of research? **

At least in theoretical physics, it is commonly admitted that a model is exactly solvable (or more precisely, exactly solved) if one can provide exact mathematical expressions for various quantities of interest, such as free energies, critical exponents or even correlation functions. This is, broadly speaking, the ocean where I have spent the most of my swimming time. One can obviously strengthen this criterion and require the results to be mathematically rigorous, or one can weaken it and content oneself with approximation methods or numerical simulations.

The first emphasis has led me to publish a real math paper, “Is the five-flow conjecture almost false?” (J. Combin. Theory B **103**, 532-565 (2013)), jointly with Jesús Salas, on a conjecture due to William Tutte about the roots of the flow polynomial on general graphs. Getting one referee to accept the title, despite of its obvious allusion to a well-known paper by Beraha and Kahane, was not the easiest part of this endeavour! The second emphasis has led me in various directions, notably to a graph polynomial method, developed with Christian Scullard, that has allowed for very precise determinations of percolation thresholds on various lattices. One paper in this series (J. Phys. A: Math. Theor. **47**, 135001 (2014)) earned me the JPhysA Best Paper Prize 2016, and I was interviewed by JPhys+ on that occasion.

**What kind of problems appeal to you?**

It should be clear from the above that I prefer problems for which definitive solutions can be provided. I like to think that once an exact solution of an interesting problem has been found, it will remain useful for many years to come. I also have a propensity to work on models that have somehow withstood the test of time, hence proving their importance. Also, I am especially fond of statistical models that can be interpreted geometrically. Finally, I rather like models which can not only be solved exactly but also studied “experimentally” on a computer, in particular if advanced algorithmic ideas can be applied. Maybe this last comment betrays my working methods…

**What are you currently working on? **

One subject that I am particularly interested in these days is to determine precisely all geometrical four-point correlation functions in the Fortuin-Kasteleyn random cluster model. Earlier work by Gesualdo Delfino and Jacopo Viti (J. Phys. A: Math. Theor. **44**, 032001 (2011)), that we generalised with Yacine Ikhlef and Hubert Saleur quite recently (Phys. Rev. Lett. **116**, 130601 (2016)), has shown that the three-point functions are related to the structure constant of an analytic continuation of quantum Liouville theory. The latter was originally introduced by Polyakov to describe the seemingly remote subject of two-dimensional quantum gravity. To fix the four-point functions of FK clusters, and hence the full dynamical content of the theory, we believe that this field theory should be combined with ideas coming from the representation theory of the affine Temperley-Lieb algebra. Furthermore, to address the most interesting special cases, such as bond percolation, logarithmic CFT will play an important role as well. We are currently in the process of combining all these elements.

**What do you consider to be the most significant problems to be addressed in your field? **

There is an urgent need to produce exact solutions of two-dimensional models with quenched disorder, such as the Chalker-Coddington model describing the plateaux transitions in the integer quantum Hall effect. I hope this will turn out to be possible in the foreseeable future.

**What would you say has been your career highlight/ biggest achievement to date?**

I leave that for others to decide. As for myself, I have found that the papers that I am most fond of, and that have cost me the greatest effort, are not always the ones that are the most well-known or best cited.

**What are the challenges facing researchers in mathematics and theoretical physics?**

Each field comes of course with its own scientific challenges. However, these days the greatest challenge to science in general comes from the surrounding society where the post-factual credo seems to have become the norm, at least in some significant parts of the world. It is important for our community to be able to convince policy makers and the general public that scientific research remains of vital importance for our society, even in fields that do not appear to have immediate practical applications.

**Where do you think your research will take you next? Are there any other fields you are interested in exploring?**

There is an element of unpredictability to research, in particular in theoretical physics. Although I could list enough problems to keep me occupied for the next two or three years, I am convinced that something completely unexpected will come up before the end of this year. This is one of the blessings being a researcher — and one of the curses when trying to write an honest grant application.

**Finally, do you have any advice for young researchers entering the field?**

Anybody who is tempted to offer advice to younger people should be aware of Karen Blixen’s words that “experience is bought dearly, offered for nothing, and then most often refused”. In my view, young people should trust their own motivation, choose the field that they find the most stimulating intellectually, and succeed in their own way. Hard work and plain stubbornness often helps a bit in achieving one’s goals. Sometimes a lot.

On behalf of Journal of Physics A I would like to thank Professor Jacobsen for his work as a board member and for taking the time to talk to us.

**Read more:**

- On the growth constant for square-lattice self-avoiding walks
*Q*-colourings of the triangular lattice: exact exponents and conformal field theory- Potts-model critical manifolds revisited
- Dilute oriented loop models
- Critical points of Potts and O(
*N*) models from eigenvalue identities in periodic Temperley–Lieb algebras - High-precision phase diagram of spin glasses from duality analysis with real-space renormalization and graph polynomials

This work is licensed under a Creative Commons Attribution 3.0 Unported License.

Author image owned by Jesper Lykke Jacobsen, used with permission.

Categories: Journal of Physics A: Mathematical and Theoretical, JPhys+