Adrien Hardy

Mathematician | Quantitative Researcher at QRT | Maître de conférences at Université de Lille.

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Here I share my research publications, some teaching resources, and a few thoughts on (applied) mathematics more broadly.

About me: I'm Quantitative Research Director at Qube Research and Technologies, an algorithmic trading investement fund. I am on leave from my academic position (Maître de conférences, i.e., Associate professor) from the department of Mathematics at Université de Lille, France.

My academic research interests lie principally in understanding large random interacting particle systems, including random matrix models, determinantal point processes, or Gibbs measures such as the Coulomb gas. More recently, I became interested in using such models for applications (numerical integration, machine learning & AI, signal processing, telecomunications, finance...).

I was member of the INRIA team PARADYSE, and the ERC funded project BlackJack led by Rémi Bardenet.

Zeros of a spherical Gaussian analytic function, taken from Bardenet-Hardy 2019.

Academic research

Academic research publications :

See also: Google Scholar | MathSciNet | ArXiv.

From point processes to quantum optics and back
with Rémi Bardenet, Alexandre Feller, Jérémie Bouttier, Pascal Degiovanni, Adam Rançon, Benjamin Roussel, Grégory Schehr, Christophe I. Westbrook, Preprint (2022) [arXiv]
CLT for circular beta-Ensembles at high temperature
with Gaultier Lambert. Journal of Functional Analysis (2020) [arXiv , JFA]
Mutual information of wireless channels and block-Jacobi ergodic operators
with Walid Hachem, Shlomo Shamai. IEEE Transactions on Information Theory (2019) [arXiv, I3EIT]
DLR equations and rigidity for the Sine-beta process
with David Dereudre, Thomas Leblé, Mylène Maïda. Communications on Pure and Applied Mathematics (2020) [arXiv , CPAM]
Time-frequency transforms of white noises and Gaussian analytic functions
with Rémi Bardenet. Applied and Computational Harmonic Analysis (2019) [arXiv, ACHA]
Energy of the Coulomb gas on the sphere at low temperature
with Carlos Beltrán. Archive for Rational Mechanics and Analysis (2018) [arXiv, ARMA]
Polynomial ensembles and recurrence coefficients
Constructive Approximation (2018) [arXiv, CA]
Concentration for Coulomb gases and Coulomb transport inequalities
with Djalil Chafaï, Mylène Maïda. Journal of Functional Analysis (2018) [arXiv, JFA]
Monte Carlo with determinantal point processes
with Rémi Bardenet. Annals of Applied Probability (2019) [arXiv, AAP]
A survey on the eigenvalues local behavior of large complex correlated Wishart matrices
with Walid Hachem, Jamal Najim. ESAIM: Proceedings and surveys (2015) [arXiv, ESAIM]
Large complex correlated Wishart matrices: The Pearcey kernel and expansion at the hard edge
with Walid Hachem, Jamal Najim. Electronic Journal of Probability (2016) [arXiv, EJP]
Large complex correlated Wishart matrices: Fluctuations and asymptotic independence at the edges
with Walid Hachem, Jamal Najim. Annals of Probability (2016) [arXiv, AOP]
Average characteristic polynomials of determinantal point processes
Annales de l'Institut Henri Poincaré - Probabilités et Statistiques (2015) [arXiv, AIHP]
Large deviations for a non-centered Wishart matrix
with Arno Kuijlaars. Random Matrices: Theory and Applications (2013) [arXiv, RMTA]
A note on large deviations for 2D Coulomb gas with weakly confining potential
Electronic Communications in Probability (2012) [arXiv, ECP]
Weakly admissible vector equilibrium problems
with Arno Kuijlaars. Journal of Approximation Theory (2012) [arXiv, JAT]

Conference proceedings, other publications and notes:

A correspondence between zeros of time-frequency transforms and Gaussian analytic functions
with Rémi Bardenet, Pierre Chainais, Julien Flamant. 13th International conference on sampling theory and applications, SampTA 2019, Aug 2019, Bordeaux, France (2018) [HAL]
Processus ponctuels déterminantaux
with Mylène Maïda. Gazette des Mathématiciens (2018) [SMF]
An english version has also been published in the Newsletter of the EMS [EMS]
From random matrices to Monte Carlo integration via Gaussian quadrature
with Rémi Bardenet. IEEE Statistical Signal processing workshop, 2018, Freiburg, Germany (2018) [HAL]
A note gathering some thoughts on the most used probability result in applications that is still confusing to me: the law of large numbers.

PhD students:

Lucas Morisset (2024- ), with Alain Durmus and Emmanuel Gobet at Ecole Polytechnique + QRT.
Mohamed Slim Kammoun (2017-2020), with Mylène Maïda at Université de Lille.

Teaching material

Some academic lectures I gave (mainly in french):

(2025-) Machine learning for quantitative trading, Portfolio Management Program (Univ. Zürich & ETH).
(2019-2020) Concentration de la mesure et applications, M2 Recherche (Math), Cours + TD.
(2019-2020) Chaînes de Markov et applications, M2 Ingénierie Statistique et Numérique (Math), Cours + TP Python.
(2019-2020) Probabilités discrètes, L2 (Math), TD.
(2018-2020) Probabilité, modèles et applications, M1 Ingénierie mathématique (Math), Cours + TD.
(2016-2020) Séries temporelles, M1 Mathématiques pour la finance (Math), Cours + TP Python + TP R (older).
(2016-2018) Introduction to statistics, M1 Biomedical engineering (Centrale Lille), cours + TP R.
(2016-2018) Introduction aux processus ponctuels déterminantaux, M2 Recherche (Math), Cours + TD.
(2015-2018) Traitement informatique de la statistique des données, M1 Ingénierie mathématique (Math), cours + TP R & SAS.
(2015-2017) Mathématiques de base, L1 SVTE parcours aménagé (Biologie), cours + TD.
(2015-2016) Mathématiques (analyse, algèbre, probabilités), Telecom Lille, TD.

Curriculum

Since October 2023, I moved to the brand new QRT office in Zürich, in quality of Quantitative Research Director.

In November 2020, I obtained my "Habilitation à diriger des recherches" (HDR) from the University of Lille; the manuscript can be found here.

Since September 2020, I am on leave (en disponibilité) to work as a Quantitative Researcher at QRT (Paris).

Since September 2015, I am Maître de conférences (~Associate professor) in the Laboratoire Paul Painlevé, which is the mathematic department of the University of Lille.

During 2013-2015, I had a postdoctoral position at the Royal Institute of Technology (KTH) in the research team of Kurt Johansson.

In June 2013, I obtained a joint PhD degree (see the thesis) from KU Leuven, supervised by Arno Kuijlaars, and the Institut de Mathématiques de Toulouse, supervised by Michel Ledoux.

Before that, I studied in the Magistère de mathématiques de Strasbourg, including a Bachelor thesis with Janos Polonyi on quantum physics' axioms, a Magistère thesis with Jean-Bernard Zuber on quantum integrable systems (internship at the Laboratoire de Physique Théorique et Hautes Energies de Jussieu), and a Master thesis with Pierre van Moerbeke on random matrices and tillings (Erasmus exchange program with the Université Catholique de Louvain).

Miscellaneous

Recommended science resources:

Libres pensées d'un mathématicien ordinaire (Djalil Chafaï's math blog)

What's new (Terence Tao's math blog)

Quanta Magazine (general science blog from the Simons Foundation)

Science étonnante (general science Youtube channel by David Louapre)

Recommended economics and finance resources:

Freakonometrics (Arthur Charpentier's blog on actuarial science, statistics, and more)

Heu?reka (economy & finance Youtube channel by Gilles Mitteau)

Money stuff (Matt Levine's newsletter at Bloomberg opinion)

A mathematician's survival kit:

Wikipedia

ArXiv (open-access repository of e-prints mainly funded by the Simons Foundation)

Math Overflow (research level math questions)

Math Stackexchange (student level math questions)

Stack Overflow (programming questions)

Digital Library of Mathematical Functions (when looking for a special function)

The On-Line Encyclopedia of Integer Sequences (when looking for a special sequence)

And of course, ChatGPT, mostly educated by the fine literature listed above. Obviously.