Algorithmic number theory dates back to the dawn of mathematics
itself, cf. Eratosthenes's sieve to enumerate consecutive prime numbers.
With the
arrival of computers, previously unsolvable problems have come into reach,
which has boosted the development of more or less practical algorithms
for essentially all number theoretic problems. The field is now mature
enough for a more computer science driven approach, taking into account
the theoretical complexities and practical running times of the algorithms.

Concerning the lower level multiprecision arithmetic, folklore has asserted for a long time that asymptotically fast algorithms such as SchÃ¶nhage–Strassen multiplication are impractical; nowadays, however, they are used routinely. On a higher level, symbolic computation provides numerous asymptotically fast algorithms (such as for the simultaneous evaluation of a polynomial in many arguments or linear algebra on sparse matrices), which have only partially been exploited in computational number theory. Moreover, precise complexity analyses do not always exist, nor do sound studies to choose between different algorithms (an exponential algorithm may be preferable to a polynomial one for a large range of inputs); folklore cannot be trusted in a fast moving area such as computer science.

Another problem is the reliability of the computations; many number
theoretic algorithms err with a
small probability, depend on unknown constants or rely on a Riemann
hypothesis. The correctness of their output can either be ensured by a
special design of the algorithm itself (slowing it down) or by an a
posteriori verification. Ideally, the algorithm outputs a certificate,
providing an independent fast correctness proof. An example is integer
factorisation, where factors are hard to obtain but trivial to
check; primality proofs have initiated sophisticated generalisations.

One of the long term goals of the Lfant project team is to make an
inventory of the major number theoretic algorithms, with an emphasis on
algebraic number theory and arithmetic geometry, and to carry out
complexity analyses. So far, most of these algorithms have been designed
and tested over number fields of small degree and scale badly. A complexity
analysis should naturally lead to improvements by identifying bottlenecks,
systematically redesigning and incorporating modern
asymptotically fast methods.

Reliability of the developed algorithms is a second long term goal of our project team. Short of proving the Riemann hypothesis, this could be achieved through the design of specialised, slower algorithms not relying on any unproven assumptions. We would prefer, however, to augment the fastest unproven algorithms with the creation of independently verifiable certificates. Ideally, it should not take longer to check the certificate than to generate it.

All theoretical results are complemented by concrete reference
implementations in Pari/Gp, which allow to determine and tune
the thresholds where the asymptotic complexity kicks in and help
to evaluate practical performances on problem instances
provided by the research community.
Another important source for algorithmic problems treated
by the Lfant project team is modern
cryptology. Indeed, the security of all practically relevant public key
cryptosystems relies on the difficulty of some number theoretic problem;
on the other hand, implementing the systems and finding secure parameters
require efficient algorithmic solutions to number theoretic problems.

Modern number theory has been introduced in the second half of the 19th
century by Dedekind, Kummer, Kronecker, Weber and others, motivated by
Fermat's conjecture: There is no non-trivial solution in integers to the
equation

The solution requires to augment the integers by algebraic
numbers, that are roots of polynomials in number
field consists of the rationals to which have been added finitely
many algebraic numbers together with their sums, differences, products
and quotients. It turns out that actually one generator suffices, and
any number field algebraic integers, “numbers without denominators”,
that are roots of a monic polynomial. For instance, ring of integers of

Unfortunately, elements in ideals, subsets of principal, that is,
generated by one element, so that ideals and numbers are essentially
the same. In particular, the unique factorisation of ideals then
implies the unique factorisation of numbers. In general, this is not
the case, and the class groupclass number

Using ideals introduces the additional difficulty of having to deal
with fundamental units. The regulator

One of the main concerns of algorithmic algebraic number theory is to
explicitly compute these invariants (

The analytic class number formula links the invariants
generalised Riemann hypothesis
(GRH), which remains unproved even over the rationals, states that
any such

When

Algebraic curves over finite fields are used to build the currently
most competitive public key cryptosystems. Such a curve is given by
a bivariate equation elliptic curves of equation
hyperelliptic curves of
equation

The cryptosystem is implemented in an associated finite
abelian group, the Jacobianrational function field with subring function field of coordinate ring

The size of the Jacobian group, the main security parameter of the
cryptosystem, is given by an genus

The security of the cryptosystem requires more precisely that the
discrete logarithm problem (DLP) be difficult in the underlying
group; that is, given elements

For any integer Weil pairingTate-Lichtenbaum pairing, that is more difficult to define,
but more efficient to implement, has similar properties. From a
constructive point of view, the last few years have seen a wealth of
cryptosystems with attractive novel properties relying on pairings.

For a random curve, the parameter

Complex multiplication provides a link between number fields and
algebraic curves; for a concise introduction in the elliptic curve case,
see 60, for more background material,
59. In fact, for most curves CM field. The CM field
of an elliptic curve is an imaginary-quadratic field Hilbert class field

Algebraically, Galois if Galois groupabelian extension is a Galois extension with abelian Galois
group.

Analytically, in the elliptic case singular valuemodular function

The same theory can be used to develop algorithms that, given an
arbitrary curve over a finite field, compute its

A generalisation is provided by ray class fields; these are
still abelian, but allow for some well-controlled ramification. The tools
for explicitly constructing such class fields are similar to those used
for Hilbert class fields.

Being able to compute quickly and reliably algebraic invariants is an invaluable aid to mathematicians: It fosters new conjectures, and often shoots down the too optimistic ones. Moreover, a large body of theoretical results in algebraic number theory has an asymptotic nature and only applies for large enough inputs; mechanised computations (preferably producing independently verifiable certificates) are often necessary to finish proofs.

For instance,
many Diophantine problems reduce to a set of Thue equations of the form

Deeper invariants such as the Euclidean spectrum are related to more theoretical
concerns, e.g., determining new examples of principal, but not norm-Euclidean number
fields, but could also yield practical new algorithms: Even if a number field
has class number larger than 1 (in particular, it is not norm-Euclidean),
knowing the upper part of the spectrum should give a partial gcd
algorithm, succeeding for almost all pairs of elements of

Algorithms developed by the team are implemented in the free Pari/Gp system
for number theory maintained by K. Belabas (see §6.1 for
details). They will thus have a high impact on the worldwide number theory
community, for which Pari/Gp is a reference and the tool of choice.

Public key cryptology has become a major application domain for algorithmic
number theory. This is already true for the ubiquitous RSA system, but even
more so for cryptosystems relying on the discrete logarithm problem in algebraic
curves over finite fields.
For the same level of security, the latter require
smaller key lengths than RSA, which results in a gain of bandwidth and
(depending on the precise application) processing time. Especially in
environments that are constrained with respect to space and computing power
such as smrt cards and embedded devices, algebraic curve cryptography has become
the technology of choice. Most of the research topics of the Lfant team
detailed in §3 concern directly problems relevant for
curve-based cryptology: The difficulty of the discrete logarithm problem in
algebraic curves (§3.2) determines the security of the
corresponding cryptosystems. Complex multiplication, point counting and
isogenies (§3.3) provide, on one hand,
the tools needed to create secure instances of curves. On the other hand,
isogenies have been found to have direct cryptographic applications to hash
functions 58 and encryption 61. Pairings in algebraic
curves (§3.2) have proved to be a a rich source for novel
cryptographic primitives. Class groups of number fields (§3.1)
also enter the game as candidates for algebraic groups in which cryptosystems can
be implemented. However, breaking these systems by computing discrete logarithms
has proved to be easier than in algebraic curves; we intend to pursue this
cryptanalytic strand of research.

Apart from solving specific problems related to cryptology, number theoretic expertise is vital to provide cryptologic advice to industrial partners in joint projects. It is to be expected that continuing pervasiveness and ubiquity of very low power computing devices will render the need for algebraic curve cryptography more pressing in coming years.

B. Allombert has been awarded the Cristal medal of CNRS for outstanding
contributions to the advancement of knowledge and the excellence of French
research, as the main developer of the Pari/Gp computer algebra
system.1

I. Tucker has received the 2020 Prix Jeunes Talents France L'Oréal–UNESCO pour les femmes et la science.2

B. Wesolowski and his coauthors have been awarded the Best Paper Award at ASIACRYPT 2020 for their article 23.

I. Tucker has defended her doctoral thesis
Functional encryption and distributed signatures based on
projective hash functions, the benefit of class groups26.

Sudarshan Shinde has defended his doctoral thesis
Cryptographic applications of modular curves25.

The PARI Group released a new version of Pari/Gp (2.13) featuring many bug
fixes and optimizations, including a better MPQS integer factorization
engine, a complete rewrite of algebraic number theory modules to use
“compact units” representations throughout (represent algebraic numbers as
formal products of small Arb).

Arb has had two new releases, 2.18 and 2.19. These releases mainly
feature a large number of bug fixes and optimizations.

The year 2020 has seen the release 1.2 Hyacinthus orientalis
of GnuMpc.
The release features the new functions mpc_sum and
mpc_dot and several bug fixes, in particular to make functions
more robust if the user reduces the exponent range. It also contains the
tool mpcheck for easier comparison with computations by the
C library on standard precision floating-point numbers.

The year 2020 was marked by the covid crisis and its impact on society and its overall activity. The world of research was also greatly affected: Faculty members have seen their teaching load increase significantly; PhD students and post-docs have often had to deal with a worsening of their working conditions, as well as with reduced interactions with their supervisors and colleagues; most scientific collaborations have been greatly affected, with many international activities cancelled or postponed to dates still to be defined.

The Lfant team was able, however, to organise a physical Pari/Gp workshop
in Grenoble in January 2020, right before the pandemic struck, with videos
of some presentations made
available51, 49, 48, 50.

Apip , Another Pairing Implementation in PARI, is a library for computing standard and optimised variants of most cryptographic pairings.

The following pairings are available: Weil, Tate, ate and twisted ate, optimised versions (à la Vercauteren–Hess) of ate and twisted ate for selected curve families.

The following methods to compute the Miller part are implemented: standard Miller double-and-add method, standard Miller using a non-adjacent form, Boxall et al. version, Boxall et al. version using a non-adjacent form.

The final exponentiation part can be computed using one of the following variants: naive exponentiation, interleaved method, Avanzi–Mihailescu's method, Kato et al.'s method, Scott et al.'s method.

Part of the library has been included into Pari/Gp proper.

AVIsogenies is a Magma package for working with abelian varieties, with a particular emphasis on explicit isogeny computation.

Its prominent feature is the computation of (l,l)-isogenies between Jacobian varieties of genus-two hyperelliptic curves over finite fields of characteristic coprime to l, practical runs have used values of l in the hundreds.

It can also be used to compute endomorphism rings of abelian surfaces, and find complete addition laws on them.

FromLatticesToModularForms is a magma package which allows to

- span the isogeny class (of principally polarised abelian varieties) of a power of an elliptic curve by enumerating unimodular hermitian lattices - compute the abelian variety A corresponding to a given lattice by exhibiting a kernel and an isogeny from Eĝ to A - A is represented by its theta null point (of level 2 or 4) in such a way that we give an affine lift of the theta null point corresponding to the pushforward of the standard diagonal differential dx/y on Eĝ - in particular one can evaluate rational modular forms on A - in dimension 2 or 3 we also provide code to recognize when A is a Jacobian and if so to find the corresponding curve.

Following the article 32, Xavier Caruso and
Thibaut Verron implemented the PoTe and the VaPoTe
algorithm for computing Gröbner bases in Tate algebras; their
implementation is part of the standard distribution of SageMath
since version 9.1.

Xavier Caruso wrote a package on Ore polynomials, which has been accepted for inclusion in SageMath, version 9.2. Beyond basic operations, this implementation includes capabilities for working in the field of fractions of Ore algebras and an optimized factorization algorithm for skew polynomials over finite fields.

A code implementing the article 46
for spanning the isogeny class of products of elliptic curves and
computing modular forms (and related obstruction) on them is available
as a Magma package called FromLatticesToModularForm.

The paper 19 was the first paper for
the reproducibility pilot of the Journal of Number Theory.
The reproducibility archive is available at
https://

The security of pairing-based cryptography requires discrete logarithms in finite fields of degree larger than 1 to be difficult to compute. After having proposed several improvements which reduced the security of the proposed pairings in the literature, R. Barbulescu together with Sylvain Duquesne suggested in 2019 a model to evaluate the security of pairings 53. In a subsequent work Nadia El Mrabet pointed out that exotic pairings, not studied in the literature before might be interesting, and this led to a joint study with Loubna Ghammam and R. Barbulescu of over 200 curve families 27, providing very precise security estimates.

The presumed hardness of the discrete logarithm problem (DLP) in
finite fields (or other families of groups) is a foundation of classical public-key
cryptography. It has recently been discovered that the DLP is much
easier than previously believed in an important family: finite fields
of small characteristic. Algorithms of quasi-polynomial
complexity have been discovered. In 37,
R. Granger, T. Kleinjung, A. K. Lenstra, B. Wesolowski and J. Zumbrägel
demonstrate the practicality of these new methods through the
computation of a discrete logarithm in

In 21, G. Castagnos, D. Catalano,
F. Laguillaumie, F. Savasta and I. Tucker propose a new cryptographic
protocol to compute threshold EC-DSA signatures with two parties.
EC-DSA (Elliptic Curves Digital Signature Algorithm) is a widely
adopted standard for electronic signatures. For instance, it is used in the TLS
(Transport Layer Security) protocol and in many cryptocurrencies such
as Bitcoin.
Threshold Signatures allow

It has been known since the work of Shor in 1994 that a functional,
large-scale quantum computer would be able to break most classical
public-key cryptosystems deployed today. The cryptographic community
has since then investigated new families of post-quantum
cryptosystems, meant to resist the advance of quantum computing.
Lattice-based cryptography, one of the leading post-quantum
candidates, relies on the presumed hardness of certain computational
problems in euclidean lattices. There is strong confidence in the
hardness of these problems in general, but the use of algebraic
lattices (necessary for efficiency or advanced functionalities) opens
new angles of attack. In 14, R. Cramer,
L. Ducas and B. Wesolowski expose an unexpected quantum hardness
gap between generic lattices and an important family of algebraic lattices,
so-called cyclotomic ideal lattices. This journal article
expands upon preliminary results presented at Eurocrypt 2017.

An ideal lattice is essentially an ideal in the ring on integers of a
number field that is stable by multiplication, with a geometry induced
by the Minkowski embedding. Fixing a number field, the space of all
ideal lattices, up to isometry, is naturally an abelian group called the
Arakelov class group. In 22, K. De Boer,
L. Ducas, A. Pellet-Mary and B. Wesolowski study the relative hardness
of computational problems within the Arakelov class group. More precisely,
it is shown that the worst-case of the Shortest Vector Problem
(Ideal-SVP) reduces to
its average-case (up to an approximation factor that depends on the field).
In other words, “random” instances of Ideal-SVP are as hard as the hardest
ones, an essential property for building cryptography.
This result assumes the Riemann Hypothesis for Hecke

Isogeny-based cryptography is another popular candidate for
post-quantum cryptography. Their main asset: they allow for smaller keys
than other post-quantum candidates, and more confident key-size selection.
For a while, is was unknown whether one could build an isogeny-based
digital signature scheme (besides the immediate but inefficient construction
from the Jao–De Feo–Plût identification protocol). In 23,
L. De Feo, D. Kohel, A. Leroux, C. Petit and B. Wesolowski introduce the
signature scheme SQISign. Its most notable feature is its compactness:
the signature and public key sizes combined are an order of magnitude smaller
than all other post-quantum signature schemes. It is however less efficient than
its competitors: on a modern workstation, the proof-of-concept C implementation
takes 2.5s for signing, and 50ms for verification.

In 20, B. Wesolowski constructs the first practical verifiable delay function (VDF). A VDF is a function whose evaluation requires running a given number of sequential steps, yet the result can be efficiently verified. They have applications in decentralised systems, such as the generation of trustworthy public randomness in a trustless environment, or resource-efficient blockchains. This journal article expands upon preliminary results presented at Eurocrypt 2019.

The construction is based on groups of unknown order such as an RSA
group or the class group of an imaginary quadratic field. The “delaying”
property relies on the assumption that in groups of unknown order, exponentiating
a random element by

In 12, H. Cohen and F. Thorne give explicit
formulæ for the Dirichlet series generating function of

In 11, Razvan Barbulescu in a joint work with
Jishnu Ray (University of British Columbia, Vancouver) brings elements to
support Greenberg's

In 13 and 34,
Jean-Marc Couveignes constructs small models
of number fields and functions fields.
One option is to
look for local equations rather than a full set of generators of the ideal of these models.
Another option is to provide approximations of a small collection of algebraic
numbers or functions in the field of interest, that are sharp enough to recover the ideal of relations.
A consequence for number fields
is a better bound for the number of number fields of given
degree

In 29, A. Page and his coauthors analyse in detail the
subfield method to accelerate the computation of

The best algorithms for integer factorisation use a non-negligible proportion of the time to enumerate smaller integers and to test if all their prime factors are below a given bound. A lot of effort has been spent in the literature to improve the best algorithm for this task, the elliptic curve method (ECM). In 28, R. Barbulescu and his doctoral student Sudarshan Shinde have given a simple method which allows to find rapidly, in a unified manner, all the previously known families of elliptic curves for ECM. They proved that there are precisely 1525 ECM-friendly families using the theory of modular forms.

In 46, M. Kirschmer, F. Narbonne,
C. Ritzenthaler and D. Robert give an algorithm to span the isomorphism
classes of principally polarized abelian varieties in the isogeny class
of

In

31, Xavier Caruso, Tristan Vaccon and Thibaut Verron continued to develop the theory of Gröbner bases over Tate algebras: they designed two F5-like algorithms, called

(

sition over

rm) and

(

luation over

sition over

rm) respectively and implemented them in the software

.

In the note 32, Xavier Caruso studied the
localisation of roots in an algebraic closure of random polynomials with
coefficients in

In

18, Chloe Martindale, former doctoral student in the team, presents an algorithm to compute higher dimensional Hilbert modular polynomials. She also explains applications of this algorithm to point counting, walking on isogeny graphs, and computing class polynomials.

The paper by E. Milio, former doctoral student in the team, and D. Robert 19 on computing cyclic modular polynomials has been published. This was the first paper of the Journal of Number Theory with a reproducible archive for computations.

J. Kieffer, A. Page and D. Robert have updated their article 44 on computing isogenies between abelian surfaces using modular polynomials. They added a purely algebraic description of the deformation map and gave precise geometric conditions for the algorithm to work.

A. Maiga and D. Robert examine in 24 modular polynomials for abelian surfaces with good reduction modulo 2, which enables them to compute canonical lifts of such surfaces over a finite field of characteristic 2 and to ultimately deduce their cardinality, the main security parameter for hyperelliptic curve cryptosystems.

In 42, J. Kieffer gives degree and height bounds for modular equations on PEL Shimura varieties in terms of their level. In particular, this result answers previous questions about Hilbert and Siegel modular polynomials and the complexity of algorithms manipulating them.

In 45, J. Kieffer shows that the sign choices made in Dupont's algorithm to evaluate genus 2 theta constants in quasi-linear time in the precision are indeed correct. This gives a positive answer to a question raised by Dupont in his 2006 thesis, and lifts one of the heuristic that Dupont's algorithm uses.

In 43, J. Kieffer designs an algorithm to evaluate Siegel and Hilbert modular polynomials over number fields, based on complex approximations and fast computations of theta functions in genus 2. Analyzing the possible precision losses and using interval arithmetic makes the output provably correct. In many situations, using this algorithm to evaluate modular equations on the fly is more efficient than precomputing and storing them.

In 16, Sorina Ionica, former postdoc of the team, and Emmanuel Thomé look at the structure of isogeny graphs of genus 2 Jacobians with maximal real multiplication. They generalise a result of Kohel's describing the structure of the endomorphism rings of the isogeny graph of elliptic curves. Their setting considers genus 2 jacobians with complex multiplication, with the assumptions that the real multiplication subring is maximal and has class number 1. Over finite fields, they derive a depth first search algorithm for computing endomorphism rings locally at prime numbers, if the real multiplication is maximal.

In 30, X. Caruso, E. Eid and Reynald Lercier
designed a new algorithm for computing isogenies between elliptic curves
over an extension of the field of 2-adic numbers. Their methods rely
on a highly efficient and numerically stable algorithm for solving
certain types of nonlinear singular 2-adic differential equations.
From this work, they deduced fast algorithms for computing isogenies
between elliptic curves in characteristic 2 and generating irreducible
polynomials of large degrees over

In 35, E. Eid extended the above strategy to the case of isogenies between Jacobians of hyperelliptic curves in odd characteristic. The obtained algorithm has quasi-linear complexity with respect to the degree of the isogeny.

H. Cohen in 33 examines the branches of the complex
Lambert

In 38, F. Johansson describes Calcium, a new library for exact real and complex arithmetic with the ability to prove equalities for a large class of numbers.

In 36, E. Friedman, F. Johansson and G. Ramirez-Raposo prove a conjecture from 2014 by Katok, Katok and Rodriguez Hertz, rigorously establishing the minimal value of the Fried average entropy for higher-rank Cartan actions.

In 41, F. Johansson reviews the Preparata-Sarwate algorithm for computing the characteristic polynomial and determinant of matrices, finding that it outperforms more widely used algorithms in some applications.

In 40, F. Johansson describes FunGrim, a semantic database of special function identities.3

In 17, F. Johansson gives an algorithm for computing all the complex branches of the Lambert W function in arbitrary-precision arithmetic with rigorous error bounds.

In 39, F. Johansson describes a new algorithm
for computing coefficients of the

With his contribution 15 to the Ten Years
Reproducibility
Challenge4,
A. Enge has endeavoured to reproduce the results of his 20 year old
article on volume computation for convex polytopes 55.
While the content is not related to number theory, the success of
the reproduction confirms the choice of the Lfant team to provide
software mainly as portable and standard C code.

G. Castagnos has a three years contract with Orange (Orange Labs Cesson-Sévigné) for the supervision of the PhD of Élie Bouscatié (Thèse CIFRE) from November 2020 to November 2023.

A. Bartel visited the team for two weeks in February.

https://

The Alambic project is a research project formed by members of the
INRIA Project-Team CASCADE of ENS Paris, members of the AriC INRIA
project-team of ENS Lyon, and members of the CRYPTIS of the university
of Limoges. G. Castagnos is an external member of the team of Lyon for
this project.

Non-malleability is a security notion for public key cryptographic encryption schemes that ensures that it is infeasible for an adversary to modify ciphertexts into other ciphertexts of messages which are related to the decryption of the first ones. On the other hand, it has been realized that, in specific settings, malleability in cryptographic protocols can actually be a very useful feature. For example, the notion of homomorphic encryption allows specific types of computations to be carried out on ciphertexts and generate an encrypted result which, when decrypted, matches the result of operations performed on the plaintexts. The homomorphic property can be used to create secure voting systems, collision-resistant hash functions, private information retrieval schemes, and for fully homomorphic encryption enables widespread use of cloud computing by ensuring the confidentiality of processed data.

The aim of the Alambic project to investigate further theoretical
and practical applications of malleability in cryptography. More
precisely, this project focuses on three different aspects: secure
computation outsourcing and server-aided cryptography, homomorphic
encryption and applications and << paradoxical >> applications of
malleability.

The

The CLap–CLap ANR project aims at accelerating the expansion of the

This project will also be the opportunity to contribute to the
development of the mathematical software SageMath and to the expansion
of computational methodologies.

The CIAO ANR project is a young researcher ANR project led by Damien Robert October 2019.

The aim of the CIAO project is to study the security and improve the efficiency of the SIDH (supersingular isogenies Diffie Helmann) protocol, which is one of the post-quantum cryptographic project submitted to NIST, which passed the first round selection.

The project include all aspects of SIDH, from theoretical ones (computing the endomorphism ring of supersingular elliptic curves, generalisation of SIDH to abelian surfaces) to more practical aspects like arithmetic efficiency and fast implementations, and also extending SIDH to more protocols than just key exchange.

Applications of this project is to improve the security of communications in a context where the currently used cryptosystems are vulnerable to quantum computers. Beyond post-quantum cryptography, isogeny based cryptosystems also allow to construct new interesting cryptographic tools, like Verifiable Delay Functions, used in block chains.

X. Caruso is an editor and one of the founders of the journal
Annales Henri Lebesgue.

J.-M. Couveignes is a member of the editorial board (scientific committee)
of the Publications mathématiques de Besançon since 2010.

K. Belabas acts on the editorial board of Journal de Théorie des
Nombres de Bordeaux since 2005 and of Archiv der Mathematik since
2006.

A. Enge is an editor of Designs, Codes and Cryptography
since 2004.

K. Belabas is a member of the “conseil scientifique” of the Société Mathématique de France.

A. Enge has acted as an evaluator for the German National Research Data Infrastructure5 on the panel on mathematics, particle physics and astrophysics.

Since January 2015, K. Belabas is vice-head of the Mathematics Institute (IMB). He also leads the computer science support service (“cellule informatique”) of IMB and coordinates the participation of the institute in the regional computation cluster PlaFRIM.

He is an elected member of “commission de la recherche” in the academic senate of Bordeaux University.

Between January 2017 and June 2020, A. Enge was “délégué scientifique” of the Bordeaux-Sud-Ouest Inria Research Centre. As such, he was also a designated member of the “commission d'évaluation” of INRIA.

He is a member of the administrative council of the Société Arithmétique
de Bordeaux, which edits the
Journal de théorie des nombres de Bordeaux
and supports number theoretic conferences.

G. Castagnos is responsible for the bachelor programme in mathematics and informatics.

X. Caruso and C. Ménini are leaders of the popularisation group at IMB (Institut de Mathématiques de Bordeaux).

R. Barbulescu, X. Caruso, A. Enge and B. Wesolowski have taken part as evaluators in the Tournois Français des Jeunes Mathématiciennes et Mathématiciens6, a competition between high school classes on mathematical research questions.

R. Barbulescu is one of the organizers of Concours Alkindi7, an online cryptography competition for middle and high school classes of French 4e, 3e and 2nde with 65000 participants in the 2019/2020 edition. Romania, Tunisia and Cameroun created national editions in which they use the same content as the French contest and had a few hundred participants.

X. Caruso wrote several small webpages/apps in order to present interesting mathematical objects and highlight their more striking properties:

An ongoing collaboration with the PIRVI platform8 has started; its main objective is to realise a 3D rendering engine in hyperbolic geometry.

X. Caruso gave a talk and animated a workshop on continued fractions and their applications to the construction of musical scales.