GAATI — Algebraic Geometry and Applications to Information Theory •

Connections

Description

The laboratory for Algebraic Geometry and Applications to Information Theory (GAATI in French) is a mathematics research unit accredited since 2004 by the French Ministry of Higher Education and Research (EA 3893). It is the only research group in mathematics in French Polynesia.

The efforts of the GAATI laboratory aim to increase the efficiency and security of information transport and control systems through the development of new computational and cryptographic techniques. To this extent, the laboratory develops and exploits mathematical methods based on algebraic geometry and number theory.

Members

Associate professor

Deputy Director

Associate professor

Associate professor

Associate professor

Alexander D. Rahm

Alexander D. Rahm

Associate professor

Associate professor

Phuong Dung Phan

Projects

The MELODIA Project

GAATI — Algebraic Geometry and Applications to Information Theory

Scientific Productions

Iterative constructions of irreducible polynomials from isogenies

Finite Fields and Their Applications, 2024, 97, pp.102429. ⟨10.1016/j.ffa.2024.102429⟩

GAATI — Algebraic Geometry and Applications to Information Theory

Publications mathématiques de Besançon

, 2024, 2024, 2-38549-112-5

GAATI — Algebraic Geometry and Applications to Information Theory

Empirical Risk Minimization with Relative Entropy Regularization

IEEE Transactions on Information Theory, 2024, 70 (7), pp.5122-5161. ⟨10.1109/TIT.2024.3365728⟩

GAATI — Algebraic Geometry and Applications to Information Theory

Index calculus algorithm for non-planar curves

Finite Fields and Their Applications, 2023, 90, pp.102227. ⟨10.1016/j.ffa.2023.102227⟩

GAATI — Algebraic Geometry and Applications to Information Theory

Conference paper

On the Validation of Gibbs Algorithms: Training Datasets, Test Datasets and their Aggregation

ISIT 2023 - IEEE International Symposium on Information Theory, Jun 2023, Taipei, Taiwan. ⟨10.1109/ISIT54713.2023.10206506⟩

GAATI — Algebraic Geometry and Applications to Information Theory

Contributions aux aspects effectifs des variétés abéliennes et à leurs applications

Mathématiques [math]. Université de la Polynésie française, 2023

GAATI — Algebraic Geometry and Applications to Information Theory

On the vaccination threshold for Covid-19 in French Polynesia

Pacific Health, 2022, 5, ⟨10.24135/pacifichealth.v5i.59⟩

GAATI — Algebraic Geometry and Applications to Information Theory

Conference paper

Empirical Risk Minimization with Relative Entropy Regularization: Optimality and Sensitivity Analysis

ISIT 2022 - IEEE International Symposium on Information Theory, Jun 2022, Espoo, Finland. pp.684-689, ⟨10.1109/ISIT50566.2022.9834273⟩

GAATI — Algebraic Geometry and Applications to Information Theory

Empirical Risk Minimization with Generalized Relative Entropy Regularization Minimisation du Risque Empirique avec Régularisation par l’Entropie Relative Généralisée

[Research Report] RR-9454, Inria. 2022

GAATI — Algebraic Geometry and Applications to Information Theory

Empirical Risk Minimization with Generalized Relative Entropy Regularization Minimisation du Risque Empirique avec Régularisation par l’Entropie Relative Généralisée

[Research Report] RR-9454, Inria. 2022

GAATI — Algebraic Geometry and Applications to Information Theory

Empirical Risk Minimization with Relative Entropy Regularization Minimisation du Risque Empirique avec Régularisation par l’Entropie Relative

[Research Report] RR-9454, Inria. 2022

GAATI — Algebraic Geometry and Applications to Information Theory

GAATI — Algebraic Geometry and Applications to Information Theory

Arithmetic, Geometry, Cryptography and Coding Theory

American Mathematical Society, 770, 2021, Contemporary Mathematics

GAATI — Algebraic Geometry and Applications to Information Theory

AN INTRODUCTION TO TORSION SUBCOMPLEX REDUCTION

Advanced Studies: Euro-Tbilisi Mathematical Journal, 2021, Special issue on Cohomology, Geometry, Explicit Number Theory, 9, p. 105-126

Alexander D. Rahm

GAATI — Algebraic Geometry and Applications to Information Theory

Hyperbolic tessellations and generators of K_3 for imaginary quadratic fields

Forum of Mathematics, Sigma, 2021, 9 (E40), ⟨10.1017/fms.2021.9⟩

Alexander D. Rahm

GAATI — Algebraic Geometry and Applications to Information Theory

The Distribution of Rational Numbers on Cantor’s Middle Thirds Set

Uniform Distribution Theory, 2020, 15 (2), pp.73-92. ⟨10.2478/udt-2020-0011⟩

Alexander D. Rahm

GAATI — Algebraic Geometry and Applications to Information Theory

Plasmids shape the diverse accessory resistomes of Escherichia coli ST131

Access Microbiology, 2020, ⟨10.1099/acmi.0.000179⟩

Alexander D. Rahm

GAATI — Algebraic Geometry and Applications to Information Theory

Statistique pour les Sciences de la Vie et de la Terre

Licence. Polynésie française. 2020

Alexander D. Rahm

GAATI — Algebraic Geometry and Applications to Information Theory

Bianchi’s additional symmetries

Journal of Homotopy and Related Structures, 2020, 15, pp.455-462. ⟨10.1007/s40062-020-00262-4⟩

Alexander D. Rahm

GAATI — Algebraic Geometry and Applications to Information Theory

The mod 2 cohomology rings of congruence subgroups in the Bianchi groups

Journal of Algebraic Combinatorics, 2019, ⟨10.1007/s10801-019-00912-8⟩

Alexander D. Rahm

GAATI — Algebraic Geometry and Applications to Information Theory

The Farrell–Tate and Bredon homology for PSL 4 ( Z ) via cell subdivisions

Journal of Pure and Applied Algebra, 2019, 223 (7), pp.2872-2888. ⟨10.1016/j.jpaa.2018.10.002⟩

Alexander D. Rahm

GAATI — Algebraic Geometry and Applications to Information Theory

Corrigendum to “On a question of Serre” [C. R. Acad. Sci. Paris, Ser. I 350 (2012) 741–744]

Comptes Rendus. Mathématique, 2019, 357 (7), pp.589-590. ⟨10.1016/j.crma.2019.07.008⟩

Alexander D. Rahm

GAATI — Algebraic Geometry and Applications to Information Theory

On Ruan’s Cohomological Crepant Resolution Conjecture for the complexified Bianchi orbifolds

Algebraic and Geometric Topology, 2019, 19, pp.2715-2762. ⟨10.2140/agt.2019.19.2715⟩

Alexander D. Rahm

GAATI — Algebraic Geometry and Applications to Information Theory

The Farrell–Tate and Bredon homology for PSL_4(Z) via cell subdivisions

Journal of Pure and Applied Algebra, 2019, 223 (7), pp.2872-2888. ⟨10.1016/j.jpaa.2018.10.002⟩

Alexander D. Rahm

GAATI — Algebraic Geometry and Applications to Information Theory

GENUINE BIANCHI MODULAR FORMS OF HIGHER LEVEL, AT VARYING WEIGHT AND DISCRIMINANT

Journal de Théorie des Nombres de Bordeaux, 2019, 31 (1), pp.27-48. ⟨10.5802/jtnb.1067⟩

Alexander D. Rahm

GAATI — Algebraic Geometry and Applications to Information Theory

Simulation study of the electrical tunneling network conductivity of suspensions of hard spherocylinders

Physical Review E , 2018, 98 (6), ⟨10.1103/PhysRevE.98.062611⟩

Alexander D. Rahm

GAATI — Algebraic Geometry and Applications to Information Theory

Persistence at the final stage of volcanic island ontogeny: Abiotic predictors explain native plant species richness on 111 remote Pacific atolls

Ecology and Evolution, 2018, ⟨10.1002/ece3.4680⟩

GAATI — Algebraic Geometry and Applications to Information Theory

Persistence at the final stage of volcanic island ontogeny: Abiotic predictors explain native plant species richness on 111 remote Pacific atolls

Ecology and Evolution, 2018, ⟨10.1002/ece3.4680⟩

GAATI — Algebraic Geometry and Applications to Information Theory

Conference paper

Isogeny Graphs and Endomorphism Rings of Ordinary Abelian Varieties

colloque international “L-functions and algebraic varieties”, Poncelet Scientific Center; Higher School of Economics, Feb 2018, Moscou, Russia

GAATI — Algebraic Geometry and Applications to Information Theory

Constructing Permutation Rational Functions from Isogenies

SIAM Journal on Discrete Mathematics, 2018, 32 (3), pp.1741-1749. ⟨10.1137/17M1135736⟩

GAATI — Algebraic Geometry and Applications to Information Theory

Verification of the Quillen conjecture in the rank 2 imaginary quadratic case

Homology, Homotopy and Applications(HHA), 2017, 22 (2), ⟨10.4310/HHA.2020.v22.n2.a17⟩

Alexander D. Rahm

GAATI — Algebraic Geometry and Applications to Information Theory

Torsion Subcomplex Reduction Réduction de sous-complexes de torsion

Mathematics [math]. Pierre et Marie Curie, Paris VI, 2017

Alexander D. Rahm

GAATI — Algebraic Geometry and Applications to Information Theory

On polarised class groups of orders in quartic CM-fields

Mathematical Research Letters, 2017, 24 (2), pp.247-270. ⟨10.4310/MRL.2017.v24.n2.a1⟩

GAATI — Algebraic Geometry and Applications to Information Theory

On the equivariant K-homology of PSL_2 of the imaginary quadratic integers

Annales de l'Institut Fourier, 2016, (accepted for publication on January 21, 2016)

Alexander D. Rahm

GAATI — Algebraic Geometry and Applications to Information Theory

The mod 2 cohomology rings of SL_2 of the imaginary quadratic integers

Journal of Pure and Applied Algebra, 2015, Accepted for publication on July 21, 2015

Alexander D. Rahm

GAATI — Algebraic Geometry and Applications to Information Theory

Computing endomorphism rings of abelian varieties of dimension two

Mathematics of Computation, 2015, 84 (294), pp.1977-1989. ⟨10.1090/S0025-5718-2015-02938-X⟩

GAATI — Algebraic Geometry and Applications to Information Theory

A REFINEMENT OF A CONJECTURE OF QUILLEN

Comptes Rendus. Mathématique, 2015, pp.Editorial reference: CRASS1_CRMATHEMATIQUE-D-14-00503

Alexander D. Rahm

GAATI — Algebraic Geometry and Applications to Information Theory

Special issue on GEOCRYPT 2013

GEOCRYPT 2013, Oct 2013, Punaauia, Tahiti (French Polynesia), France. 8 (4), American Institute of Mathematical Sciences (AIMS), pp.i - ii, 2014, Advances in Mathematics of Communications (AMC), ⟨10.3934/amc.2014.8.4i⟩

GAATI — Algebraic Geometry and Applications to Information Theory

THE DIOPHANTINE EQUATION Fyn + Fxn+1 = Fxm

Integers, 2014, Annual Volume 2013, 9783110298116. ⟨10.1515/9783110298161.479⟩

GAATI — Algebraic Geometry and Applications to Information Theory

Complexifiable characteristic classes

Journal of Homotopy and Related Structures, 2013, Accepted for publication

Alexander D. Rahm

GAATI — Algebraic Geometry and Applications to Information Theory

L-Functions of elliptic curves and binary recurrences

Bulletin of the Australian Mathematical Society, 2013, 88 (03), pp.509-519. ⟨10.1017/S0004972713000166⟩

GAATI — Algebraic Geometry and Applications to Information Theory

Higher torsion in the Abelianization of the full Bianchi groups

LMS Journal of Computation and Mathematics, 2013, 16, pp. 344 - 365. ⟨10.1112/S1461157013000168⟩

Alexander D. Rahm

GAATI — Algebraic Geometry and Applications to Information Theory

On Level One Cuspidal Bianchi Modular Forms

LMS Journal of Computation and Mathematics, 2013, 16, pp. 187-199. ⟨10.1112/S1461157013000053⟩

Alexander D. Rahm

GAATI — Algebraic Geometry and Applications to Information Theory

The subgroup measuring the defect of the Abelianization of SL_2(Z[i])

Journal of Homotopy and Related Structures, 2013, pp.1-6. ⟨10.1007/s40062-013-0023-x⟩

Alexander D. Rahm

GAATI — Algebraic Geometry and Applications to Information Theory

The diophantine equation F_N^Y + F_{N+1}^X = F_M^X

Integers : Electronic Journal of Combinatorial Number Theory, 2013, 13, pp.A33

GAATI — Algebraic Geometry and Applications to Information Theory

Group arithmetic in C 3 , 5 curves

Journal of Symbolic Computation, 2013, 56, pp.1-26. ⟨10.1016/j.jsc.2013.05.008⟩

GAATI — Algebraic Geometry and Applications to Information Theory

The homological torsion of PSL_2 of the imaginary quadratic integers

Transactions of the American Mathematical Society, 2012, 365, pp.1603-1635. ⟨10.1090/S0002-9947-2012-05690-X⟩

Alexander D. Rahm

GAATI — Algebraic Geometry and Applications to Information Theory

On a question of Serre

Comptes Rendus. Mathématique, 2012, 350 (15-16), pp.Pages 741-744. ⟨10.1016/j.crma.2012.09.001⟩

Alexander D. Rahm

GAATI — Algebraic Geometry and Applications to Information Theory

Some more functions that are not APN infinitely often. The case of Gold and Kasami exponents

Contemporary mathematics, 2012, Contemporary Math, 574, pp.27-36. ⟨10.1090/conm/574/11423⟩

GAATI — Algebraic Geometry and Applications to Information Theory

Endomorphism Rings in Cryptography

Computer Science [cs]. Institut National Polytechnique de Lorraine - INPL; Technische Universiteit Eindhoven, 2011. English. ⟨NNT : 2011INPL047N⟩

GAATI — Algebraic Geometry and Applications to Information Theory

Computing endomorphism rings of elliptic curves under the GRH

Journal of Mathematical Cryptology, 2011, 5 (2), pp.101-113. ⟨10.1515/JMC.2011.008⟩

GAATI — Algebraic Geometry and Applications to Information Theory

Homology and K-theory of the Bianchi groups

Comptes Rendus. Mathématique, 2011, Volume 349 (Issues 11-12), pp.Pages 615-619. ⟨10.1016/j.crma.2011.05.014⟩

Alexander D. Rahm

GAATI — Algebraic Geometry and Applications to Information Theory

An exponential Diophantine equation related to powers of two consecutive Fibonacci numbers

Proceedings of the Japan Academy. Series A. Mathematical Sciences, 2011, 87 (4), ⟨10.3792/pjaa.87.45⟩

GAATI — Algebraic Geometry and Applications to Information Theory

Computing the endomorphism ring of an ordinary elliptic curve over a finite field

Journal of Number Theory, 2011, Elliptic Curve Cryptography, 131 (5), pp.815--831. ⟨10.1016/j.jnt.2009.11.003⟩

GAATI — Algebraic Geometry and Applications to Information Theory

A low-memory algorithm for finding short product representations in finite groups

Designs, Codes and Cryptography, 2011, ⟨10.1007/s10623-011-9527-8⟩

GAATI — Algebraic Geometry and Applications to Information Theory

The integral homology of $PSL_2$ of imaginary quadratic integers with non-trivial class group

Journal of Pure and Applied Algebra, 2011, 215, pp.1443-1472. ⟨10.1016/j.jpaa.2010.09.005⟩

Alexander D. Rahm

GAATI — Algebraic Geometry and Applications to Information Theory

(Co)homologies and K-theory of Bianchi groups using computational geometric models (Co)homologies et K-théorie de groupes de Bianchi par des modèles géométriques calculatoires

Mathematics [math]. Université Joseph-Fourier - Grenoble I, 2010. English. ⟨NNT : ⟩

Alexander D. Rahm

GAATI — Algebraic Geometry and Applications to Information Theory

Non-hyperelliptic modular curves of genus 3

Journal of Number Theory, 2010, 130 (4), pp.862-878. ⟨10.1016/j.jnt.2009.12.002⟩

GAATI — Algebraic Geometry and Applications to Information Theory

Conference paper

On rationality of the intersection points of a line with a plane quartic

WAIFI 2010: Arithmetic of Finite Fields, 2010, Istanbul, Turkey. pp.224-237, ⟨10.1007/978-3-642-13797-6_16⟩

GAATI — Algebraic Geometry and Applications to Information Theory

Non-hyperelliptic modular Jacobians of dimension 3

Mathematics of Computation, 2009, 78 (266), pp.1173-1191. ⟨10.1090/S0025-5718-08-02174-1⟩

GAATI — Algebraic Geometry and Applications to Information Theory

Conference paper

More Discriminants with the Brezing-Weng Method

9th International Conference on Cryptology in India - INDOCRYPT 2008, Dec 2008, Khargapur, India. pp.389--399, ⟨10.1007/978-3-540-89754-5_30⟩

GAATI — Algebraic Geometry and Applications to Information Theory

Fast addition on non-hyperelliptic genus 3 curves

On Number Theory and its Applications, 2008, pp.1-28. ⟨10.1142/9789812793430_0001⟩

GAATI — Algebraic Geometry and Applications to Information Theory

Conference paper

Fast addition on non-hyperelliptic genus 3

Algebraic geometry and its applications (SAGA), 2007, Papeete, France

GAATI — Algebraic Geometry and Applications to Information Theory

Ate Pairing on Hyperelliptic Curves

Advances in Cryptology - EUROCRYPT 2007, 4515, Springer Berlin Heidelberg, pp.430-447, 2007, Lecture Notes in Computer Science, ⟨10.1007/978-3-540-72540-4_25⟩

GAATI — Algebraic Geometry and Applications to Information Theory

On using expansions to the base of −2

International Journal of Computer Mathematics, 2004, 81 (4), pp.403-406. ⟨10.1080/00207160410001661311⟩

GAATI — Algebraic Geometry and Applications to Information Theory

Fast Arithmetic on Jacobians of Picard Curves

2947, Springer Berlin Heidelberg, pp.55-68, 2004, Lecture Notes in Computer Science, ⟨10.1007/978-3-540-24632-9_5⟩

GAATI — Algebraic Geometry and Applications to Information Theory

Fast Arithmetic on Jacobians of Picard Curves

2947, Springer Berlin Heidelberg; Springer Berlin Heidelberg, pp.55-68, 2004, Lecture Notes in Computer Science, ⟨10.1007/978-3-540-24632-9_5⟩

GAATI — Algebraic Geometry and Applications to Information Theory

Events

Colloque international

University of French Polynesia – Amphi A2

+ Calendar 2025-08-18 08:00 2025-08-22 17:00 GMT-10 René 25 The René 25 conference will bring together renowned international researchers in mathematics to celebrate the research interests of René Schoof, which include the fields of algebraic number theory, arithmetic algebraic geometry, computational number theory and coding theory. University of French Polynesia

Image Gallery

GAATI