Joan-C. Lario

Departament de Matemàtiques

UPC, Barcelona

Facultat de Matemàtiques i Estadística
Pau Gargallo 5
E-08028 Barcelona

Telèfon: 34 93 413 7686
Fax: 34 93 413 7701
E-mail: joan.carles.lario@upc.edu

Seminari de Teoria de Nombres

STNB (UB-UAB-UPC): Informació
STNB @ UPC: Informació

Small Finite Groups: subgroup lattices and Galois realizations

F. Fité, J-C. Lario, A. Roig: (pdf) / (html) . Much more in A database of Galois polynomials

CM-computations: a horizontal page

Elliptic curves with CM defined over extensions of type (2,...,2) (html)

Diophantine Stability

Isomorphism clsasses of DS-curves over finite fields (html)

Publicacions

La primera irregularitat Lario, J-C.; Rio, A. STNB 37th (2024). (sagemath_html)
Faltings ellipitc curves in twisted Q-isogeny classes González-Jiménez, E.; Lario, J-C. In preparation (2024). Supplemetary Material (provisional)
An inverse Jacobian algorithm for Picrd curves (with an appendix by C. Vincent) Lario, J-C.; Somoza, A. Research in Number Theory 7, 32 (2021). Online
Twists of the genus 2 curve Y^2=X^6+1 Cardona, G.; Lario, J-C. Journal of Number Theory 209 (2020), 195--221. Online
Goro Shimura, el samurái de las formas modulares Guàrida, J.; Lario, J-C. Gac. R. Soc. Mat. Esp. 22 (2019) no. 3, 465--472.
Practical geometric constructions with ruler and compass in the Lemniscate curve Gómez-Molleda, M.A.; Lario, J-C. Preprint 2019.
Ruler and compass constructions of the equilateral triangle and pentagon in the Lemniscate curve Gómez-Molleda, M.A.; Lario, J-C. The Mathematical Intelligencer, Online : 25 April 2019.
Distribuciones aritméticas: errores y carreras Lario, J-C. Gac. R. Soc. Mat. Esp. 22 (2019), no. 2, 293--311.
A note on Picard curves of CM-type Lario, J-C.; Somoza, A. Preprint 2018.
The Sato-Tate conjecture for a Picard curve with complex multiplication Lario, J-C.; Somoza, A. AMS Contemporary Math. 701 (2018), 151--166.
Frobenius distribution for quotients of Fermat curves of prime exponent Fité, F.; González, J.; Lario, J-C. Canad. J. Math. 68 (2016), no. 2, 361--394.
Al-Karají y yo Lario, J-C. Gac. R. Soc. Mat. Esp. 19 (2016), no. 1, 133–-149.
The twisting representation of the L-function of a curve Fité, F.; Lario, J-C. Rev. Mat. Iberoam. 29 (2013), no. 3, 749–-764.
Cropping Euler factors of modular L-functions González, J.; Jiménez, J.; Lario, J-C. Forum Mathematicum, vol. 25, no. 5 (2013), 1039--1066.
Class number formulas for certain bicyclic biquadratic number fields as finite sums involving Jacobi elliptic functions Gómez-Molleda, M.A.; Lario, J-C. International Journal of Number Theory, vol. 8, no. 05 (2012), 1257--1270.
On sharply k-transitive Galois extensions Gómez-Molleda, M.A.; Lario, J-C. Med. Jour. of Math. 4, vol. 8 (2011), 621--636.
Modular elliptic directions with complex multiplication (with an application to Gross's elliptic curves) González, J.; Lario, J-C. Commentarii Math. Hel. 86 (2011), 317--351.
Deconstruction of a Dirichlet-Nazimow formula Gómez-Molleda, M.A.; Lario, J-C. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales, Serie A. Matemáticas 105 (2011), 109--117.
Plane quartic twists of X(5,3) Fernández, J.; González, J.; Lario, J-C. Canadian Mathematical Bulletin 50 (2007), 196--205.
On elliptic Galois representations and genus-zero modular units Fernández, J.; Lario, J-C. Journal Théorie des Nombres de Bordeaux 19 (2007), 141--165.
Rational points on twists of X_0(63) Bruin, N; Fernández, J.; González, J.; Lario, J-C. Acta Arith. 126 (2007), 361--385.
A note on dihedral polynomials of prime degree Lario, J-C.; Masdeu, M. Indian Journal of Pure and Applied Math. 36 (2005), 300--305.
On twists of the modular curves X(p) Fernández, J.; Lario, J-C.; Rio, A. Bull. London Math. Soc. 37 (2005), 342--350.
Arithmetic of Q-curves González, J.; Lario, J-C.; Quer, J. in Modular Curves and Abelian Varieties, Progress in Math. 224 (2004), 125--139.
Modular Curves and Abelian Varieties Cremona, J.; Lario, J-C.; Quer, J.; Ribet, K.; eds. Progress in Mathematics, 224. Birkhäuser (2004), 125--139.
Octahedral extensions arising form Q-curves of degree 2 Fernández, J.; Lario, J-C.; Rio, A. Canadian Journal of Mathematics 54 (2002), no. 6, 1202--1228.
Some computations with Hecke rings and deformation rings Lario, J-C.; Schoof, R. Experimental Math. 11 (2002), no. 2, 303--311.
On elliptic Q-curves and principal quartics Fernández, J.; Lario, J-C.; Rio, A. Proceedings of the Workshop on Number Theory 2001, Waseda University (Japan), 11-13 March 2001.
Q-curves and their Manin ideals González, J.; Lario, J-C. Amer. Journal of Math.123 (2001), 385--423.
On curves of genus 2 which Jacobian is of GL2-type Cardona, G.; González, J.; Lario, J-C.; Rio, A. Manuscripta Mathematica 98 (1999), 37--54.
Galois graphs: Walks, Trees, and Automorphisms Brunat, J-M.; Lario, J-C. Journal of Algebraic Combinatorics 10 (1999), 135--148.
Artimetical problems in Number Fields, Abelian Varieties and Modular Forms Bayer, P., et. al. Contributions to Science 2, no.1 (1999), 125--145.
Rational and Elliptic parametrizations of Q-curves González, J.; Lario, J-C. Journal of Number Theory 72 (1998), 13--31.
Elliptic modularity for octahedral Galois representations Lario, J-C.; Rio, A. Math. Res. Lett. 3 (1996), no. 3, 329--342.
An octahedral-elliptic type equality in Br2(k) Lario, J-C.; Rio, A. C. R. Acad. Sci. Paris Sér. I Math. 321(1995), no. 1, 39--44.
On Serre's conjecture (3.2.4 ?) and vertical Weil curves Lario, J-C. Advances in number theory (Kingston, ON, 1991), 281--291, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993.
Serre's conjecture on Galois representations attached to Weil curves with additive reduction Lario, J-C. Journées Arithmétiques, 1991 (Geneva). Astérisque No. 209 (1992), 15, 247--255.
On Galois representations defined by torsion points of modular elliptic curves Bayer, P.; Lario, J-C. Compositio Math. 84 (1992), no. 1, 71--84.
Representacions de Galois i corbes el·líptiques Lario, J-C. Tesi doctoral TDX

CV (resum)

1991

Doctor en Ciències Matemàtiques (Universitat de Barcelona). Directora de tesi: Dra. Pilar Bayer
1986

Llicenciat en Ciències Matemàtiques (Universitat de Barcelona)
2019-

Scientific Officer / Executive Team of CIMPA
2011

Acreditació CU
1993-

Professor TU (UPC)
1990-1993

Professor TEU (UPC)
1986-1990

Professor Associat (UPC)
2023

Visiting at IMUS (Sevilla)
2020

Visiting at IMUS (Sevilla)
2019

Visiting at IMUS (Sevilla)
2004

Visiting at Harvard University (Boston)
2002

Visiting at Istituto Nazionale di Alta Matematica "F. Severi" (Roma)
2001

Visiting at Advanced Research Institue for Science and Engineering, University of Waseda (Tokyo)
1997

Visiting at Waseda Univeristy and Chuo University (Tokyo)
1992-1993

Visiting Scholar at Harvard University (Boston)
1992

Premi Ferran Sunyer i Balaguer (Institut d'Estudis Catalans)
1996-1999

Director del Departament de Matemàtica Aplicada II (UPC)

Participació en Projectes Científics subvencionats

2023-2025

Aritmètica de formes modulars, equacions diofantines i functorialitat de Langlands PID2022-136944NB-IOO(MECD)
2021-2024

STNB (2021 SGR 01468)
2016-2018

Conjectura de Birch--Swinnerton-Dyer (MECD)
2013-2015

Aritmética de funciones L y estructuras de Galois (MECD)
2010-2012

Aritmética de variedades algebraicas: teoría y computación (MICINN)
2006-2010

Variedades abelianas y Teoría de Galois (MEC)
2003-2006

Curvas y variedades abelianas modulares (MEC)
2003-2006

Variedades abelianas modulares (MEC)
2009-2013

Grups de recerca consolidats (Generalitat de Catalunya)
2005-2008

Grups de recerca consolidats (Generalitat de Catalunya)
2002-2004

Grups de recerca consolidats (Generalitat de Catalunya)
1999

Curvas modulares: aplicaciones criptográficas (CCD-UPC; La Habana)
1997-1999

Aritmética de Q-curvas (DGICYT)
1993-1996

Formas modulares y representaciones de Galois (DGICYT)
1992-1993

Supersingular Galois representations and Weil curves (Post-doc, DGICYT)
1990-1993

Representaciones de Galois aritmético-geométricas (DGICYT)
1989-1990

Propiedades aritméticas de las formas modulares (Acciones integradas, MEC)
1988-1990

Algoritmes en teoria de nombres (Pre-competitius, UPC)
1987-1989

Aplicaciones aritméticas de las curvas elípticas (CICYT)

Participació en CIMPA Schools

2023

Isogenies of Elliptic Curves and their Applications to Cryptography (24 juliol-4 agost, Popayán, Colombia)
2022

p-Adic Numbers, Ultrametric Analysis, and Applications (22-31 maig, Guanajuato, México)
2022

From Dynamics to Algebra and Representation Theory and Back (7-18 febrer, Florianápolis, Brazil)
2019

Fourth Latin American School on Algebraic Geometry and Applications (2-13 desembre, Talca, Chile)

Direcció tesis doctorals

2021

Vrioni, B. A census on curves and surfaces with Diophantine stability over finite fields
2019

Somoza, A. Inverse Jacobian and related topics for certain superelliptic curves
2013

Lorenzo, E. Artihmetic properties of non-hyperelliptic genus 3 curves
2011

Fité, F. L-Functions and Artin representations attached to twisted abelian varieties
2003

Fernández, J. Elliptic realization of Galois representations

Direcció tesis de master i fi de grau

2019

Alemany, J. Museitzation of Steiner's 10 Questions on the Complete Quadrilateral (Master, FME)
2019

Anotnino, S. A minimal bound and divergence case on the elliptic curves over finite fields (Master, FME)
2019

Jofre, J. Heegner's Lemma (Master, FME)
2016

Tapia, X. Relative ideal discriminant on Kummer extensions (Master, FME)
2016

Aparicio, G. The Selberg Trace Formula (FME)
2016

Pina, S. Graficando curvas con Javascript (FNB)
2014

Blanco, G. Corbes el.líptiques i nombres congrus (FME)
2014

Somoza, A. The Sato-Tate conjecture for a Picard curve with complex multiplication (Master, FME)
2010

Lorenzo, E. Torcimiento de cuárticas planas lisas (Master, FME)
2002

Tramuns, E. Cyclotomic units (FME)
1999

Galindo, D. Construccions amb regla i compàs a la lemniscata (FME)

Conferències, comunicacions i cursos

2024

La primera irregularitat (j/w Anna Rio) (STNB 2024. 37è ANY, 5--9 febrer) 
2023

When resolving the Birch & Swinnerton-Dyer conjecture was not remunerated (International Algebra Conference, Cebu, Philippines 7-11 agost) 
2023

Faltings elliptic curves under quadratic twists (The Seventh Mini Symposium of the Roman Number Theory Association, Roma, 4-6 maig) 
2023

Beber de Weber (cuando Birch & Swinnerton-Dyer era gratis) (Programa de doctorado. Universidad de Sevilla, 12 abril) 
2023

On Faltings elliptic curves in twisted isogeny clsasses (Seminario Álgebra, Universidad de Sevilla, 30 març) 
2023

Aritmética de la regla y el compás (Salón de Actos de la Facultad de Matemáticas, Universidad de Sevilla, 22 març)
2023

Distribution of Manin-Stevens elliptic curves in twisted isogeny classes over Q (STNB 2023. 36è ANY, 23--27 gener) 
2021

Varietats algebraiques amb estabilitat diofantina sobre cossos finits (Seminari de Criptografia i Grafs. Universitat de Lleida) 
2020

Deligne-Lusztig curves are diophantine stable (STNB 2020. 34è ANY, 3--7 febrer) 
2019

Construcciones prácticas con regla y compás en la lemniscata (Seminario IMUS) 
2019

Estabilidad diofántica en característica positiva (Seminario de Álgebra, Sevilla) 
2018

Primality tests using elliptic curves (Master course at FME) 
2018

Νέες πρακτικές κατασκευές με χάρακα και διαβήτη (STNB 2018. 32è ANY, 23--27 gener) 
2017

Arithmetic properties of curves of small genus (BGSMath course, 14--24 febrer) 
2016

Al-karají y yo (STNB 2016. 30è ANY, 25--29 gener) 
2013

ST and ST (STNB 2013. 27è ANY, 28 gener -- 1 febrer) 
2013

Arithmetic of Galois representations (TANdeM, Teoría Algebraica de Números de Madrid, 26 Mayo - 1 Junio) 
2013

Serre's conjecture (3.2.4?) (TANdeM, Teoría Algebraica de Números de Madrid, 26 Mayo - 1 Junio) 
2013

Automorphic representations and Sato-Tate (TANdeM, Teoría Algebraica de Números de Madrid, 26 Mayo - 1 Junio) 
2013

Distribuciones Frobenius: errores y carreras (V Jornadas de Teoría de Números, 10 Julio, Universidad de Sevilla)
2013

Sato-Tate conjecture and its generalizations (Waseda University, Japan)
2013

The Sato-Tate conjecture for Fermat curves (Chuo University, Japan)
2013

Serre's conjecture (3.2.4?) (Chuo University, Japan)
2013

Weight one modular forms of S_4-type (Effective methods for Darmion points (Centro de Ciencias Pedro Pascual, Agost 25-31, Benasc)
2012

Number Theory Seminar in memory of Fumiyuki Momose (Maig, 21-23, UPC Barcelona)
2011

Galois, entre radicales (Galois Year 2011-2012, UPV/EHU, Bilbao)
2010

Cropping Euler Factors of modular L-functions (Galois Theory and Explicit Methods: Final conference, Bercelona)
2009

Efecto twist en L-series de curvas de género >=2 (Universidad de Salamanca)
2008

Nearfields y sus aplicaciones (Universidad del País Vasco)
2008

Optimal quotients of modular elliptic curves over number fields (Waseda University, Japan)
2006

Sharply k-transitive Galois extensions (Chuo University, Japan)
2006

Polígonos lemniscáticos (Universidad de Málaga)
2006

Gauss i els polígons (Jornada Gauss, UPC)
2004

Modular parametrizations of CM elliptic curves (Number Theory Seminar, Harvard University)
2004

Arithmetic of Q-curves (Euro-conference at CRM)
2004

Workshop Sa Conjectura de Catalan. Organizers: G. Cardona (UIB), J.-C. Lario (UPC), R. Schoof (Roma). Museu de Menorca, Maó, Setembre 1--5.
2002

Principal quartics and embedding Galois problems (Instituto Nazionale di Alta Matematica Francesco Severi, Roma)
2002

EuroConference Modular Curves and Abelian Varieties. CRM (Bellaterra), Juliol, 15--18.
2001

3-adic Hecke deformation rings (University of Waseda, Tokyo)
2001

Principal quartics and quadratic Q-curves (Workshop on Number Theory, Tokyo)
2000

Q-curves and their Manin ideals (MSRI at Berkeley, California)
2000

Explicit computations on Hecke deformation rings (EACA)
1999

Manin ideals for Q-curves (Number Theory Seminar, Harvard University)
1999

Curvas elípticas modulares sobre cuerpos de números (Univ. Aut. Madrid)
1999

Elliptic curves over Q-bar and their Manin invariants (Journées Arithmétiques, Univ. Roma, Italia)
1997

Geometry of some algebraic extensions (Tokyo Denki University, Japan)
1997

Abelian surfaces and octahedral type problems (Waseda University, Japan)
1997

Q-curves and abelian varieties of GL2-type (Chuo University, Japan)
1997

Elliptic modularity and Galois embedding problems (Waseda University)
1995

Octahedral extensions and modular elliptic curves (Fermat's Conference, Boston University)
1995

Mini-curs de Magma (STNB, Universitat de Barcelona)
1994

Mathematica a l'entorn del Teorema de Fermat (Col·legi oficial de Doctors i Llicenciats de Catalunya)
1993

Modular elliptic curves over number fields (Journées Arithmétiques, Bordeaux)
1993

Detecting Q-curves (Number Theory Seminar, Harvard University)
1992

Représentations galoisiennes des courbes elliptiques verticales (Séminaire de TN, U. de Bordeaux)
1992

Grups amb Cayley (Seminari de software matemàtic, UPC)
1991

Serre's conjecture (3.2.4?) and elliptic curves (Journées Arithmétiques, Ginebra)
1991

Ordinary Galois representations for p-torsion points (CNTA, Kingston-Ontario, Canadà)
1991

Grafos parabólicos (Seminario de Algebra y Geometría, Univ. Complutense de Madrid)
1990

Computing Serre's invariants: weight and level (Algorithmes en théorie des nombres, Luminy-Marsella)
1989

La conjecture de Serre sur les courbes elliptiques (Frey-Zimmer-Lamprecht Seminar, U. des Saarlandes, Alemanya)

Darrera actualització: Febrer 11, 2024