LEONARDO COLÒ

NUMBER THEORY & CRYPTOGRAPHY

Leonardo Colo

In my research I investigate questions related to supersingular elliptic curves, their endomorphism ring and associated isogeny graphs. I am particularly interested in: cryptography, elliptic curves, abelian varieties, algorithms for number theory, canonical lifts of elliptic curves, class field theory and modular curves.

CONFERENCES & SEMINARS

  1. Modular and formal orientations: beyond OSIDH

    Isogeny Club > Slides

  2. Oriented supersingular elliptic curves and class group actions

    Sèminaire LFANT - Lithe and fast algorithmic number theory (Bordeaux, France). > Slides

  3. Oriented supersingular elliptic curves and class group actions

    Algebraic and combinatorial methods for Coding and Cryptography (CIRM, Marseille, France). > Slides

  4. Oriented supersingular elliptic curves and class group actions

    Sèminaire ATI - Arithmètique et Thèorie de l'Information (Marseille, France) > Slides

  5. A modular approach to OSIDH

    Sèminaire ATI - Arithmètique et Thèorie de l'Information (Marseille, France) > Slides

  6. A modular approach to OSIDH

    AGC2T: Arithmetic, Geometry, Cryptography and Coding Theory (CIRM, Marseille, France) > Slides

  7. Orienting supersingular isogeny graphs

    Sèminaire de l'Èquipe IAA de Toulon (Toulon, France) - Online > Slides

  8. Orienting supersingular isogeny graphs

    Sèminaire de l'École des mines de Saint-Étienne (Gardanne, France) > Slides

  9. Orienting supersingular isogeny graphs

    Sèminaire de Cryptographie (Rennes, France) > Slides

  10. Orienting supersingular isogeny graphs

    Sèminaire ATI - Arithmètique et Thèorie de l'Information (Marseille, France) > Slides

  11. Orienting supersingular isogeny graphs

    Number-Theoretic Methods in Cryptology 2019 (Institut de Mathèmatiques de Jussieu, Paris, France) > Slides

  12. Orienting supersingular isogeny graphs

    Sèminaire CCA - Codage, Cryptologie, Algorithmes (Paris, France) > Slides

  13. Orienting supersingular isogeny graphs

    Journès Nationales de Calcul Formel 2019 (CIRM, Marseille, France) > Slides

CONFERENCES & SEMINARS

Modular and formal orientations: beyond OSIDH

Isogeny Club (Online), Oct. 2023 > Slides

Oriented supersingular elliptic curves and class group actions

Sèminaire LFANT - Lithe and fast algorithmic number theory (Bordeaux, France), Mar. 2023 > Slides

Oriented supersingular elliptic curves and class group actions

Algebraic and combinatorial methods for Coding and Cryptography (CIRM, Marseille, France), Feb. 2023 > Slides

Oriented supersingular elliptic curves and class group actions

Sèminaire ATI - Arithmètique et Thèorie de l'Information (Marseille, France), Nov. 2022 > Slides

A modular approach to OSIDH

Sèminaire ATI - Arithmètique et Thèorie de l'Information (Marseille, France), May 2022 > Slides

A modular approach to OSIDH

AGC2T: Arithmetic, Geometry, Cryptography and Coding Theory (CIRM, Marseille, France), May 2021 > Slides

Orienting supersingular isogeny graphs

Sèminaire de l'Èquipe IAA de Toulon (Toulon, France) - Online, Mar. 2021 > Slides

Orienting supersingular isogeny graphs

Sèminaire de l'École des mines de Saint-Étienne (Gardanne, France), Dec. 2019 > Slides

Orienting supersingular isogeny graphs

Sèminaire de Cryptographie (Rennes, France), Oct. 2019 > Slides

Orienting supersingular isogeny graphs

Sèminaire ATI - Arithmètique et Thèorie de l'Information (Marseille, France), Sep. 2019 > Slides

Orienting supersingular isogeny graphs

Number-Theoretic Methods in Cryptology 2019 (Institut de Mathèmatiques de Jussieu, Paris, France), Jun. 2019 > Slides

Orienting supersingular isogeny graphs

Sèminaire CCA - Codage, Cryptologie, Algorithmes (Paris, France), Jun 2019 > Slides

Orienting supersingular isogeny graphs

Journès Nationales de Calcul Formel 2019 (CIRM, Marseille, France), Feb. 2019 > Slides

WORKING GROUPS

  1. Weil's bounds

    Groupe de Travail on Rational Points on Curves over Finite Fields > webpage
    Aix-Marseille Université, Marseille, FR
    > slides

  2. Completion and topology

    The Hasse-Arf Theorem

    Groupe de Travail on Local fields > webpage
    Aix-Marseille Université, Marseille, FR
    > notes   notes

  3. Ternary Forms

    Local fields and ternary quadratic forms

    Groupe de Travail on Quaternion algebras > webpage
    Aix-Marseille Université, Marseille, FR
    > notes   notes

  4. Quadratic forms

    Modular functions and complex multiplication

    Groupe de travail on "Primes of the form x^2 + ny^2"
    Aix-Marseille Université, Marseille, FR
    > notes   notes

  5. Modular forms and Galois representations

    Graduate student seminar on modularity and the proof of Fermat's Last Theorem > webpage
    Concordia University & McGill University, Montreal, CA
    > notes

  6. Iwasawa algebras and p-adic Measures

    Graduate student seminar on Iwasawa theory > webpage
    Concordia University & McGill University, Montreal, CA
    > notes

WORKING GROUPS

Weil's bounds

Groupe de Travail on Rational Points on Curves over Finite Fields > webpage

Aix-Marseille Université, Marseille, FR, 2022/2023

> slides

Completion and topology
The Hasse-Arf Theorem

Groupe de travail on Local fields > webpage

Aix-Marseille Université, Marseille, FR, 2020/2021

> notes   notes

Ternary forms
Local fields and ternary quadratic forms

Groupe de travail on Quaternion algebras > webpage

Aix-Marseille Université, Marseille, FR, 2019/2020

> notes   notes

Quadratic forms
Modular functions and complex multiplication

Groupe de travail on "Primes of the form x^2 + ny^2"

Aix-Marseille Université, Marseille, FR, 2018/2019

> notes   notes

Modular forms and Galois representations

Graduate student seminar on modularity and the proof of Fermat's Last Theorem > webpage

Concordia University & McGill University, Montreal, CA, Winter 2016.

> notes

Iwasawa algebras and p-adic Measures

Graduate student seminar on Iwasawa theory > webpage

Concordia University & McGill University, Montreal, CA, Fall 2016.

> notes

SCHOOLS

  1. Orienting supersingular isogeny graphs

    Isogeny-based cryptography school (Bristol, UK) - Online.

SCHOOLS

Orienting supersingular isogeny graphs

Isogeny-based cryptography school (Bristol, UK) - Online, Jul. 2021.

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