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. Orientations, modular symbols and p-adic periods for cryptography

    JMM, AMS Special Session on Mathematics of Isogeny-Based Cryptography (Washington, DC, USA) > Slides

  2. From orientations to p-adic period vectors: the modular symbol inversion problem

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

  3. Supersingular isogeny graphs and Galois representations

    William Tutte Colloquium (Waterloo, Canada) > Slides

  4. Orientations and class group actions

    Crypto Research Seminar (Waterloo, Canada) > Slides

  5. Modular and formal orientations: beyond OSIDH

    Isogeny Club > Slides

  6. Oriented supersingular elliptic curves and class group actions

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

  7. Oriented supersingular elliptic curves and class group actions

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

  8. Oriented supersingular elliptic curves and class group actions

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

  9. A modular approach to OSIDH

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

  10. A modular approach to OSIDH

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

  11. Orienting supersingular isogeny graphs

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

  12. Orienting supersingular isogeny graphs

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

  13. Orienting supersingular isogeny graphs

    Sèminaire de Cryptographie (Rennes, France) > Slides

  14. Orienting supersingular isogeny graphs

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

  15. Orienting supersingular isogeny graphs

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

  16. Orienting supersingular isogeny graphs

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

  17. Orienting supersingular isogeny graphs

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

CONFERENCES & SEMINARS

Orientations, modular symbols and p-adic periods for cryptography

AMS Special Session on Mathematics of Isogeny-Based Cryptography, I, JMM (Washington, DC, USA), Jan. 2026 > Slides

From orientations to p-adic period vectors: the modular symbol inversion problem.

Sèminaire ATI - Arithmètique et Thèorie de l'Information (Marseille, France), Dec. 2025 > Slides

Supersingular isogeny graphs and Galois representations

Tutte Colloquium (Waterloo, Canada), July. 2024 > Slides

Orientations and class group actions

Crypto Research Seminar (Waterloo, Canada), Oct. 2023 > Slides

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

READING GROUPS

  1. IS-CUBE: An isogeny-based compact KEM using a boxed SIDH diagram

    Reading group on Advanced KEMs/PKE > webpage
    University of Waterloo, Waterloo, ON, CA

  2. CSI-Otter: Isogeny-based Blind Signatures from the Class Group Action

    Reading group on Signature schemes with post-quantum approach > webpage
    University of Waterloo, Waterloo, ON, CA

  3. Weil's bounds

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

  4. Completion and topology

    The Hasse-Arf Theorem

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

  5. Ternary Forms

    Local fields and ternary quadratic forms

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

  6. 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

  7. 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

  8. Iwasawa algebras and p-adic Measures

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

READING GROUPS

IS-CUBE: An isogeny-based compact KEM using a boxed SIDH diagram

Reading group on Advanced KEMs/PKE > webpage

University of Waterloo, Waterloo, ON, CA

CSI-Otter: Isogeny-based Blind Signatures from the Class Group Action

Reading group on Signature schemes with post-quantum approach > webpage

University of Waterloo, Waterloo, ON, CA

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. The Sato–Tate and Galois representations

    CIMPA School on Effective Algebra and the LMFDB (Kampala, UG).

  2. Orienting supersingular isogeny graphs

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

SCHOOLS

The Sato–Tate and Galois representations

IMPA School on Effective Algebra and the LMFDB (Kampala, UG), Jan. 2025.

Orienting supersingular isogeny graphs

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

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