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A list of all the posts and pages found on the site. For you robots out there is an XML version available for digesting as well.
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Posts
Perpendicular lines
Published:
Perpendicular lines
A fact about lines, taught midway through highschool where I live, is that two lines with slope $m$ and $-1/m$ are perpendicular. As it is often the case with simple facts, we can show this in many different ways by using more or less justified techniques. In this document, I want to explore different proofs that are well justified and motivated.
publications
On the Northcott property of zeta functions over function fields
Published in Finite Fields and Their Applications, 2022
Joint work with Matilde Lalín and Wanlin Li
Recommended citation: Xavier Généreux, Matilde Lalín, Wanlin Li, On the Northcott property of zeta functions over function fields, Finite Fields and Their Applications, Volume 83, 2022, 102080, ISSN 1071-5797, https://www.sciencedirect.com/science/article/abs/pii/S1071579722000892
On the Northcott property of Dedekind zeta functions
Published in The Ramanujan Journal, 2024
Joint work with Matilde Lalín
Recommended citation: Généreux, Xavier, and Matilde Lalín. "On the Northcott property of Dedekind zeta functions", Ramanujan J. 63 (2024), no. 4, 1135--1178. https://link.springer.com/article/10.1007/s11139-023-00809-y
Incremental Forward Reasoning for White-Box Proof Search
To appear in TACAS 2026, 2025
Joint work with Jannis Limperg
Recommended citation: Jannis Limperg and Xavier Généreux, Incremental Forward Reasoning for White-Box Proof Search, 2025,
talks
Number theory in a parallel world (translated)
Published:
Talk exploring elementary number theory results over the field of functions $\mathbb F_q (t)$.
On the Northcott property of zeta functions over function fields
Published:
Talk on my joint work with Wanlin Li and Matilde Lalin on the Northcott property of $\zeta$-functions over function fields.
The Northcott property of zeta functions over families of extensions
Published:
Talk on my joint work with Matilde Lalin on the Northcott property of Dedekind $\zeta$-functions over number fields.
Efficient Forward Reasoning for Aesop
Published:
Talk on my joint work with Jannis Limperg on incremental forward reasoning.
Formalization of Drinfeld Modules
Published:
Talk on my joint work with María Inés de Frutos Fernández on the formalization of Drinfeld Modules.
teaching
Teaching assistant: Group Theory
Undergraduate course, Université de Montréal, Département de mathématiques et statistique, 2021
I was the TA of Olivier Mila for the intro class to group theory.
Teaching assistant: Group Theory
Undergraduate course, Université de Montréal, Département de mathématiques et statistique, 2022
I was the TA of Matilde Lalín for the intro class to group theory. The course follows more or less the first few chapters of Dummit and Foote.
Teaching assistant: Rings and Modules
Undergraduate course, Université de Montréal, Département de mathématiques et statistique, 2023
I was the TA of Matilde Lalín for the intro class to rings and modules. The course followed the excellent notes by Dimitris Koukoulopoulos.
Seminar: Algebra and Computer Science
Undergraduate course, Ludwig-Maximilians-Universität München, Lehr- und Forschungseinheit für Theoretische Informatik und Theorembeweisen, 2024
I led a seminar on the application of algebra to computer science. See the course’s page.
Teaching assistant: Interative Theorem Proving
Graduate course, Ludwig-Maximilians-Universität München, Lehr- und Forschungseinheit für Theoretische Informatik und Theorembeweisen, 2024
I was the TA of Jasmin Blanchette for Interactive Theorem Proving. The course followed The Hitchhiker’s Guide to Logical Verification.
Practical: Formalization In Lean
Graduate course, Ludwig-Maximilians-Universität München, Lehr- und Forschungseinheit für Theoretische Informatik und Theorembeweisen, 2024
I led a practical on formalization in Lean. See the course’s page.
Seminar: Algebra and Computer Science
Undergraduate course, Ludwig-Maximilians-Universität München, Lehr- und Forschungseinheit für Theoretische Informatik und Theorembeweisen, 2025
I will lead a seminar on the application of algebra to computer science. See the course’s page.
Teaching assistant: Interative Theorem Proving
Graduate course, Ludwig-Maximilians-Universität München, Lehr- und Forschungseinheit für Theoretische Informatik und Theorembeweisen, 2025
I will be the TA of Jasmin Blanchette for Interactive Theorem Proving. The course followed The Hitchhiker’s Guide to Logical Verification.