Victor Saunier

Hello! I'm Victor Saunier, currently pursing a PhD in the Algebraic Topology team of Université Sorbonne Paris Nord, under the supervision of Yonatan Harpaz. I am a part of his 5-year ERC project on Foundations of Motivic Real K-theory and my interests span all things K-theory, with a distinct taste for higher categorical ideas. The goal of my thesis is to bring the celebrated Dundas-Goodwillie-McCarthy theorem to the context of stable ∞-categories and provide a proof for it which is purely ∞-categorical in its flavour.

◆ Research

Preprints & Papers

With Jordan Levin and Gugliermo Nocera, A model for the assembly map of bordism-invariant functors (🔗 Local version, arxiv). June 2025 Preprint.
With Christoph Winges, On exact categories and their stable envelopes (🔗 Local version, arxiv). February 2025 Submitted.
With Yonatan Harpaz and Thomas Nikolaus, Trace methods for stable categories I: The linear approximation of algebraic K-theory (🔗 Local version (sans serif font!), arxiv). November 2024 Preprint.
A Theorem of the Heart for the K-theory of Endomorphisms (🔗 Local version, arxiv). November 2023 Submitted.
The fundamental theorem of localizing invariants (🔗 Local version, Journal, arxiv). Annals of K-theory, Vol. 8, No. 4, 2023.

Projects

Trace methods for stable categories II: The cyclotomic trace map with Yonatan Harpaz and Thomas Nikolaus and Maxime Ramzi
Trace methods for stable categories III: Goodwillie approximations of localizing invariants with Yonatan Harpaz and Thomas Nikolaus and Maxime Ramzi
And even more in the series of papers on trace methods for stable ∞-categories, joint with Yonatan Harpaz and Thomas Nikolaus and Maxime Ramzi.
Exact categories of additive motives Upcoming.

◆ Talks and notes

Conferences and colloquiums

Categorical trace methods, at Recent Developments in Algebraic K-Theory in Warwick. April 2025.
Exact categories and their stable envelopes, at the oberseminar of Mathematics Münster. January 2025.
Categorical trace methods, at the seminar of the Université Paul-Sabatier in Toulouse. November 2024.
Trace methods for stable ∞-categories, at the Young Topologist Meeting in Münster. August 2024.
A generalized resolution theorem in K-theory, at the seminar of the University of Amsterdam. February 2024.
Trace methods for stable ∞-categories, at the seminar of the University of Regensburg. February 2024.
Trace methods for stable ∞-categories, at the seminar of the University of Lille. December 2023.
The universal property of THH and the Dundas-McCarthy theorem, at the oberseminar in University of Bonn. April 2023.
The universal property of THH and the Dundas-McCarthy theorem, at the workshop on Hermitian K-theory and THH at Radboud University Nijmegen. March 2023.
The "fundamental" theorem of localizing invariants (🔗), at the annual conference of the GDR Théorie de l'homotopie. October 2022. Beamer also accessible at the conference's webpage.

LAGA's algebraic topology team seminar

The Chain Rule (after Blans and Blom) (February 2025)
Compactifications and the six operations (🔗). (March 2024) also accessible at Geoffroy Horel's webpage.
Trace methods for stable ∞-categories. (October 2023)
Deformation theory and spherical Witt vectors. (November 2022)
Spectres et stabilisations d'∞-catégories (🔗). October 2021. Notes for the first talk of a workgroup on Gijs Heuts' thesis, also accessible at Geoffroy Horel's webpage. In French, but strongly inspired from Yonatan Harpaz's 2017 talk on a similar topic, available at his webpage.

◆ Teaching material

Geoffroy Horel's M2 course (2022-2023)

The TDs are held on Wednesday from 13h45 to 15h45, in Halles aux Farines (salle 475F). You can find below the Worksheets:

Worksheet I on model categories. Link to the pdf
Worksheet II on more model categories. Link to the pdf
Worksheet III on homotopical (co)limits & (very few) stable homotopy theory. Link to the pdf