Victor Saunier

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.

Thesis

• Trace methods for stable categories, (🔗 Local final version, see also the historic of versions)

Conferences and colloquiums

• Non-commutative motives of Poincaré categories as localisation, at GAUS Workshop: Motives and Higher Categories in Mainz. October 2025. (Beamer upcoming)
• 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.

Local team seminars

• c-categories and trace methods beyond connective rings (after Levy and Sosnilo) (October 2025)
• 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.

Lecture on Topological Hochschild homology (Winter 2025)

Held on Thursdays from 12h30 to 14h, usually in M4-122/126 --- see ekVV. I will upload notes once they are written.

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