PhD student at Paris 13 - saunier (?) math.univ-paris13.fr

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.

- 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.

- A twisted Shaneson splitting for Poincaré categories, joint with Gugliermo Nocera. Upcoming.
- Untitled manuscript answering questions about heart structures, joint with Christoph Winges. Upcoming.
- Untitled manuscript on trace methods for stable ∞-categories, joint with Yonatan Harpaz and Thomas Nikolaus. Upcoming (and likely to split in multiple papers).

- 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*.

- 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*.

- 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*