master thesis
In my master thesis, I calculate the étale cohomology (with torsion coefficients) of Fargues-Scholze's stack \( \mathrm{Bun}_G \) for \( G = \mathrm{GL}_2 \). More precisely, I can show that the inclusion \(\mathrm{Bun}_2^{\mathrm{ss}} \hookrightarrow \mathrm{Bun}_2 \) of the semi-stable locus induces an isomorphism on étale cohomology. This calculation involves a proof that the dualizing complex \( R(\mathrm{Bun}_2 \to \mathrm{Spd}(\overline{\mathbb{F}}_q))^{!}\Lambda\) is given just by \( \Lambda \) itself. I am currently trying to remove the errors in a previous version, and will upload a new one as soon as this is done.
lecture notes
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Condensed Mathematics
(Lecture notes for a lecture by A.C. Le Bras, LAGA, Summer 2022) -
Hochschild (Co)Homology
(Lecture notes for a lecture by P. Belmans, Bonn, Summer 2021)
seminar talks
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Waldhausen \(S\)-construction
(Graduate Seminar on Higher Segal spaces, October 2023) -
Cohomology of Galois Gerbes
(Graduate Seminar on the local Langlands conjecture for non quasi-split groups, July 2023) -
Motivic aspects of mixed Hodge theory
(Graduate Seminar on Motivic aspects of Hodge theory, June 2023) -
Tannakian Reconstruction and semi-simplicity of the Satake category
(Kleine AG on Satake equivalence, March 2023)