Institut für Mathematik Universität Heidelberg | Deutsch English Français Italiano | |

Christian Dahlhausen

Institut für Mathematik

Im Neuenheimer Feld 205

69120 Heidelberg

Germany

email: c {no space} surname }at{ mathi.uni-heidelberg.de (PGP key)

phone: +49 6221 54 14216

office: 03.324

office hour: by appointment

About me

I am a postdoc in the working group of Alexander Schmidt at the Institute for Mathematics at the Faculty of Mathematics and Computer Science at the University of Heidelberg. Furthermore, I am a member of CRC326 - GAUS: "Geometry and Arithmetic of Uniformizing Structures". My research areas are K-theory and Nonarchimdedean Homotopy Theory.During the academic year 2019/20 I was a postdoc in the working group of Andrew Kresch at the Institute of Mathematics at the University of Zurich and financed by the Swiss National Science Foundation. Until September 2019 I was a PhD student at the Faculty of Mathematics at the University of Regensburg. My PhD thesis is about continuous K-theory and its relation to the cohomology of rigid spaces. My advisors were Moritz Kerz and Georg Tamme. I was a member of the DFG GRK 1692 “Curvature, Cycles, and Cohomology” and I was partially supported by the DFG SFB 1085 “Higher Invariants”.

I wrote my master's thesis “Milnor K-theory of integers of p-adic local fields” and my bachelor's thesis “Serres Problem und der Satz von Quillen-Suslin” (Serre's problem and the Quillen-Suslin theorem) both with Moritz Kerz.

Publications and Preprints

Towards A^1-homotopy theory of rigid analytic spaces (joint with Can Yaylali). (arXiv:2407.09606 )Regularity of semi-valuation rings and homotopy invariance of algebraic K-theory. (arXiv:2403.02413)

Continuous K-Theory and Cohomology of Rigid Spaces,

K-Theory of admissible Zariski-Riemann spaces,

On continuous K-theory and cohomology of rigid spaces,

Milnor K-theory of complete discrete valuation rings with finite residue fields,

Notes

A counterexample to pro-cdh descent for non-noetherian schemes (PDF)Organised Events

09/2023: Fall School "Algebraic K-Theory and Redshift" (together with Lorenzo Mantovani and Georg Tamme)02/2023: GAUS-workshop "Condensed Mathematics and K-Theory" (together with Georg Tamme)

Talks, Posters etc.

05/2024: Invited talk on Towards A^1-homotopy theory of rigid analytic spaces at the Mathematics Institute of the University of Warwick.11/2023: Invited talk (online) on

11/2023: Invited talk on Representability of analytic K-theory within a rigid analytic motivic homotopy category at the University of Zurich.

12/2020: Invited talk on K-theory of admissible Zariski-Riemann spaces at the University Freiburg.

06/2020: Invited talk on Continuous K-theory and K-theory of Zariski-Riemann spaces at the online conference Motives and What Not.

01/2020: Invited talk on Continuous K-theory and K-theory of Zariski-Riemann spaces at the University of Duisburg-Essen.

05/2019: Invited talk on Continuous K-theory and cohomology of rigid spaces at the University of Heidelberg.

05/2019: Invited talk on Continuous K-theory and cohomology of rigid spaces at the University Freiburg.

07/2018: Poster for the conference Berkovich spaces 30 years in Paris (pdf).

06/2018: Poster for the Homotopy Theory Summer in Berlin (pdf).

02/2018: Talk on Continuous K-theory and cohomology of analytic spaces at the conference K-theory, A1-homotopy and quadratic forms in Warwick.

05/2017-06/2017: Participant at the Hausdorff Trimester Program on K-theory and Related Fields in Bonn.

05/2017: Talk on Improved Milnor K-theory of valuation rings of local fields in Bonn (video).

Teaching (at University of Heidelberg)

WS 2024/25: Seminar on Quadradic Forms and Milnor-Witt K-Theory (together with Morten Lüders).SS 2024: Exercise class for the course Étale Cohomology 2 by Alexander Schmidt.

WS 2023/24: Course on Group Schemes.

WS 2023/24: Seminar on Homotopical Category Theory (together with Lukas Waas).

SS 2023: Exercise sheets for the course Algebraic Geometry 2 by Denis Vogel.

WS 2022/23: Seminar on K-theory of the integers and the Kummer-Vandiver Conjecture (together with Alexander Schmidt).

WS 2022/23: Exercise sheets and example class for the course Algebraic Geometry 1 by Denis Vogel.

SS 2022: Exercise sheets for the course Algebraic Number Theory 2 by Katharina Hübner.

SS 2022: Exercise sheets for the course Algebra 2 by Denis Vogel.

WS 2021/22: Seminar on Valuation Theory (together with Katharina Hübner).

SS 2021: Exercise sheets and example class for the course Algebra 2 by Alexander Schmidt.

WS 2020/21: Exercise sheets and example class for the course Algebraic Number Theory 2 by Denis Vogel.

WS 2020/21: Proseminar on p-adic numbers (together with Marius Leonhardt).

Teaching (at University of Zurich)

FS 2020: Course on Algebra and Topology (together with Lorenzo Mantovani).HS 2019/20: Seminar on Categories, Sheaves, and Locales.

HS 2019/20: Seminar on Prismatic Cohomology (together with Lorenzo Mantovani).

Teaching (at University of Regensburg)

SS 2019: Assistance and exercise class for the course Perfectoid Spaces by Georg Tamme.SS 2019: Higher Invariants Oberseminar on Resolution of Singularities in characteristic zero (together with Federico Binda and Johann Haas).

WS 2018-19: Seminar on Homotopical Methods (together with Denis-Charles Cisinski).

SS 2018: Seminar on Derived Categories and Sheaf Cohomology (together with Denis-Charles Cisinski).

WS 2014/15: Exercise class for the course Algebra by Patrick Forré.

SS 2014: Exercise class for the course Commutative Algebra by Uwe Jannsen.

WS 2013/14: Exercise class for the course Algebra by Guido Kings.

WS 2012/13: Exercise class for the course Linear Algebra I by Guido Kings.

SS 2012: Exercise corrector for the course “Einführung in die moderne Logik” (Introduction to modern logic) by Tim Kraft.

WS 2011/12: Exercise class for the course Linear Algebra II by Uwe Jannsen.

SS 2011: Exercise class for the course Linear Algebra I by Uwe Jannsen.

CV

since 10/2020: Postdoc at University of Heidelberg.10/2019-09/2020: Postdoc at University of Zurich.

07/2019: PhD (Dr. rer. nat) in Mathematics at University of Regensburg.

03/2015: Master of Science in Mathematics at University of Regensburg.

03/2013: Bachelor of Science in Mathematics at University of Regensburg.

06/2009: Final secondary exam at Staatliches Landschulheim Marquartstein.

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