## Prof. Dr. Timo Richarz

### Contact

richarz@mathematik.tu-...

work +49 6151 16-22471

Work
S2|15 414

Schlossgartenstraße 7

64289
Darmstadt

- Seminar, Tuesdays, 14:00-15:30: GAUS AG on Vector bundles on Curves (joint with T. Wedhorn)
- Seminar, Fridays, 15:30-17:00: ERC Seminar on Arithmetic Geometry

- Seminar, Tuesdays, 14:00-15:30: GAUS AG on Chromatic Homotopy Theory
- Seminar, Fridays, 15:30-17:00: ERC Seminar on Arithmetic Geometry
- Lecture course, Tuesdays, 9:50-11:30 and Fridays, 11:40-13:20: Algebraic number theory (Exercises by Ronald Solodov, Wednesdays, 11:40-13:20)
- Workshop, Heidelberg, September 9-13, 2024: Ramification in geometric Langlands and non-abelian Hodge theory (joint with A. Hohl, J. Horn, K. Jakob and J. Ludwig)
- Oberwolfach Seminar, October 20-25, 2024: Reduction of Arithmetic Varieties (joint with T. Haines, E. Viehmann and T. Wedhorn)

**Winter term 2023/2024:**- Seminar, Thursdays, 15:00-16:30: GAUS AG on Rigid analytic motives
- Seminar, Fridays, 15:30-17:00: ERC Seminar on Arithmetic Geometry
- Lecture course, Fridays, 11:40-13:20: Intersection Theory (Exercises by R. Ciloglu: Mondays, 9:50-11:30)
- Conference, 2-6 Oct 2023: Arithmetic Algebraic Geometry (joint with E. Hellmann, A. Mihatsch, E. Viehmann)
- Conference, 23-27 Oct 2023: Geometric and categorical representation theory (joint with A. Lacabanne, S. Riche)

- Seminar: Seminar on Arithmetic Geometry(joint with S. Pauli, T. Wedhorn)
- Seminar: Moduli spaces of L-parameters (opens in new tab) (joint with G. Böckle, T. van den Hove, J. Ludwig and T. Wedhorn)
- Seminar: Non-hypergeometric E-functions (opens in new tab) (K. Jakob, G. Bogo)
- Research School: Condensed Mathematics (joint with S. Morel, A.-C. Le Bras, V. Pilloni)
- Conference: Arithmetic Algebraic Geometry (joint with U. Görtz, T. Wedhorn)
- Seminar: Étale motives (joint with R. Çiloglu, T. van den Hove)
- Conference: Women in Arithmetic Geometry (joint with K. Hübner, H. Krieger)
- Workshop: Clermont-Darmstadt workshop on the geometric Satake equivalence
- Lecture Course: Algebraic Geometry II (opens in new tab) (joint with T. Wedhorn)
- Lecture Course: Einführung in die Algebra (opens in new tab)
- Lecture Course: Introduction to the Langlands program (opens in new tab)
- Seminar: Condensed Mathematics (opens in new tab) (joint with T. Wedhorn)
- Lecture Course: Galois Cohomology (opens in new tab)
- Seminar: Homological Algebra and sheaves (opens in new tab) (joint with T. Wedhorn)
- Seminar: ZAGA – Zoom Algebraic Geometry and Arithmetic (joint with U. Görtz, E. Hellmann, A. Mihatsch, T. Richarz, M. Rapoport, P. Scholze, E. Viehmann).
- Summer School Luminy, 2019: Notes on affine Grassmannians (opens in new tab)
- Lecture Course: Algebraic Geometry II (opens in new tab) (joint with T. Wedhorn)
- Lecture Course: Algebraic Geometry I (opens in new tab)
- Lecture Course: Weil Conjectures (opens in new tab)
- Workshop: Infinity Categories (joint with T. Wedhorn)
- Lecture Course: (Pro-)Étale Cohomology (opens in new tab) (joint with T. Wedhorn)
- Seminar: Masterseminar on Stacks (joint with J. Heinloth)
- Seminar: Research Seminar Arithmetic Geometry
- Seminar: The Fargues-Fontaine Curve
- Seminar: Research Seminar Arithmetic Geometry
- Seminar (joint with M. Wong): Research Seminar Arithmetic Geometry
- Exercises: Algebra II
- Exercises: Algebra I
- Exercises: Einführung in die Algebra (Introduction to Algebra)
- Seminar: The unramified Drinfeld Langlands correspondence (opens in new tab)

Chirantan Chowdhury, 04/2024 — present

Paul Ziegler, 10/2023 — present

Fabio Tanania, 06/2023 — present

Konstantin Jakob, 04/2022 — present

Moritz Dittmann, 08/2022 — 09/2023

Paul Siemon, 05/2023 — present

Rızacan Çiloğlu, 04/2022 — present

Thibaud van den Hove, 10/2021 — present

Patrick Bieker 04/2019 – 10/2022, Integral Models of Moduli Spaces of Shtukas with Deep Level Structures

- Varun Kumar, 11/2022 — 05/2023, Minimal degeneration singularities in the affine Grassmannian for PGL2 over Z (opens in new tab)
- Helena Kuhr, 05/2022 — 11/2022, Arc descent for constructible adic sheaves (opens in new tab)
- Benedikt Müller, 04/2022 — 10/2022, Drinfeld’s Lemma for Schemes (opens in new tab)

- Moritz Reinhard, 11/2023 – 04/2024, Unendliche Galoistheorie (opens in new tab)

- A categorical Künneth formula for constructible Weil sheaves (with Tamir Hemo, Jakob Scholbach), Algebra and Number theory, Vol. 18 (2024), No. 3, 499-536, Journal,arXiv.
- Constructible sheaves on schemes (with Tamir Hemo, Jakob Scholbach), Advances in Mathematics, Volume 429 (2023), 109-179, Journal, arXiv.
- Néron blowups and low-degree cohomological applications (with Arnaud Mayeux, Matthieu Romagny), Algebraic Geometry, Volume 10, Issue 6 (2023), 729-753, Journal, arXiv.
- On the normality of Schubert varieties: Remaining cases in positive characteristic (with Thomas J. Haines, João N. P. Lourenço), accepted 2023 in Annales scientifiques de l’ENS, arXiv.
- Normality and Cohen-Macaulayness of Parahoric Local Models (with Thomas J. Haines), Journal of the European Mathematical Society, Vol. 25, No. 2 (2023), 703-729, Journal, arXiv.
- Tate motives on Witt vector affine flag varieties (with Jakob Scholbach), Selecta Mathematica 27 (2021), Journal, arXiv.
- The motivic Satake equivalence (with Jakob Scholbach), Mathematische Annalen 380 (2021), 1595-1653. Journal, arXiv.
- The Test Function Conjecture for Parahoric Local Models (with Thomas J. Haines), Journal of the American Mathematical Society 34 (2021), 135-218. Journal, arXiv.
- Smoothness of Schubert varieties in twisted affine Grassmannians (with Thomas J. Haines), Duke Math. Journal 169 (2020), 3223-3260. Journal, arXiv.
- The Test Function Conjecture for Local Models of Weil-restricted groups (with Thomas J. Haines), Compositio Mathematica 156 (2020), 1348-1404. Journal, arXiv.
- The intersection motive of the moduli stack of shtukas (with Jakob Scholbach), Forum of Mathematics, Sigma 8 (2020), 1-99. Journal, arXiv, Corrigendum (opens in new tab) .
- Spaces with G
_{m}-action, hyperbolic localization and nearby cycles, Journal of Algebraic Geometry 28 (2019), 251-289. Journal, arXiv. - On the Iwahori Weyl group, Bulletin de la SMF 144 (2016), 117- 124. Journal, arXiv.
- Affine Grassmannians and geometric Satake equivalences, Int. Math. Res. Not. 12 (2016), 3717-3767. Journal, arXiv, Erratum (opens in new tab).
- Construction of the full Langlands dual group via the geometric Satake correspondence (with Xinwen Zhu), Appendix to Xinwen Zhu: The geometric Satake correspondence for ramified groups, Annales scientifiques de l’ENS 48 (2015), 409-451. Journal, arXiv.
- A new approach to the geometric Satake equivalence, Documenta Mathematica 19 (2014), 209-246. Journal, arXiv.
- Schubert varieties in twisted affine flag varieties and local models, Journal of Algebra 375 (2013), 121-147. Journal, arXiv.

- A modular ramified geometric Satake equivalence (with Pramod N. Achar, João N. P. Lourenço, Simon Riche), 79 pages, preprint Mar 2024, arXiv.
- Frobenius Rigidity in A^1-homotopy theory (with Jakob Scholbach), 16 pages, preprint Mar 2024, arXiv.
- Normality of Schubert varieties in affine Grassmannians (with Patrick Bieker), 14 pages, preprint Dec 2023, arXiv.
- Fixed points under pinning-preserving automorphisms of reductive group schemes (with Pramod N. Achar, João N. P. Lourenço, Simon Riche), 36 pages, preprint Dec 2022, arXiv.
- Singularities of local models (with Najmuddin Fakhruddin, Thomas J. Haines, João N. P. Lourenço), 32 pages, preprint Aug 2022, arXiv.
- On the p-adic theory of local models (with Johannes Anschütz, Ian Gleason, João N. P. Lourenço), 53 pages, preprint Jan 2022, arXiv.

- Categorical Künneth formula for Weil sheaves, OWR 2021
- Non-normality of Schubert varieties, OWR 2021
- Cohen-Macaulayness of local models, OWR 2020
- The test function conjecture for parahoric local models, OWR 2019
- The stack Bun and Hecke stacks, OWR 2017
- Affine Grassmannians and Geometric Satake Equivalences, OWR 2014

### Research interests

Arithmetic algebraic geometry, Langlands program, moduli spaces of bundles, geometric representation theory

### Current appointment

Since 2019: Professor, Technical University of Darmstadt, Germany

### Studies

2006-2014: Diploma and PhD in Mathematics, Bonn University, Germany

Advisor: Michael Rapoport

### Selected publications

- The Test Function Conjecture for Parahoric Local Models (with Thomas J. Haines), Journal of the American Mathematical Society 34 (2021), 135-218.
- The motivic Satake equivalence (with Jakob Scholbach), Mathematische Annalen 380 (2021), 1595-1653.
- Smoothness of Schubert varieties in twisted affine Grassmannians (with Thomas J. Haines), Duke Math. Journal 169 (2020), 3223-3260.

### Awards and grants

- 2022, LOEWE-Start-Professur
- 2021, PI in ERC Starting Grant MotLang
- 2021, PI in Subprojects B07, C04 of Collaborative Research Center 326 – GAUS
- 2020, Partner in ERC Consolidator Grant RedLang of Simon Riche

### Detailed CV

For more information, please consult my detailed CV (opens in new tab) .

Project – MotLang (opens in new tab) , PRj, pages 82-85, Oct 2022

Mathematik ist ein sehr interaktiver Prozess, May 2022

LOEWE-Start-Professur, May 2022

Drei Millionen Euro für Pionierprojekte, Jan 2022