Squares in Dortmund
31 March - 4 April 2025
A conference on quadratic forms and related topics -
on the occasion of Detlev Hoffmann's 64th birthday
Invited Speakers
- Olivier Benoist (Paris)
- Greg Blekherman (Georgia Tech)
- David Leep (Kentucky)
- Vlerë Mehmeti (Paris)
- Anne Quéguiner-Mathieu (Paris)
- Gabriele Nebe (Aachen)
- R. Parimala (Emory)
- Federico Scavia (Paris)
- Stephen Scully (Victoria)
- Alexander Vishik (Nottingham)
Organizers
Karim Johannes BecherDaniel Plaumann
The conference is supported by Deutsche Forschungsgemeinschaft.
Participants
Vincent Astier (University College Dublin)Karim Johannes Becher (University of Antwerp)
Eberhard Becker (TU Dortmund)
Olivier Benoist (CNRS Paris)
Nicolas Grenier-Boley (University of Rouen Normandy)
Adam Chapman (Academic College of Tel-Aviv Yaffo)
Safiétou Cissé (University of Antwerp)
Nicolas Daans (KU Leuven)
Ido Efrat (Ben-Gurion University)
Uriya First (University of Haifa)
Mathieu Florence (Sorbonne University)
Nicolas Garrel (University of Antwerp)
Stefan Gille (University of Alberta)
Dustin Hegner (TU Dortmund)
Detlev Hoffmann (TU Dortmund)
Franz Kalhoff (TU Dortmund)
Jakub Krásenský (Czech Technical University, Prague)
Ahmed Laghribi (Artois University)
David Leep (University of Kentucky)
Nico Lorenz (Ruhr University Bochum)
Anne Quéguiner-Mathieu (Sorbonne University)
Vlerë Mehmeti (Sorbonne University)
Archita Mondal (University of Antwerp)
Anton Mors (TU Dortmund)
Gabriele Nebe (RWTH Aachen)
R. Parimala (Emory University)
Albrecht Pfister (University of Mainz)
Daniel Plaumann (TU Dortmund)
Nils Poprawski (TU Dortmund)
Om Prakash (Charles University, Prague)
Remi Rasson (University of Antwerp)
Federico Scavia (Sorbonne University)
Rudolf Scharlau (TU Dortmund)
Claus Scheiderer (University of Konstanz)
Alexander Schönert (TU Dortmund)
Stephen Scully (University of Victoria)
Pavel Sechin (University of Regensburg)
Michele Serra (TU Dortmund)
Rainer Sinn (University of Leipzig)
Abhay Soman (University of Hyderabad)
Azad Tasan (Cote d'Azur University)
Magdaléna Tinková (Czech Technical University, Prague)
Thomas Unger (University College Dublin)
Jan Van Geel (University of Ghent)
Alexander Vishik (University of Nottingham)
Jannik Wesner (TU Dortmund)
Magnus Wiedeking (TU Dortmund)
Pavlo Yatsyna (Charles University, Prague)
Jongheun Yoon (Charles University, Prague)
Marco Zaninelli (University of Pennsylvania)
Maksim Zhykhovich (LMU Munich)
Marc Zimmermann (University of Cologne)
Talks and Schedule
Programme and Abstracts (pdf)Monday, 31 March
| 9:00 | Welcome | |
| 9:15-10:15 | O. Benoist: Sums of squares of analytic functions | |
| Notes | ||
| - Coffee break - | ||
| 10:45-11:15 | M. Zaninelli: Sums of squares in hyperelliptic function fields | |
| 11:30-12:30 | G. Nebe: Orthogonal representations of finite groups | |
| Slides | ||
| - Lunch - | ||
| 14:30-15:00 | J. Krásenský: Sums of integral squares in totally real number fields | |
| Slides | ||
| 15:10-15:40 | M. Tinková: Bounds on the Pythagoras number and indecomposables in biquadratic fields | |
| Slides | ||
| - Coffee break - | ||
| 16:10-16:40 | J. Yoon: Minimal rank of primitively n-universal quadratic forms over local fields | |
| Slides | ||
| 16:50-17:20 | O. Prakash: Universality beyond quadratic forms | |
| Slides |
Tuesday, 1 April
| 9:15-10:15 | A. Vishik: Varieties and pure symbols | |
| - Coffee break - | ||
| 10:45-11:15 | P. Sechin: Morava motives of quadrics | |
| 11:30-12:30 | S. Scully: On the holes in I^n for symmetric bilinear forms in characteristic 2 | |
| - Lunch - | ||
| 14:30-15:00 | N. Lorenz: Isotropy indices of Pfister multiples in characteristic 2 | |
| Slides | ||
| 15:10-15:40 | A. Laghribi: Around the 3-Pfister number in characteristic 2 | |
| - Coffee break - | ||
| 16:10-16:40 | A. Schönert: Witt rings of fields with 64 square classes | |
| 16:50-17:20 | N. Garrel: Adams operations on hermitian forms | |
| Slides |
Wednesday, 2 April
| 9:15-10:15 | F. Scavia: The lifting problem for Galois representations |
|
| References: arXiv:2410.12560, arXiv:2501.18906 | ||
| - Coffee break - | ||
| 10:45-11:15 | R. Sinn: Graded Pythagoras numbers | |
| References: arXiv:2101.05773, arXiv:1606.04387, arXiv:2410.17123 | ||
| 11:30-12:30 | E. Becker: A Waring problem for real function fields over R | |
| References: Seminaire de Structures Algebriques Ordonnees: 1) A note on sums of powers in real algebraic function fields over R, No. 91, 2015-2016, Mai 2017; 2) Sums of powers in real function fields and topology, 2018-2020, Fevrier 2021 (p.131); A note on approximation and homotopy in C(X,Sn), n=1,3,7 | ||
| - Lunch - | ||
| 13:45 | Excursion to Zeche Zollern (Taxi-transfer from university) | |
| 19:00 | Conference Dinner at Restaurant Schönes Leben |
Thursday, 3 April
| 9:15-10:15 | A. Quéguiner-Mathieu: Higher Tate trace and classification of Chow motives | |
| References: arXiv:2403.11030, Higher Tate traces of Chow motives (J. Reine und angewandte Mathematik) | ||
| - Coffee break - | ||
| 10:45-11:15 | M. Zhykhovich: The J-invariant of algebraic groups of outer type and symplectic involutions | |
| Reference: arXiv:2205.02884 | ||
| 11:30-12:30 | R. Parimala: Projective homogeneous spaces and Hasse principle | |
| - Lunch - | ||
| 14:30-15:00 | A. Mondal: R-triviality of groups of projective similitudes over special fields | |
| 15:10-15:40 | A. Chapman: Zeros of multivariate quaternionic polynomials | |
| Reference: arXiv:2408.08246 | ||
| - Coffee break - | ||
| 16:10-16:40 | U. First: The number of generators of Azumaya algebras with involution | References: On the number of generators of an algebra over a commutative ring (Transactions AMS), Spaces of generators for matrix algebras with involution (Linear and Multilinear Algebra), Spaces of generators for Azumaya algebras with unitary involution (J. Pure and Applied Algebra) |
| 16:50-17:20 | A. Soman: Totally positive field extensions and Pythagorean index | |
| Slides |
Friday, 4 April
| 9:15-10:15 | V. Mehmeti: Local-global principles and the u-invariant | |
| - Coffee break - | ||
| 10:45-11:15 | N. Daans: Linkage of Pfister forms over local and semi-global fields | |
| 11:30-12:30 | D. Leep: Systems of quadratic forms and u-invariants |
