Christian Lucius Urech
Fields of expertise
My research interests include: Cremona groups, groups of birational transformations, degree sequences, polynomial automorphisms of affine spaces, classical algebraic geometry, birational geometry, affine algebraic geometry, algebraic group actions, geometric group theory, actions of groups on CAT(0) cube complexes, asymptotically rigid mapping class groups.
Biography
- since 2019: Bernoulli Instructor at EPFL
- 2018-2019: Postdoc at Imperial College London
- 2013-2017: PhD in Mathematics at the University of Basel and the University of Rennes 1. Advisors: Jérémy Blanc and Serge Cantat.
Research
Publications
Preprints:
1. A. Genevois, A. Lonjou, C. Urech, ``'Cremona groups over finite fields, Neretin groups, and non-positively curved cube complexes'' https://arxiv.org/abs/2110.14605
2. A. Genevois, A. Lonjou, C. Urech, ``Asymptotically rigid mapping class groups II: strand diagrams and nonpositive curvature'' https://arxiv.org/abs/2110.06721
1. A. Genevois, A. Lonjou, C. Urech, ``'Cremona groups over finite fields, Neretin groups, and non-positively curved cube complexes'' https://arxiv.org/abs/2110.14605
2. A. Genevois, A. Lonjou, C. Urech, ``Asymptotically rigid mapping class groups II: strand diagrams and nonpositive curvature'' https://arxiv.org/abs/2110.06721
Published/accepted papers:
3. A. Liendo, R. Regeta, C. Urech, ``Characterization of affine toric varieties by their automorphism groups", https://arxiv.org/abs/1805.03991, accepted for publication in Annali della Scuola Normale Superiore di Pisa
4. A. Genevois, A. Lonjou, C. Urech, ``Asymptotically rigid mapping class groups I: Finiteness properties of braided Thompson's and Houghton's groups'', https://arxiv.org/abs/2010.07225, accepted for publication in Geometry & Topology
5. C. Urech, S. Zimmermann, ``Continuous automorphisms of Cremona groups'', https://arxiv.org/abs/1909.11050, International Journal of Mathematics, Vol. 32, No. 04, 2150019 (2021).
6. A. Lonjou, C. Urech, ``Actions of Cremona groups on CAT(0) cube complexes'', https://arxiv.org/abs/2001.00783, accepted for publication in the Duke Mathematical Journal
3. A. Liendo, R. Regeta, C. Urech, ``Characterization of affine toric varieties by their automorphism groups", https://arxiv.org/abs/1805.03991, accepted for publication in Annali della Scuola Normale Superiore di Pisa
4. A. Genevois, A. Lonjou, C. Urech, ``Asymptotically rigid mapping class groups I: Finiteness properties of braided Thompson's and Houghton's groups'', https://arxiv.org/abs/2010.07225, accepted for publication in Geometry & Topology
5. C. Urech, S. Zimmermann, ``Continuous automorphisms of Cremona groups'', https://arxiv.org/abs/1909.11050, International Journal of Mathematics, Vol. 32, No. 04, 2150019 (2021).
6. A. Lonjou, C. Urech, ``Actions of Cremona groups on CAT(0) cube complexes'', https://arxiv.org/abs/2001.00783, accepted for publication in the Duke Mathematical Journal
7. A. Liendo, R. Regeta, C. Urech, `` On the characterization of Danielewski surfaces by their automorphism group", https://arxiv.org/abs/1905.00423, Transformation Groups (2020). https://doi.org/10.1007/s00031-020-09606-z.
8. C. Urech, ``Simple groups of birational transformations in dimension two", https://arxiv.org/abs/1802.09258, Commentarii Mathematici Helvetici, Vol. 95, Issue 2, 2020, pp. 211–246.
9. C. Urech, ``Subgroups of elliptic elements of the Cremona group", https://arxiv.org/abs/1606.04822, Journal für die reine und angewandte Mathematik (Crelles Journal), 2021, Issue 770, pp. 27-57.
10. C. Urech, S. Zimmermann, ``A new presentation of the plane Cremona group", Proc. Amer. Math. Soc. 147 (2019), no. 7, 2741–2755.
11. C. Urech, ``Remarks on the degree growth of birational transformations", https://arxiv.org/abs/1802.02735, Mathematical Research Letters, Vol. 25, No. 1 (2018), pp. 291-308
12. C. Urech, ``On homomorphisms between Cremona groups", https://arxiv.org/abs/1603.03294, Annales de l'Institut Fourier, Vol. 68, No. 1 (2018), pp. 53-100.
8. C. Urech, ``Simple groups of birational transformations in dimension two", https://arxiv.org/abs/1802.09258, Commentarii Mathematici Helvetici, Vol. 95, Issue 2, 2020, pp. 211–246.
9. C. Urech, ``Subgroups of elliptic elements of the Cremona group", https://arxiv.org/abs/1606.04822, Journal für die reine und angewandte Mathematik (Crelles Journal), 2021, Issue 770, pp. 27-57.
10. C. Urech, S. Zimmermann, ``A new presentation of the plane Cremona group", Proc. Amer. Math. Soc. 147 (2019), no. 7, 2741–2755.
11. C. Urech, ``Remarks on the degree growth of birational transformations", https://arxiv.org/abs/1802.02735, Mathematical Research Letters, Vol. 25, No. 1 (2018), pp. 291-308
12. C. Urech, ``On homomorphisms between Cremona groups", https://arxiv.org/abs/1603.03294, Annales de l'Institut Fourier, Vol. 68, No. 1 (2018), pp. 53-100.
Other texts:
C. Urech,``Subgroups of Cremona groups'', PhD Thesis at the University of Basel and the University of Rennes 1. Advisors: Jérémy Blanc and Serge Cantat.
C. Urech, ``On automorphisms of the affine Cremona group'', Master's Thesis at the University of Basel. Advisor: Hanspeter Kraft.
C. Urech, “Subgroups of elliptic elements of the plane Cremona group”, in: Oberwolfach Report 28/2018.
C. Urech, ``On automorphisms of the affine Cremona group'', Master's Thesis at the University of Basel. Advisor: Hanspeter Kraft.
C. Urech, “Subgroups of elliptic elements of the plane Cremona group”, in: Oberwolfach Report 28/2018.
Teaching & PhD
Teaching
Mathematics