I am a Senior Lecturer at ETH Zürich. Before that, I worked as a Bernoulli Instructor at EPFL and as a research associate at Imperial College London. I completed my PhD in 2017 at the University of Basel and the University of Rennes 1 under the supervision of Jérémy Blanc and Serge Cantat. Here you find my CV.

My research lies at the intersection of algebraic geometry, geometric group theory, and dynamics. I apply tools from geometric group theory to study Cremona groups. But I am excited by everything related to groups of birational transformations or polynomial automorphisms. Recently, I have also worked on braided Thompson’s groups and their finiteness properties.

Preprints

1. Group Theoretical Characterizations of Rationality, with A. Regeta, and I. van Santen, ArXiv.

2. The Structure of Algebraic Families of Birational Transformations, with A. Regeta, and I. van Santen, ArXiv.

Published papers:

1. On a Theorem by Lin and Shinder through the Lens of Median Geometry, with A. Genevois and A. Lonjou, ArXiv, to appear in Selecta Mathematica.

2. Finitely generated subgroups of algebraic elements of plane Cremona groups are bounded, with A. Lonjou and P. Przytyzki, ArXiv, to appear in Journal de l’École polytechnique.

3. Asymptotically rigid mapping class groups II: strand diagrams and nonpositive curvature, with A. Genevois and A. Lonjou, ArXiv, to appear in Transactions of the AMS.

4. Cremona groups over finite fields, Neretin groups, and non-positively curved cube complexes, with A. Genevois and A. Lonjou, ArXiv, International Mathematics Research Notices, Vol. 2024, Issue 1, January 2024, 554–596.

5. Characterization of affine toric varieties by their automorphism groups, with A. Liendo and A. Regeta, ArXiv, Ann. Sc. Norm. Sup. Pisa-Cl. Sci. (2023), Vol. XXIV, 249-289.

6. Asymptotically rigid mapping class groups I: Finiteness properties of braided Thompson’s and Houghton’s groups, with A. Genevois and A. Lonjou, ArXiv, Geom. Topol. 26 (2022) 1385–1434.

7. Continuous automorphisms of Cremona groups, with S. Zimmermann, ArXiv, Int. J. Math., Vol. 32 (2021), No. 04, 2150019.

8. Actions of Cremona groups on CAT(0) cube complexes, with A. Lonjou, ArXiv, Duke Math. J. 170.17 (2021): 3703-3743.

9. On the characterization of Danielewski surfaces by their automorphism group, with A. Liendo and A. Regeta, ArXiv, Transform. Groups 27, 181–187 (2022).

10. Simple groups of birational transformations in dimension two, ArXiv, Comment. Math. Helv., Vol. 95, Issue 2, 2020, pp. 211–246.

11. Subgroups of elliptic elements of the Cremona group, ArXiv, J. fur Reine Angew. Math., 2021, Issue 770, pp. 27-57.

12. A new presentation of the plane Cremona group, with S. Zimmermann, ArXiv, Proc. Amer. Math. Soc. 147 (2019), no. 7, 2741–2755

13. Remarks on the degree growth of birational transformations, ArXiv, Math. Res. Lett., Vol. 25, No. 1 (2018), pp. 291-308.

14. On homomorphisms between Cremona groups, ArXiv, Ann. Inst. Fourier, Vol. 68, No. 1 (2018), pp. 53-100.

Other texts:

1. Actions of Cremona groups on CAT(0) cube complexes, contribution to the ZAG Volume.

2. Lecture Notes for a Mini-course on median graphs with applications to Cremona groups, given together with A. Genevois and A. Lonjou at the University of Rennes 1 in May 2023.

3. Subgroups of elliptic elements of the plane Cremona group, in: Oberwolfach Report 28/2018.

4. Subgroups of Cremona groups, PhD thesis at the University of Basel and the University of Rennes 1, defended in September 2017.

Teaching:

I enjoy teaching mathematics on all levels, be it in person or online. During the last years I got interested in evidence-based teaching strategies and I have started teaching my courses in the mode of a flipped classroom (integrating peer instruction). This has been received very positively by the students.

Courses I have taught as an instructor:

• Fall 2024: 401-3132-00L Commutative Algebra, ETH
• Spring 2024: 401-0302-10L Komplexe Analysis für ITET und RW, ETH, together with Meike Akveld
• Spring 2024: 401-2534-00L Geometrie für MATH, ETH
• Spring 2023: MATH 479 Linear algebraic groups (graduate), EPFL (flipped classroom)
• Spring 2023: MATH 323 Algebraic topology, EPFL (flipped classroom)
• Fall 2022: MATH 111 (pi) Algèbre linéaire classe inversée, EPFL (flipped classroom)
• Spring 2022: MATH 479 Linear algebraic groups (graduate), EPFL (flipped classroom)
• Spring 2022: MATH 323 Algebraic topology, EPFL (flipped classroom)
• Fall 2021: MATH 111(pi) Algèbre linéaire classe inversée, EPFL (flipped classroom)
• Spring 2021: MATH 479 Linear algebraic groups (graduate), EPFL (online)
• Spring 2021: MATH 323 Algebraic topology, EPFL (online)
• Fall 2020: MATH 735 Topics in geometric group theory (doctoral), together with Yash Lodha and Marc Troyanov EPFL (partially online)
• Fall 2020: MATH 111(e) Algèbre linéaire pour IN/SC, EPFL (hybrid format)
• Spring 2020: MATH 429 Lie groups (graduate), EPFL (partially online)
• Spring 2020: MATH 323 Algebraic topology, EPFL (partially online)
• Fall 2019: MATH 111(e) Algèbre linéaire pour IN/SC, EPFL (in person)
• Spring 2019: M3P21 Algebraic topology, Imperial College London (in person)

Between 2010 and 2017 I worked as a teaching assistant at the University of Basel for around a dozen different courses in various fields of mathematics, which included grading homework and giving weekly tutorials.

In Summer 2018 I taught two courses at the 2018 TMD Undergraduate and Graduate Summer School at the Nesin Math Village, Turkey - a wonderful place!

Supervision and Mentorship

Do not hesitate to get in touch, if you want to do a project with me. At the intersection of algebraic geometry, group theory, and topology there are many beautiful and fun subjects on all levels.

Supervised student projects:

• Céline Berthaud (Bachelor’s project on hyperbolic groups)
• Marie Abadie, EPFL (Master’s project on mapping class groups and Master’s thesis on asymptotically rigid mapping class groups and their actions on CAT(0) cube complexes), which has lead to the following publication: ArXiv
• Jeanette Fernandez, EPFL (Master’s project on Weil’s regularization theorem and Master’s thesis on automorphisms of Aut(A^2)), publication forthcoming
• Amandine Favre, EPFL (Bachelor’s project on completions)
• Valentin Prost, EPFL (Bachelor’s project on the Dehn-Nielsen-Baer theorem)
• Blerton Rashiti, EPLF (Bachelor’s project on groups and graphs)
• Peter Whalley, ICL (UROP (Undergraduate Research Opportunity) on the Lickorish-Wallace theorem)
• JiaJie Tao, ICL (UROP on geometric group theory)
• Tom Buhl-Nielsen, ICL (UROP on the classification of compact surfaces)

Circus

I thoroughly enjoy all kinds of performing arts (and I think a good math talk might very well fall into this category). I have cofounded and I still coorganize the following charming project in Basel: Station Circus - a venue for contemporary circus performances, as well as space for creation and community.