Livio Liechti
Département de Mathématiques
Université de Fribourg
Chemin du Musée 23
1700 Fribourg
Suisse
e-mail: livio.liechti(makeawildguess)unifr.ch

Current teaching.

In Spring 2024, I am teaching Mapping class groups in Fribourg.

In 2023-2024, I am teaching Mathematical Methods for Computer Science / Discrete Mathematics in Fribourg.

Past teaching.

In Fall 2022, I was teaching Complex Algebraic Curves in Fribourg.

In 2022-2023, I was teaching Mathematical Methods for Computer Science / Discrete Mathematics in Fribourg.

In Spring 2022, I was teaching Low-dimensional topology in Fribourg.

In 2021-2022, I was teaching Mathematical Methods for Computer Science / Discrete Mathematics in Fribourg.

In Spring 2021, I was teaching Dynamical systems in Fribourg.

In 2020-2021, I was teaching Mathematical Methods for Computer Science / Discrete Mathematics in Fribourg.

In Fall 2019, I was teaching a student seminar on complex algebraic curves in Fribourg.

In Spring 2019, I was teaching a student seminar on surfaces in Fribourg.

Past events.

In Fall 2021, we had a reading seminar on Teichmüller theory in Fribourg.

From July 6 to 9, Swiss Knots 2021 took place in Fribourg.

CV.

Research interests.

Low-dimensional topology and geometry. In particular, everything concerning fibred knots, concordance, the mapping class group, pseudo-Anosov homeomorphisms and their stretch factors, hyperbolic volume.

Papers.

23. Minimal stretch factors of orientation-reversing fully-punctured pseudo-Anosov maps (joint with Erwan Lanneau and Chi Cheuk Tsang), preprint.

22. On the signature of a positive braid (joint with Joshua Evan Greene), preprint.

21. On the minimal spectral radii of skew-reciprocal integer matrices, New York J. Math 30 (2024), 307-322.

20. Trace field degrees of Abelian differentials (joint with Erwan Lanneau), Comment. Math. Helv. 99 (2024), no. 1, 81-110.

19. Minor theory for quasipositive surfaces (joint with Sebastian Baader and Pierre Dehornoy), in Essays in Geometry - Dedicated to Norbert A'Campo, EMS Press (2023).

18. The geometry of bi-Perron numbers with real or unimodular Galois conjugates (joint with Joshua Pankau), Int. Math. Res. Not. (2022), no. 23, 18526-18540.

17. Salem numbers, spectral radii and growth rates of hyperbolic Coxeter groups (joint with Ruth Kellerhals), Transform. Groups 28 (2023), no. 2, 831-852.

16. Divide knots of maximal genus defect, Comm. Anal. Geom. 31 (2023), no. 2, 367-379.

15. Divide monodromies and antitwists on surfaces (joint with Pierre Dehornoy), preprint.

14. Overcommuting pairs in groups and 3-manifolds bounding them (joint with Julien Marché), J. London Math. Soc. 102 (2020), no. 3, 1160-1177.

13. On the arithmetic and the geometry of skew-reciprocal polynomials, Proc. Amer. Math. Soc. 147 (2019), no. 12, 5131-5139.

12. Minimal Penner dilatations on nonorientable surfaces (joint with Balázs Strenner), J. Topol. Anal. 13 (2021), no. 1, 187-218.

11. Minimal pseudo-Anosov stretch factors on nonoriented surfaces (joint with Balázs Strenner), Algebr. Geom. Topol. 20 (2020), no. 1, 451-485.

10. On the genus defect of positive braid knots, Algebr. Geom. Topol. 20 (2020), no. 1, 403-428.

9. The Arnoux-Yoccoz mapping classes via Penner's construction (joint with Balázs Strenner), Bull. Soc. Math. France 148 (2020), no. 3, 383-397.

8. Checkerboard graph monodromies (joint with Sebastian Baader and Lukas Lewark), Enseign. Math. 64 (2018), no. 1-2, 65-88.

7. Teichmüller polynomials of fibered alternating links (joint with Robert Billet), Osaka J. Math. 56 (2019), no. 4, 787-806.

6. On the topological 4-genus of torus knots (joint with Sebastian Baader, Peter Feller and Lukas Lewark), Trans. Amer. Math. Soc. 370 (2018), no. 4, 2639-2656.

5. Minimal dilatation in Penner's construction, Proc. Amer. Math. Soc. 145 (2017), no. 9, 3941-3951.

4. Positive braid knots of maximal topological 4-genus, Math. Proc. Cambridge Philos. Soc. 161 (2016), no. 3, 559-568.

3. On Coxeter mapping classes and fibered alternating links (joint with Eriko Hironaka), Michigan Math. J. 65 (2016), no. 4, 799-812.

2. Signature and concordance of positive knots (joint with Sebastian Baader and Pierre Dehornoy), Bull. London Math. Soc. 50 (2018), no. 1, 166-173.

1. Signature, positive Hopf plumbing and the Coxeter transformation (with an appendix jointly written with Peter Feller), Osaka J. Math. 53 (2016), no. 1, 251-266.

PhD thesis.