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 2024-2025, I am teaching Algèbre et Géométrie I & II in Fribourg.
In 2024-2025, I am teaching Ergänzungen I & II zur Analysis und linearen Algebra in Fribourg.
In Spring 2024, I was teaching Mapping class groups in Fribourg.
In 2023-2024, I was teaching Mathematical Methods for Computer Science / Discrete Mathematics in Fribourg.
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.
Events.
CUSO Swiss Doctoral Program in Mathematics
The Swiss Knots 2025 conference will take place in Geneva, June 2025.
CUSO Summer School in Mathematics in Magliaso, August 18-22 2025.
Leonardo Math Camp for high-school students in Les Diablerets, October 8-11 2025.
In Fall 2023, we organised the Leonardo Math Camp in Les Diablerets.
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.
Here is a (slightly outdated) CV.Research interests.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.
24. Trace field degrees in the Torelli group (joint with Erwan Lanneau), preprint.
23. Minimal stretch factors of orientation-reversing fully-punctured pseudo-Anosov maps (joint with Erwan Lanneau and Chi Cheuk Tsang), accepted for publication in Trans. Amer. Math. Soc. (2024).
22. On the signature of a positive braid (joint with Joshua Evan Greene), Ann. Henri Lebesgue 7 (2024), 823-839.
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.
On the spectra of mapping classes and the 4-genera of positive knots, written under the supervision of Sebastian Baader at Universität Bern, 2017.