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 4-6 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Here is a (slightly outdated) CV.Research interests.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.