Lukas Lewark

Logo Uni Bern

Mailing address:

Universität Bern
Mathematisches Institut
Alpeneggstrasse 22
3012 Bern, Switzerland

Contact information:

Office 107
Email: lukas at
Phone: +41 31 631 51 78

Swiss Knots 2017 is happening in Bern soon!

I'm a mathematics post-doc working on low-dimensional topology, knot theory, and in particular on the slice genus and on Khovanov-Rozansky homologies.


Employment and Education

Since August 2014, I am a post-doc working with Sebastian Baader at the Universität Bern.

From April 2013 till April 2014 I was a research associate working with Andrew Lobb at Durham University.

My PhD thesis titled Khovanov-Rozansky homologies, knotted weighted webs and the slice genus was supervised by Christian Blanchet at the Institut de Mathématiques de Jussieu (Paris VII - Denis Diderot). The defence took place on June 28th 2013.

My Master thesis The Rasmussen Invariant of Arborescent and of Mutant Links from April 2009 was supervised by Sebastian Baader at the ETH Zürich.

My Bachelor thesis Die Riemann-Hurwitz Formel für kompakte Riemannsche Flächen from December 2007 was supervised by Richard Pink at the ETH Zürich.

Scientific visits

The Isaac Newton Institute for Mathematical Sciences in Cambridge invited me for the programme Homology Theories in Low Dimensional Topology in 2017. I will come from February 5th to 17th and June 19th to 30th.

The Max Planck Institute for Mathematics invited me to spend October 2016 in Bonn.

The Max Planck Institute for Mathematics in Bonn invited me to stay from April till August 2014.

Preprints and Publications

My papers on the arXiv, and on MathSciNet.

9.On calculating the slice genera of 11- and 12-crossing knots
joint with Duncan McCoy
submitted to a journal
arXiv:1508.01098v2 pdf
8.On classical upper bounds for slice genera
joint with Peter Feller
submitted to a journal
arXiv:1611.02679 pdf
7.Khovanov width and dealternation number of positive braid links
joint with Sebastian Baader, Peter Feller and Raphael Zentner
submitted to a journal
arXiv:1610.04534 pdf
6.On the topological 4-genus of torus knots
joint with Sebastian Baader, Peter Feller and Livio Liechti
Transactions of the American Mathematical Society (accepted for publication)
arXiv:1509.07634 pdf
5.The stable 4-genus of alternating knots
joint with Sebastian Baader
Asian Journal of Mathematics (accepted for publication)
arXiv:1505.03345 pdf
4.New Quantum Obstructions to Sliceness
joint with Andrew Lobb
Proceedings of the London Mathematical Society 112 (2016), no. 1, pp. 81–114
arXiv:1501.07138 pdf, MR3458146
3.On stable sl3-homology of torus knots
joint with Eugene Gorsky
Experimental Mathematics 24 (2015), no. 2, pp. 162–174
arXiv:1404.0623 pdf, MR3350523
2.Rasmussen's spectral sequences and the sl(N)-concordance invariants
Advances in Mathematics 260C (2014), pp. 59–83
arXiv:1310.3100 pdf, MR3209349
1.sl3-foam homology calculations
Algebraic & Geometric Topology 13 (2013), no. 6, 3661–3686
arXiv:1212.2553 pdf, MR3248745

Recent and upcoming Talks

April 27th 2017, at the Séminaire de Topologie et Géométrie in Geneva: L'homologie de Khovanov-Rozansky entre les nœuds positifs et négatifs.

April 5th 2017, at the University of Zurich: Khovanov-Rozansky homology in between positive and negative knots.

March 27th 2017, at the Séminaire quantique in Strasbourg: Khovanov-Rozansky homology in between positive and negative knots.

February 16th 2017, at the seminar of the programme Homology theories in low dimensional topology at the Isaac Newton Institute in Cambridge: The Seifert form's optimal bounds for slice genera.

October 26th 2016, at the Seminar on knot concordance and 4-manifolds of the Topology Trimester at the HIM (Bonn): Slice genus bounds from the Seifert form.

May 4th 2016, at Oberseminar Globale Analysis of the University of Regensburg: Seifert Form and Slice Genus of Knots.

February 23rd 2016, at the BIRS Workshop about Synchronizing Smooth and Topological 4-Manifolds in Banff: Upper bounds for the topological slice genus of knots.

September 15th 2015, at the Topology Seminar of the IMJ in Paris: Théorie des nombres et genre slice topologique des nœuds.

June 13th 2015, at the special session Categorification of Quantum groups, Representations and Knot Invariants of the Joint AMS-EMS-SPM meeting in Porto: New quantum obstructions to sliceness.

April 28th 2015, at the Zurich Graduate Colloquium: What is... a knot's slice genus?

April 15th 2015, at the Seminar "Quantum Groups and Low-Dimensional Topology" of the University Zurich: Khovanov-Rozansky homologies with non-standard potentials.


2017: Quantum topology and categorified representation theory in Cambridge
Swiss Knots in Bern (I'm one of the organisers)
2016: Conference on 4-manifolds and knot concordance at the MPIM, Bonn
BIRS Workshop about Synchronizing Smooth and Topological 4-Manifolds in Banff
2015: La Llagonne
Categorification in Algebra, Geometry and Physics in Cargèse
Swiss Knots in Geneva
Joint AMS-EMS-SPM meeting in Porto (talk)
2014: Knots in Washington XXXVII (talk)
Topologie géométrique et quantique en dimension 3 at the CIRM
Oberwolfach Workshop "Topologie" (talk)
DMV-PTM Joint Meeting in Poznań (talk)


2017 (fall) at Bern University: Mathematik für Biologie.

2017 (summer) at Bern University: Introductory mathematics course.

2017 (spring) at Bern University: Seminar on Quadratic Forms in Topology.

2016 (fall) at Bern University: Tutor for Mathematik I für Naturwissenschaften.

2016 (summer) at Bern University: Introductory mathematics course.

2016 (spring) at Bern University: Lecture on Topology.

2015 (fall) at Bern University: Tutor for Representation Theory of Lie Algebras and for Mathematik I für Naturwissenschaften.

2015 (spring) at Bern University: Lecture on Graph Theory.

2014 (fall) at Bern University: Tutor for Linear Algebra I.

2013 at Paris Diderot: Lecture on MM2 (Linear Algebra and Analysis for first-year mathematics students).

2011 and 2012 at Paris Diderot: Tutor for Elementary Algebra and Analysis II for first-year informatics students.

2006 – 2009 at the ETHZ: Tutor for Linear Algebra I and II (first-year students), Complex Analysis, Topology and Algebra II (second-year students).


I review articles for zbMATH.

From 2011 to 2013, I was a member of the self-administration team of the IMJ's PhD-students, the BDD.

Last update: April 29th, 2017.