Lukas Lewark

Logo Uni Bern

Mailing address:

Universität Bern
Mathematisches Institut
Alpeneggstrasse 22
3012 Bern, Switzerland

Contact information:

(without spelling mistakes)
Phone:+41 31 631 51 78

I'm a mathematics post-doc working on low-dimensional topology, knot theory, and in particular on knot concordance and Khovanov-Rozansky homologies. Here are some randomly chosen open questions I like to think about:

  • Is there a knot with genus one and unknotting number four?
  • Is there an algorithm deciding whether a given knot is strongly quasipositive?
  • What information about knot concordance do Khovanov-Rozansky homologies carry, and what is the best way to encapsulate that information?
  • What is the topological four-genus of torus knots?

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, and I spent a total of four weeks in Cambridge.

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

See here for a list of my papers on the arXiv, and on MathSciNet.

List in reverse chronological order of appearance on the arXiv:

12.Almost positive links are strongly quasipositive
joint with Peter Feller and Andrew Lobb
submitted for publication
arXiv:1809.06692 pdf
11.Upsilon-like concordance invariants from sl(n) knot cohomology
joint with Andrew Lobb
Geometry & Topology (accepted for publication)
arXiv:1707.00891 pdf
10.Checkerboard graph monodromies
joint with Sebastian Baader and Livio Liechti
L'Enseignement Mathématique (accepted for publication)
arXiv:1706.09210 pdf
9.On calculating the slice genera of 11- and 12-crossing knots
joint with Duncan McCoy
Experimental Mathematics (accepted for publication)
arXiv:1508.01098v2 pdf
8.On classical upper bounds for slice genera
joint with Peter Feller
Selecta Mathematica 24 (2018), no. 5, pp. 4885–4916
arXiv:1611.02679 pdf
7.Khovanov width and dealternation number of positive braid links
joint with Sebastian Baader, Peter Feller and Raphael Zentner
Mathematical Research Letters (accepted for publication)
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 370 (2018), pp. 2639–2656
arXiv:1509.07634 pdf, MR3748580
5.The stable 4-genus of alternating knots
joint with Sebastian Baader
Asian Journal of Mathematics 21 (2017), no. 6, pp. 1183–1190
arXiv:1505.03345 pdf, MR3778124
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

June 2019, at the conference Knot concordance and low-dimensional manifolds in Le Croisic: tba.

April 18th 2019, at the Topology Seminar of the IMJ in Paris: tba.

January 18th 2019, at the Institut Fourier, Grenoble: tba.

November 27th 2018, at the Topology Seminar at the Math Institute of the University of Bonn: Linking pairings and unknotting numbers.

November 13th 2018, at the Seminar Algebra and Geometry of the University of Basel: Positivity, Graphs and Unknotting.

April 27th 2018, at the Knot theory seminar at Warsaw University: Genus and Unknotting.

April 17th 2018, at the Seminar of the SFB Higher Invariants at Regensburg: Balanced unknotting, Blanchfield form, and surfaces in 3- and 4-space.

March 15th 2018, at the Boston College Geometry/Topology seminar: Balanced unknotting, Blanchfield form, and surfaces in 3- and 4-space.

March 7th 2018, at the conference Quantum Knot Homology and Supersymmetric Gauge Theories at the Aspen Center for Physics: Upsilon-like invariants from Khovanov-Rozansky sl(n) homologies.

(Show more)


2019: Knot concordance and low-dimensional manifolds in Le Croisic (talk)
Swiss Knots at the ETHZ (I'm one of the organisers)
2018: Knotted embeddings in dimensions 3 and 4 at the CIRM
Quantum Knot Homology and Supersymmetric Gauge Theories at the Aspen Center for Physics (talk)
2017: Quantum topology and categorified representation theory in Cambridge (talk)
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 (talk)
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)


Lectures and courses

2018 (fall) at Bern University: Lecture Algebraic Topology.

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

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

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

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

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


2018 (spring) at Bern University: Tutor for Low Dimensional Topology.

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

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

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

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).

Other teaching

2016, 2017, 2018 (summer) at Bern University: Introductory mathematics course.


I review articles for zbMATH and Mathematical Reviews.

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

Last update: 17 December 2018.