Lukas Lewark

Logo Uni Bern

Mailing address:

Universität Bern
Mathematisches Institut
Alpeneggstrasse 22
3012 Bern, Switzerland

Contact information:

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

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.

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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:

11. Upsilon-like concordance invariants from sl(n) knot cohomology
joint with Andrew Lobb
submitted to a journal
arXiv:1707.00891 pdf
10.Checkerboard graph monodromies
joint with Sebastian Baader and Livio Liechti
submitted to a journal
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
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

November 27th 2017, at the Séminaire Géométrie, Dynamique et Topologie of the Institut de Mathématiques de Marseille: L'homologie de Khovanov-Rozansky entre les nœuds positifs et négatifs.

November 24th 2017, at the Séminaire Topologies of the Institut Montpelliérain Alexander Grothendieck: Graphes planaires et clôtures de tresses positives.

June 27th 2017, at the workshop Quantum topology and categorified representation theory at the Isaac Newton Institute in Cambridge: An Upsilon-like invariant from Khovanov-Rozansky homology.

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.

(Show more)

Conferences

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)

Teaching

Lectures and courses

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).

Exercises

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

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

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

Misc

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: November 13th, 2017.