Lukas Lewark

Logo Uni Bern

Mailing address:

Universität Bern
Mathematisches Institut
Sidlerstrasse 5
3012 Bern
Switzerland

Contact information:

Office 107 at Alpeneggstrasse 22
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 working as a post-doc with Sebastian Baader at the Universität Bern.

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

From April 2013 till April 2014 I was working as a research associate 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.


Preprints, Publications and Proceedings

(All my papers are on the arXiv).

On the topological 4-genus of torus knots: arXiv:1509.07634 (joint with Sebastian Baader, Peter Feller and Livio Liechti).

The stable 4-genus of alternating knots: arXiv:1505.03345 (joint with Sebastian Baader).

New Quantum Obstructions to Sliceness: Proceedings of the London Mathematical Society 112 (2016), no. 1, pp. 81–114, arXiv:1501.07138 (joint with Andrew Lobb).

On stable sl3-homology of torus knots: Experimental Mathematics 24 (2015), no. 2, pp. 162–174, arXiv:1404.0623 (joint with Eugene Gorsky).

Rasmussen's spectral sequences and the sl(N)-concordance invariants: Advances in Mathematics 260C (2014), pp. 59–83, arXiv:1310.3100.

sl3-foam homology calculations: Algebraic & Geometric Topology 13 (2013), no. 6, 3661–3686, arXiv:1212.2553.

Khovanov-Rozansky homologies induce non-additive four-ball genus bounds: Oberwolfach Reports 11 (2014), no. 3, pp. 2381–2382 (abstract of a 10 minute talk, joint with Andrew Lobb).


Recent Talks

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 Zürich Graduate Colloquium: What is... a knot's slice genus?

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

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Conferences

2016: 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

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

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).


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: May 13th, 2016.