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.
Employment and Education
The Max Planck Institute for Mathematics invited me to spend October 2016 in Bonn. I will be in contact with the participants of the Junior Hausdorff Trimester Program Topology at the Hausdorff Research Institute for Mathematics.
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.
Preprints, Publications and Proceedings
My papers on the arXiv, and on MathSciNet.
Khovanov width and dealternation number of positive braid links: arXiv:1610.04534
(joint with Sebastian Baader, Peter Feller, Raphael Zentner).
On the topological 4-genus of torus knots: arXiv:1509.07634 (joint with Sebastian Baader, Peter Feller and Livio Liechti). Accepted for publication by the Transactions of the American Mathematical Society.
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.
-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).
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.
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.