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

I'm a mathematics postdoc working on lowdimensional topology, knot theory, and in particular on knot concordance and KhovanovRozansky 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 KhovanovRozansky homologies carry, and what is the best way to encapsulate that information?
 What is the topological fourgenus of torus knots?

Employment and Education
Since August 2014, I am a postdoc 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 KhovanovRozansky 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.

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.  Upsilonlike concordance invariants from sl(n) knot cohomology joint with Andrew Lobb submitted to a journal arXiv:1707.00891 
10.  Checkerboard graph monodromies joint with Sebastian Baader and Livio Liechti L'Enseignement Mathématique (accepted for publication) arXiv:1706.09210 
9.  On calculating the slice genera of 11 and 12crossing knots joint with Duncan McCoy Experimental Mathematics (accepted for publication) arXiv:1508.01098v2 
8.  On classical upper bounds for slice genera joint with Peter Feller submitted to a journal arXiv:1611.02679 
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 
6.  On the topological 4genus 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 
5.  The stable 4genus of alternating knots joint with Sebastian Baader
Asian Journal of Mathematics (accepted for publication)
arXiv:1505.03345 
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 , MR3458146 
3.  On stable homology of torus knots joint with Eugene Gorsky Experimental Mathematics 24 (2015), no. 2, pp. 162–174 arXiv:1404.0623 , MR3350523 
2.  Rasmussen's spectral sequences and the concordance invariants Advances in Mathematics 260C (2014), pp. 59–83 arXiv:1310.3100 , MR3209349 
1.  foam homology calculations Algebraic & Geometric Topology 13 (2013), no. 6, 3661–3686 arXiv:1212.2553 , 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 KhovanovRozansky 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 Upsilonlike invariant from KhovanovRozansky homology.
April 27th 2017, at the Séminaire de Topologie et Géométrie in Geneva: L'homologie de KhovanovRozansky entre les nœuds positifs et négatifs.
April 5th 2017, at the University of Zurich: KhovanovRozansky homology in between positive and negative knots.
March 27th 2017, at the Séminaire quantique in Strasbourg: KhovanovRozansky 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

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 firstyear mathematics students).
Exercises
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 firstyear informatics students.
2006 – 2009 at the ETHZ: Tutor for Linear Algebra I and II (firstyear students), Complex Analysis, Topology and Algebra II (secondyear students).
Other teaching
2016, 2017, 2018 (summer) at Bern University: Introductory mathematics course.

Misc
I review articles for zbMATH.
From 2011 to 2013, I was a member of the selfadministration team of the IMJ's PhDstudents, the BDD.

