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|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.
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
Geometry & Topology (accepted for publication)
|10.||Checkerboard graph monodromies|
joint with Sebastian Baader and Livio Liechti
L'Enseignement Mathématique (accepted for publication)
|9.||On calculating the slice genera of 11- and 12-crossing knots|
joint with Duncan McCoy
Experimental Mathematics (accepted for publication)
|8.||On classical upper bounds for slice genera|
joint with Peter Feller
Selecta Mathematica (accepted for publication)
|7.||Khovanov width and dealternation number of positive braid links|
joint with Sebastian Baader, Peter Feller and Raphael Zentner
submitted to a journal
|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 , 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 , 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 , 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
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.
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.
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).
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.