What I am working on...
What I am working on...
Embedded Files
- Thurston–Bennequin invariant in branched covers
My Master's thesis goal was the calculation of the Thurston–Bennequin invariant of a Legendrian knot L in a branched cover over the 3-sphere along a transverse knot T with all information given in a front projection and a coloring of T.
- Knot invariants of census knots
In collaboration with students at HU Berlin under the supervision of Marc Kegel, I computed various knot invariants for census knots. My calculations included torsion numbers, Morse–Novikov numbers, bridge numbers, and canonical genus.
While working on the Morse–Novikov number, I may have identified two 12-crossing prime knots with MN(K)=4, though this has yet to be verified. Additionally, in my work on the bridge index, I was able to prove that the HFK-minus order is multiplicative under cabling when the cable is an L-space knot.
- Algorithms for topological 4-manifolds
I participated in the Workshop on 4-Manifolds & Algorithms in Regensburg to further explore the role of algorithms in low-dimensional topology. The topics I engaged with included trisections, computational approaches to determining the Kirby–Siebenmann invariant, and the development of an algorithm for deciding the homomorphism problem in simply connected (smooth) 4-manifolds.
You can find the workshop results here.
References
References
Klaus Mohnke, Humboldt-Universität zu Berlin
Ph.D. supervisorMarc Kegel, Humboldt-Universität zu Berlin
Master's degree supervisoryou might also be interested in...
you might also be interested in...
Naageswaran Manikandan, Humboldt-Universität zu Berlin
Chun-Sheng Hsueh, Humboldt-Universität zu Berlin
Gerard Bargalló i Gómez, Humboldt-Universität zu Berlin
Viktor Majewski, Humboldt-Universität zu Berlin
Talks
Talks
up-coming
up-coming
Multiplicity of knot Floer order under cabling of L-spaces - AG Geometric Topology
past
past
two-bridge knots & Lens spaces - AG Geometric Topology
The bridge index - AG Geometric Topology
HFK and the 4-ball genus - HF Homology Seminar
Distinguishing Legendrian knots - Topological persistence in symplectic topology
Fukaya Categories - Categorical Symplectic Geometry
Gromov Compactness - Symplectic Geometry
Lagrangian Floer (Co)homology - Categorical Symplectic Geometry
Almost Kähler structures in GRT - Lorentzgeometrie und Mathematische Relativitätstheorie
Cheeger–Gromov 𝐶^{𝑘,𝛼} Topology - Riemannian Convergence Theory
Symplectic and Contact basics - h-Principal
de Rham Cohomology & de Rham's Theorem - selected topics in Algebraic and Differential Topology
Participation
Participation
Regular attendance
Regular attendance
AG Geometric Topology Seminar, HU, Berlin
Mon 11:00 - 12:00Seminar Symplektische Geometrie, HU, Berlin
Mon 15:00 - 17:00FS Differentialgeometrie und geometrische Analysis, HU, Berlin
Wed 16:30 - 18:30Berlin-Hamburg Seminar zur symplektischen Geometrie, HU Berlin & Uni Hamburg
some FridaysWorkshops, Conferences, and Seminars
Workshops, Conferences, and Seminars
Swiss Knots 2025, UNIGE, Geneva
Jun 25Berlin-Brandenburg Workshop V: Knot Theory and its Application, Universität Potsdam
Apr 25Berlin-Brandenburg Workshop IV: Knot Theory and its Application, HU, Berlin
Dec 24Workshop on 4-manifolds & algorithms, Regensburg
Sep 24Berlin-Brandenburg Workshop III: Knot Theory and its Application, Universität Potsdam
May 24CAST 2024 - RUB, Bochum
Feb 24Berlin-Brandenburg Workshop II: Knot Theory and its Application, FU, Berlin
Nov 23Arbeitsgemeinschaft - Cluster Algebras, MFO, Oberwolfach.
Okt 23Symplectic Field Theory 10, HU, Berlin.
Aug 23Berlin-Brandenburg Workshop: Knot Theory and its Application, HU, Berlin
Jul 23Books I refer to...
Books I refer to...
Knot Theory
Knot Theory
G. Burde, H. Zieschang and M. Heusener, Knots, third, fully revised and extended edition, De Gruyter Studies in Mathematics, 5, De Gruyter, Berlin, 2014; MR3156509
D. P. O. Rolfsen, Knots and links, corrected reprint of the 1976 original, Mathematics Lecture Series, 7, Publish or Perish, Houston, TX, 1990; MR1277811
V. V. Prasolov and A. B. Sossinsky, Knots, links, braids and 3-manifolds, translated from the Russian manuscript by Sossinsky, Translations of Mathematical Monographs, 154, Amer. Math. Soc., Providence, RI, 1997; MR1414898
J. B. Etnyre, Legendrian and transversal knots, in Handbook of knot theory, 105--185, Elsevier B. V., Amsterdam, ; MR2179261
Contact Topology
Contact Topology
H. Geiges, An introduction to contact topology, Cambridge Studies in Advanced Mathematics, 109, Cambridge Univ. Press, Cambridge, 2008; MR2397738
J. B. Etnyre, Lectures on open book decompositions and contact structures, in Floer homology, gauge theory, and low-dimensional topology, 103--141, Clay Math. Proc., 5, Amer. Math. Soc., Providence, RI, ; MR2249250
Topology
Topology
R. H. Bott and L. W. Tu, Differential forms in algebraic topology, Graduate Texts in Mathematics, 82, Springer, New York-Berlin, 1982; MR0658304
A. E. Hatcher, Algebraic topology, Cambridge Univ. Press, Cambridge, 2002; MR1867354
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