Supervision

This page lists Ph.D., Master, and Bachelor theses supervised by me, as well as publications arising from these and other papers co-authored with students and postdocs.

Supervised Ph.D. students

• Naageswaran Manikandan, Ph.D. (2025), Humboldt University Berlin, joint supervision with Chris Wendl; now postdoc at the MPI Bonn.
  • M. Kegel, N. Manikandan, L. Mousseau, and M. Silvero, Khovanov homology of positive links and of L-space knots, arXiv:2304.13613.
  • M. Kegel, L. Lewark, N. Manikandan, F. Misev, L. Mousseau, and M. Silvero, On unknotting fibered positive knots and braids, arXiv:2312.07339, to appear in Ann. Sc. Norm. Super. Pisa Cl. Sci.
• Chun-Sheng Hsueh, funded by the Claussen-Simon Stiftung, Ph.D. student, Humboldt University Berlin, in progress.
  • C.-S. Hsueh, Handle decompositions and stabilizations of open books, arXiv:2505.19343.
  • B. Bode and C.-S. Hsueh, Mutual arc presentations and braided open books, arXiv:2511.21837.
• David Suchodoll, Ph.D. student, Humboldt University Berlin, joint supervision with Klaus Mohnke, in progress.
  • D. Suchodoll, On the multiplicity of Knot Floer order under cabling, arXiv:2506.09577.

Postdocs mentored

• Monika Yadav, May–July 2024, Humboldt University Berlin, funded by the Hannah–Neumann Fellowship via MATH+.
  • M. Kegel, I. Nonino, and M. Yadav, Contact surgery distance, arXiv:2512.14904.
• Monika Yadav, November–December 2024, Humboldt University Berlin, funded by the WINS Postdoctoral Fellowship.
  • M. Kegel and M. Yadav, Contact surgery numbers of projective spaces, Mediterr. J. Math., 22 (2025), arXiv:2504.05032.

Supervised Master students

• Leo Mousseau, The L-space conjecture, (2025), Humboldt University Berlin; now Ph.D. student at the University of Neuchatel.
• Sarah Pestkowski, Ein optimales Papier-Möbius-Band, (2025), Humboldt University Berlin.
• Chun-Sheng Hsueh, Kirby diagrams of 4-dimensional open books, (2023), Humboldt University Berlin; now Ph.D. student at the HU Berlin.
  • C.-S. Hsueh, Kirby diagrams of 4-dimensional open books, arXiv:2306.16942, Proc. Edinb. Math. Soc. (2) 68 (2025), no. 2, 319–347.
• David Suchodoll, The Thurston–Bennequin invariant in branched covers, (2022), Humboldt University Berlin; now Ph.D. student at the HU Berlin.

Supervised Bachelor students

• Arthur Berns, The 6-theorem, (2024), Humboldt University Berlin.
• Annika Thiele, Algorithmic detections of fibered and positive knots, (2023), Humboldt University Berlin.
  • This thesis was awarded with a price from the Berlin Mathematical Society.
• Luis Kristic, Hyperbolic knot theory and the A-polynomial, (2023), Humboldt University Berlin.
• Frank Selensky, Chern classes of high dimensional contact structures via open books, (2023), Humboldt University Berlin.
• Leo Mousseau, Algorithms for computing the slice 4-genus and the unknotting number, (2023), Humboldt University Berlin.
• Pau Punset, Fibered links and orientations, (2023), Universidad de Barcelona (external supervisor).
• Fetih Ayaz, Classification of surfaces via normal curves, (2021), Humboldt University Berlin.
  • F. Ayaz, M. Kegel, and K. Mohnke, The classification of surfaces via normal curves, Jahresber. Dtsch. Math.-Ver. , 125 (2023), 121–134.
• Max Huneshagen, Das HOMFLYPT-Polynom, (2020), Humboldt University Berlin.
• Leo Duc, Regular homotopy classes of Legendrian immersions, (2019), Humboldt University Berlin.
• Paulina Bock de Barillas, Der Satz von Whitney–Graustein, (2019), Humboldt University Berlin.
• Bernhard Albach, Reidemeisterbewegungen von Legendre-, transversalen und glatten Verschlingungen, (2018), University of Cologne (joint supervision with H. Geiges).

Other publications with students

• V. Bais, A. Di Prisa, D. Hartman, C.-S. Hsueh, M. Kegel, A. Merz, M. Pencovitch, A. Ray, D. Santoro, P. Truöl, L. Wakelin, On the detection of knotted spheres by their traces in high dimensions, arXiv:2511.07251
• T. Abe, M. Kegel, and N. Weiss, Complexity of equal 0-surgeries, to appear in New York J. Math., arXiv:2401.06015
• S. Bastl, R. Burke, R. Chatterjee, S. Dey, A. Durst, S. Friedl, D. Galvin, A. Garcia Rivas, T. Hirsch, C. Hobohm, C.-S. Hsueh, M. Kegel, F. Kern, S. M. S. Lee, C. Löh, N. Manikandan, L. Mousseau, L. Munser, M. Pencovitch, P. Perras, M. Powell, J. P. Quintanilha, L. Schambeck, D. Suchodoll, M. Tancer, A. Thiele, P. Truöl, M. Uschold, S. Vesela, M. Weiß, and M. von Wunsch-Rolshoven, Algorithms in 4-manifold topology, to appear in Algebr. Geom. Topol., arXiv:2411.08775

Hausarbeiten zur Vorlesung Kirby-Kalkül

• Bernhard Albach: Blätterungen von 3-Mannigfaltigkeiten (pdf)
• Franziska Frede: Nicht-destabilisierbare Heegaard-Zerlegungen (pdf)
• Konstantin Müller: Heegaard- und Henkelzerlegungen von 3-Mannigfaltigkeiten mit Rand (pdf)
• Laura Maria Poreschack: Homologie und Henkelzerlegungen (pdf)
• Lennart Struth: Hakens Lemma (pdf)

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