Michael Brandenbursky

I am a faculty member at Ben-Gurion University, Israel.

Office: Deichmann 306
Email address: brandens@bgu.ac.il


Research interests

  • Knot Theory: Vassiliev invariants, concordance group, Heegaard Floer and Khovanov homologies
  • Hamiltonian dynamics, symplectic geometry, low-dimensional topology
  • Braid groups, mapping class groups and transformation groups of smooth manifolds: quasi-isometries, quasi-morphisms, cohomology, quasi-norms
  • Geometric group theory: quasi-isometric embeddings of finitely generated groups, bi-invariant word metrics


My Research Papers

  1. M. Brandenbursky and M. Marcinkowski, Volume and Euler classes in bounded cohomology of transformation groups, Glasgow Mathematical Journal (in press), (2024).
  2. M. Brandenbursky and M. Verbitsky, Non-commutative Barge-Ghys quasimorphisms, IMRN (in press), (2024).
  3. L. Birbrair, M. Brandenbursky and A. Gabrielov, Lipschitz geometry of surface germs in $R^4$: metric knots, Selecta Math. (N.S.), vol. 28 (2023), no. 3, Paper No. 43, 20 pp.
  4. M. Brandenbursky and M. Khanevsky, C^0-gap between entropy-zero Hamiltonians and autonomous diffeomorphisms of surfaces, Israel Journal of Mathematics, vol. 255 (2023), no. 1, 311-324.
  5. M. Brandenbursky, M. Marcinkowski and E. Shelukhin, The Schwarz-Milnor lemma for braids and area-preserving diffeomorphisms, Selecta Math. (N.S.), vol. 28 (2022), no. 4, Paper No. 74, 20 pp.
  6. M. Brandenbursky and J. Kedra, Fragmentation norm and relative quasimorphisms, Proceedings of the American Mathematical Society, vol. 150 (2022), no. 10, 4519–4531.
  7. M. Brandenbursky and M. Marcinkowski, Bounded cohomology of transformation groups, Mathematische Annalen, vol. 382 (2022), no. 3-4, 1181–1197.
  8. M. Brandenbursky and E. Shelukhin, On the entropy norm on $Ham(S^2)$, Annales mathematiques du Quebec, vol. 45 (2021), no. 1, 231--237.
  9. M. Brandenbursky and A. Kabiraj, On the entropy norm on the group of diffeomorphisms of closed oriented surface, Journal of Topology and Analysis vol. 12, No. 1 (2020), 105-111.
  10. M. Brandenbursky and M. Marcinkowski, Entropy and quasimorphisms, Journal of Modern Dynamics, vol. 15, 143–163, (2019).
  11. M. Brandenbursky and M. Marcinkowski, Aut-invariant norms and Aut-invariant quasimorphisms on free and surface group, Commentarii Mathematici Helvetici, vol. 94, No. 4 (2019), 661–687.
  12. M. Brandenbursky, J. Kedra and E. Shelukhin On the autonomous norm on the group of Hamiltonian diffeomorphisms of the torus, Communications in Contemporary Mathematics, (2018), 20(2):1750042.
  13. M. Brandenbursky and E. Shelukhin The $L^p$-diameter of the group of area-preserving diffeomorphisms of $S^2$, Geometry & Topology, (2017), 21(6):3785-3810.
  14. M. Brandenbursky and J. Kedra, The autonomous norm on $Ham(R^2n)$ is bounded, Annales mathematiques du Quebec, 41 (2017), 63--65.
  15. M. Brandenbursky, Concordance of certain 3-braids and Gauss diagrams, Topology and its Applications, 214 (2016), 180-185.
  16. M. Brandenbursky, S. Gal, J. Kedra and M. Marcinkowski, Cancelation norm and the geometry of bi-invariant word metrics, Glasgow Mathematical Journal, 58 (2016), no. 1, 153–176.
  17. M. Brandenbursky and E. Shelukhin, On the L^p-geometry of autonomous Hamiltonian diffeomorphisms of surfaces, Mathematical Research Letters, 22 (2015), no. 5, 1275-1294.
  18. M. Brandenbursky, Bi-invariant metrics and quasi-morphisms on groups of Hamiltonian diffeomorphisms of surfaces, International Journal of Mathematics, 26 (2015), no. 9, 1550066, 29 pp.
  19. M. Brandenbursky and J. Kedra, Concordance group and stable commutator length in braid groups, Algebraic & Geometric Topology, 15 (2015), no. 5, 2861–2886.
  20. M. Brandenbursky, Link invariants via counting surfaces, Geometriae Dedicata 173 (2014), 243–270.
  21. M. Brandenbursky, Coloring link diagrams and Conway-type polynomial of braids, Topology and its Applications, 161 (2014), 141-158.
  22. M. Brandenbursky and J. Kedra, Quasi-isometric embeddings into diffeomorphism groups, Groups, Geometry and Dynamics, vol. 7, No. 3 (2013), 523-534.
  23. M. Brandenbursky and J. Kedra, On the autonomous norm on the group of area-preserving diffeomorphisms of the 2-disc, Algebraic & Geometric Topology 13 (2013), 795-816.
  24. M. Brandenbursky, Invariants of closed braids via counting surfaces, Journal of Knot Theory and its Ramifications, vol. 22, No. 3 (2013), 1350011 (21 pages).
  25. M. Brandenbursky, Quasi-morphisms and L^p metrics on groups of volume-preserving diffeomorphisms, Journal of Topology and Analysis vol. 4, No. 2 (2012), 255-270.
  26. M. Brandenbursky, On quasi-morphisms from knot and braid invariants, Journal of Knot Theory and its Ramifications, vol. 20, No. 10 (2011), 1397-1417.


Papers in Conference Proceedings

  1. M. Brandenbursky and E. Shelukhin, On the large-scale geometry of the L^p-metric on the symplectomorphism group of the two-sphere, Preprints of the IHES M/15/09.


Theses

  • Knot invariants and their applications to constructions of quasi-morphisms on groups, Ph. D. Thesis under supervision of Prof. Michael Entov and Prof. Michael Polyak, Technion, Israel, 2010.
  • Compact Lie groups, M. Sc. Thesis under supervision of Prof. Emmanuel Farjoun, Hebrew University, Israel, 2005.


Curicullum Vitae