Michael Brandenbursky

I am a Visiting Professor at Max Planck Institute for Mathematics in Bonn

Office: 217
Email address: brandem@mpim-bonn.mpg.de


Research interests

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


Teaching

    I am currently supported by a fellowship without teaching duties.


My Research Papers

  1. M. Brandenbursky and J. Kedra, Quasi-isometric embeddings into diffeomorphism groups, to appear in Groups, Geometry and Dynamics.
  2. M. Brandenbursky, On the autonomous metric on groups of Hamiltonian diffeomorphisms of closed hyperbolic surfaces, Oberwolfach Preprints, OWP 2013-18.
  3. 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.
  4. M. Brandenbursky, Invariants of closed braids via counting surfaces, Journal of Knot Theory and its Ramifications, vol. 22, No 3 (2013), 1350011 (21 pages).
  5. 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.
  6. M. Brandenbursky, On quasi-morphisms from knot and braid invariants, Journal of Knot Theory and its Ramifications, vol. 20, No 10 (2011), 1397-1417.
  7. M. Brandenbursky, Bi-invariant metrics and quasi-morphisms on groups of Hamiltonian diffeomorphisms of surfaces, Arxiv:1306.3350, submitted, 2013.
  8. M. Brandenbursky and E. Shelukhin, On the large-scale geometry of the L^p-metric on the symplectomorphism group of the two-sphere, Arxiv:1304.7037, submitted, 2013.
  9. M. Brandenbursky, Coloring link diagrams and Conway-type polynomial of braids, Arxiv:1302.6967, submitted, 2013.
  10. M. Brandenbursky, Link invariants via counting surfaces, Arxiv:1209.0420, submitted, 2012.
  11. M. Brandenbursky, S. Gal, J. Kedra and M. Marcinkowski, Cancelation norm and the geometry of bi-invariant word metrics, preprint, 2013.


Papers in Conference Proceedings

  1. M. Brandenbursky and J. Kedra, On bi-invariant word metrics on groups, Oberwolfach reports, 35/2012, DOI:104171/OWR/2012/35, 2012.
  2. M. Brandenbursky, Quasi-morphisms defined by knot invariants, Oberwolfach reports, 30/2010, DOI:104171/OWR/2010/30, 2010.


Theses


Curriculum Vitae


Research Statement