Michael Brandenbursky

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

• This semester I am an Instructor for multi-variable Calculus 175
• Office hours: MW 17:30-19:00 at SC 1527

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 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.
3. M. Brandenbursky, Invariants of closed braids via counting surfaces, Journal of Knot Theory and its Ramifications, vol. 22, No 3 (2013), 1350011 (21 pages).
4. 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.
5. M. Brandenbursky, On quasi-morphisms from knot and braid invariants, Journal of Knot Theory and its Ramifications, vol. 20, No 10 (2011), 1397-1417.
6. M. Brandenbursky and J. Kedra, On bi-invariant word metrics on groups, Oberwolfach reports, 35/2012, DOI:104171/OWR/2012/35, 2012.
7. M. Brandenbursky, Quasi-morphisms defined by knot invariants, Oberwolfach reports, 30/2010, DOI:104171/OWR/2010/30, 2010.
8. M. Brandenbursky, On the autonomous metric on groups of Hamiltonian diffeomorphisms of closed hyperbolic surfaces, Arxiv:1305.2757, 2013.
9. 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, 2013.
10. M. Brandenbursky, Coloring link diagrams and Conway-type polynomial of braids, Arxiv:1302.6967, 2013.
11. M. Brandenbursky, Link invariants via counting surfaces, Arxiv:1209.0420, 2012.
12. M. Brandenbursky, Bi-invariant metrics and quasi-morphisms on groups of Hamiltonian diffeomorphisms of surfaces, preprint.

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.

Curriculum Vitae

• CV

Short Research Statement

• Short Research Statement