Research Interests

My main interest is in symplectic topology, geometric topology, and applications to mathematical physics. Currently, my research focuses on the homotopy theoretic, geometric, and algebraic properties of groups of symplectic diffeomorphisms, on related embedding problems, and on physical interpretations of symplectic rigidity phenomena. Symplectic geometry was initially developped as the mathematical framework of classical physics. It evolved into an independent field of research, very topological in nature, which is at the crossroads of differential topology, algebraic geometry, dynamics, and gauge theory. Nowadays, most of the new developments involve Gromov's theory of \(J\)-holomorphic curves, Hofer geometry, Donaldson's theory of topological Lefschetz fibrations, and Floer homology theory.

Seminars

The UWO Mathematics Department hosts a number of research seminars. See the Math Department calendar for a list of upcoming talks.

Students

  • Sina Hazrantpour, Ph.D. 2014 - 2015.
  • Chandrasekar Rajamani, Ph.D. 2014 - Present.
  • Baran Serajelahi, Ph.D. 2010 - Present. (Co-supervised with T. Barron).
  • Martin Van Hoof, Ph.D, 2009 - 2013: Thesis title: Symplectomorphism Groups of Weighted Projective Spaces.
  • Sayed Mehdi Mousavi, Ph.D, 2009 - 2012: Thesis title: A convexity Theorem for Symplectomorphism Groups.

Research Opportunities

I encourage eligible people in geometry or topology to apply for an NSERC Postdoctoral Fellowship, an NSERC Banting Postdoctoral Fellowship (domestic and international applicants eligible), an NSF PDF (e.g. a International Research Fellowship Program postdoc, or a Mathematical Sciences Postdoctoral Research Fellowships or a Distinguished International Postdoctoral Research Fellowship), or similar to be held at Western.

Citizens of New Zealand, the United Kingdom, Brazil, France, Germany, Italy, Japan, Norway, Russia, South Korea and Switzerland are eligible to apply for postdoctoral support from the Government of Canada.

Upcoming and Recent Conferences

  • July 5 - July 9, 2016: Conference on Differential Geometry - CRM - Montréal - Canada
  • May 15 - May 19, 2016: Quantum Mechanics meets Symplectic Topology - Tel Aviv - Israel
  • September 21 - September 25, 2015: Elliptic Methods and Moduli Spaces - CIRM - Luminy - France
  • August 31 - September 4, 2015 : Topologie, Géométrie et Dynamique (Lalondefest) - CRM - Montréal - Canada
  • June 20 - July 4, 2015 : Rencontres en binôme - CIRM - Luminy - France

Recent Papers

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