Casim Abbas' Home Page



Research

I am currently working on Hamiltonian dynamical systems and on symplectic and contact geometry.
  1. Finite energy surfaces and the chord problem, Duke Math. J., Vol 96, No.2, (1999), pp. 241--316
  2. A Note on V.I. Arnold's Chord Conjecture, Int. Math. Res. Notices, No. 4, (1999), pp. 217--222
  3. Pseudoholomorphic strips in symplectisations I: Asymptotic behavior, Annales de l'Institut Henri Poincare, Analyse non lineaire, (2004), Vol. 21/2 pp. 139-185.
  4. Pseudoholomorphic strips in symplectisations II: Fredholm theory and Transversality, Comm. Pure Appl. Math., Vol. 57 (2004), no. 1, 1--58
  5. Pseudoholomorphic strips in symplectisation III: Embedding properties and Compactness, Journal of Symplectic Geometry, Vol. 2, No. 2, (2004), 219--260
  6. The Chord Problem and a new method of filling by pseudoholomorphic curves, Int. Math. Res. Notices, No. 18, (2004), pp. 913--927
  7. The Weinstein conjecture for planar contact structures in dimension three (joint work with Helmut Hofer and Kai Cieliebak), Commentarii Mathematici Helvetici, 80, (2005), pp. 771-793
  8. Holomorphic open book decompositions Duke Math. J., Vol 158, No. 1, (2011), pp. 29-82
The material in items #3-#6 is based upon work supported by the National Science Foundation under Grant No. 0196122. The material in #7 is based upon work supported by a Michigan State University IRGP grant. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

Teaching

Lecture Notes

Math 921 (Functional Analysis II)

Contact: abbas@math.msu.edu

Last Revised 09/11/12