Casim Abbas' Home Page

Personal Information

• Associate Professor of Mathematics
• Office: A202 Wells Hall
• Phone: (517) 353-8499
• Fax: (517) 432-1562

Research

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, click here to get to the publisher's webpage.
3. Pseudoholomorphic strips in symplectisations I: Asymptotic behavior, Annales de l'Institut Henri Poincare, Analyse non lineaire, (2004), Vol. 21/2 pp. 139-185. Click here to get to the article on the publisher's webpage.
4. Pseudoholomorphic strips in symplectisations II: Fredholm theory and Transversality, Comm. Pure Appl. Math., Vol. 57 (2004), no. 1, 1--58, click here to get to the publisher's webpage.
5. Pseudoholomorphic strips in symplectisation III: Embedding properties and Compactness, Journal of Symplectic Geometry, Vol. 2, No. 2, (2004), 219--260, here is the link to the paper on the publisher's website..
6. The Chord Problem and a new method of filling by pseudoholomorphic curves, Int. Math. Res. Notices, No. 18, (2004), pp. 913--927, click here to get to the publisher's webpage.
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

Teaching

Lecture Notes

• Functional Analysis I , Math 920, Spring Semester 2003.

• Nonlinear Functional Analysis , Math 992, Fall Semester 2003.
• Introduction to Symplectic Field Theory , Math 993, Fall Semester 2005 and Spring Semester 2006.
  The notes cover part I of the lecture, the topic was the SFT-compactness results as in the paper by F. Bourgeois, Y. Eliashberg, H. Hofer, K. Wysocki and E. Zehnder.

Math 133, Calculus II

Math 234, Calculus III (not this semester)