Casim Abbas

Casim Abbas is an Associate Professor of Mathematics at Michigan State University's Department of Mathematics, part of the College of Natural Science. His research focuses on Hamiltonian dynamical systems and symplectic/contact geometry, with significant contributions to pseudoholomorphic curves, Weinstein conjectures, and compactness results in symplectic field theory. He has authored influential books such as An Introduction to Compactness Results in Symplectic Field Theory (2014) and co-authored Holomorphic Curves and Global Questions in Contact Geometry (2019). Abbas has held NSF grants for his research on pseudoholomorphic curves and symplectization dynamics. His teaching includes advanced courses like Functional Analysis and Honors Multivariable Calculus.

Research Interests

Abbas specializes in the intersection of differential geometry and dynamical systems, particularly in symplectic and contact structures. His work emphasizes the application of pseudoholomorphic curve techniques to solve global questions in geometry, such as the Weinstein conjecture and Arnold's chord problem. He explores geometric analysis through symplectizations and asymptotic behaviors of curves, contributing to foundational theories in symplectic topology.

Key Research Trends

His publications consistently address core challenges in symplectic geometry, including compactness theorems, embedding properties, and applications of holomorphic methods to contact structures. His work bridges theoretical frameworks with concrete geometric constructions, influencing both topological and analytical approaches in the field.