Title: Invariants in Contact Topology

Contact topology studies contact manifolds and their Legendrian submanifolds up to contact diffeomorphisms. It was born, together with its sister Symplectic topology, less than 20 years ago, essentially in seminal works of D. Bennequin and M. Gromov ( see \cite{Bennequin,Gromov-holomorphic}). However, despite several remarkable successes the development of Contact topology is still significantly behind its symplectic counterpart. In this talk we will discuss the state of the art and some recent breakthroughs in this area.

1991 Mathematics Subject Classification: 53C, 55N, 57R, 58G, 81T

Keywords and Phrases: Contact manifolds, Legendrian submanifolds, holomorphic curves, contact homology algebra

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