
Legendrian Barriers
Emmanuel Opshtein of the Institut de Recherche Mathématique Avancée in Strasbourg presents a research seminar talk given through the joint IAS, Princeton, Montreal, Paris, and Tel Aviv Symplectic Geometry Zoominar. He builds on earlier work with Felix Schlenk showing that Lagrangian barriers have a contact-geometric analogue in the three-sphere: explicit Legendrian complexes of arcs whose Reeb chords to many Legendrian loops are forced to be short. The talk's goal is to extend that phenomenon beyond S3, arguing it holds generally in prequantization bundles of arbitrary dimension. Opshtein walks through the construction of these Legendrian complexes, the estimates controlling chord lengths, and how the argument generalizes the original three-dimensional case to higher-dimensional contact manifolds fibering over symplectic bases. The talk assumes graduate-level familiarity with symplectic and contact geometry and is aimed at specialists following current research in Reeb dynamics and Legendrian submanifolds rather than a general audience.