Anchored Symplectic Embeddings and Non-Squeezing Phenomena in Four Dimensions

Explore advanced concepts in symplectic geometry through this mathematics seminar lecture focusing on anchored symplectic embeddings and their fascinating properties. Delve into the intriguing behavior of symplectic manifolds at the intersection of rigidity and flexibility, starting with Gromov's groundbreaking non-squeezing phenomenon from the 1980s. Learn about the complex relationships between standard symplectic shapes and their embedding capabilities, including unexpected connections to Markov numbers, Fibonacci sequences, and infinite staircases. Examine innovative construction techniques like folding for finding embeddings, and discover recent research findings on four-dimensional symplectic shapes and their relationship with symplectic surfaces (anchors). The lecture, presented by Agniva Roy from Boston College, covers both theoretical foundations and cutting-edge developments in the field, concluding with proof methodologies and open questions in symplectic geometry.