Symplectic Manifolds Courses and Certifications

Institute for Advanced Study

Lagrangian Correspondence for Microlocal Sheaves

Explore advanced symplectic geometry through Lagrangian correspondences and their relationship to microlocal sheaves, connecting geometric and algebraic perspectives in Fukaya categories.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

IMSA

Lagrangian Torus Fibrations Over Affine Manifolds with Gross-Siebert Singularities

Delve into advanced mathematical concepts of Lagrangian torus fibrations, exploring local models, torus symmetry, and hypersurfaces in toric varieties through construction and analysis methods.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Equivariant Floer Theory for Symplectic C*-manifolds

Delve into equivariant Floer theory for symplectic C*-manifolds, exploring recent progress on non-compact symplectic manifolds with Hamiltonian circle actions and the resulting filtrations on quantum cohomology.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

University of Chicago Department of Mathematics

Symplectic Manifolds and Derived Orbifolds - Lecture 3

Explore symplectic manifolds and derived orbifolds in this advanced geometry lecture, examining 40 years of developments since Floer's groundbreaking work in symplectic topology.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

University of Chicago Department of Mathematics

Symplectic Manifolds and Bordism - Lecture 2

Explore symplectic manifolds and bordism in this advanced topology lecture, building on Gromov-Floer theory to understand modern developments combining homotopy theory with Morse theory.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

On Symplectic Transformations of OG10-Type Hyperkähler Manifolds via Cubic Fourfolds

Explore symplectic birational transformations on OG10-type hyperkähler manifolds, focusing on LSV manifolds derived from cubic fourfolds and their cohomological actions.

• YouTube
• 30 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Stein and Weinstein Manifolds - An Introduction to Topological and Symplectic Aspects

Explore topological and symplectic aspects of Stein manifolds, including handlebody construction, Weinstein manifolds, and flexibility versus rigidity in complex variables theory.

• YouTube
• 50 minutes
• On-Demand
• Free Video

Fields Institute

Symplectic Quotient Construction of Toric Manifolds

Explore symplectic quotient construction in toric manifolds with Lisa Jeffrey, delving into advanced mathematical concepts and their applications in toric topology.

• YouTube
• 42 minutes
• On-Demand
• Free Video

Stony Brook Mathematics

Symplectic Capacities, Viterbo Isoperimetric Conjecture, and Contact Manifolds with Closed Reeb Orbits

Explore symplectic capacities, Viterbo's conjecture, and their impact on symplectic geometry. Gain insights into convex geometry applications and closed Reeb orbits in contact manifolds.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Stony Brook Mathematics

Hodge Theory and Lagrangian Fibrations in Holomorphic Symplectic Manifolds

Explore Hodge theory and Lagrangian fibrations in holomorphic symplectic manifolds. Delve into conjectures, isomorphisms, and decomposition theorems in this advanced mathematical discourse.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Hamiltonian Dynamics on Poisson Manifolds and Symplectic Groupoids

Delve into advanced mathematical concepts exploring Hamiltonian dynamics through symplectic Lie groupoids, covering approximation methods and applications in conservative mechanics and PDEs.

• YouTube
• 42 minutes
• On-Demand
• Free Video

Instituto de Matemática Pura e Aplicada

Non-Squeezing and Other Global Rigidity Results on Locally Conformal Symplectic Manifolds

Explore non-squeezing and global rigidity results on locally conformal symplectic manifolds in this advanced mathematical workshop lecture.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Equivariant Cohomology and the (Symplectic) Diffeotype of Complexity-One Four-Manifolds

Delve into the relationship between geometry and topology of complexity-one four-manifolds, exploring how equivariant cohomology determines diffeotype but not complex structure through examples and visual illustrations.

• YouTube
• 59 minutes
• On-Demand
• Free Video

IMSA

Symplectic Fillings of Contact Manifolds and Contact Convexity

Explore recent advances in contact convexity and discover how these developments reveal numerous Stein fillings of contact manifolds, with insights into constructions and emerging challenges.

• YouTube
• 53 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

A Local Torelli Theorem for Log Symplectic Manifolds

Explore log symplectic manifolds, their moduli space, and local Torelli theorem. Discover new components in Pn's moduli space of log symplectic structures.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video