Symplectic Geometry

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Related lectures (30)

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Lie Theorems and Group Algebra

Covers Lie theorems, group algebra, Ado's theorem, and spacetime symmetries.

Symmetry in Quantum Field Theory

Explores associativity, Lie algebra, Lie groups, relativity, and symmetry preservation in quantum field theory.

General Fields: Lorentz Representations

Covers the representation of Lorentz transformations through general fields and the consequences of symmetry.

Mechanics: Introduction and Calculus

Introduces mechanics, differential and vector calculus, and historical perspectives from Aristotle to Newton.

The Weil Representation: Part 2

Covers the Weil representation, Heisenberg group actions, and symplectic group concepts.

Lie Groups and Lorentz Transformations

Covers Lie groups, Lorentz transformations, boosts, rotations, and complexified Lie algebras.

Simple Lie Algebras: Classification and Properties

Explores the classification and properties of simple complex Lie algebras, emphasizing their connection with Lie groups.

Riemannian connections

Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.

Symplectic Rigidity: Forms of Symplectic Rigidity

Explores symplectic rigidity, including rigidity, flexibility, and dynamical rigidity, with a focus on symplectic manifolds and Lagrangian submanifolds.

Differentiating Vector Fields: Definition

Introduces differentiating vector fields along curves on manifolds with connections and the unique operator satisfying specific properties.