Instructors: Nicolas Martinez Alba (Universidad Nacional de Colombia), Ivan Contreras (Amherst College)

Zoom link: https://amherstcollege.zoom.us/j/91885350020

Syllabus: here

• Session 1: Thursday, March 10 (9:00-10:30 AM): Introduction, Overview of manifolds and vector fields. Recording: here

• Session 2: Thursday, March 17 (9:00-10:30 AM): Tangent and cotangent bundles, differential forms. Recording: here, Notes: here

• Session 3: Thursday, March 24 (8:30-10:00 AM): Operations on differential forms. Recording: here, Notes: here

• Session 4: Thursday, March 31 (8:30-10:00 AM): Lagrangian-Hamiltonian Mechanics. Recording: here. Notes: here

• Session 5: Thursday, April 7 (9:00-10:30 AM): Symplectic Manifolds and Mechanics I. Notes: here

• Session 6: Thursday, April 14: Easter break

• Session 7: Thursday, April 21 (9:00-10:00): Symplectic Manifolds and Mechanics II. Recording: here. Notes: here

• Session 8: Thursday, April 21 (10:00-11:00): Ivan Roa's talk on Discrete Exterior Calculus. Recording: here

Project Samples:

• 1. Discrete Curvature: link to an explanatory video here

  2. Toric manifolds: link to an explanatory video here. Código de acceso: 1oWp+vg4

• Session 9:

• Session 10:

• Session 11:

• Session 12:

• Session 13:

• Session 14:

• Session 15:

Resources

The following are resources for the topics discussed during the sessions:

• Non holonomic systems

• Computational Poisson Geometry I

• Computational Poisson Geometry II

• Hamiltonian Dynamical Systems

• Geometric Discretization of Lagrangian Mechanics