Symplectic Geometry, Contact Dynamics and Billiards

Science / Mathematics

My research lies at the intersection of symplectic geometry, billiard theory, and Hamiltonian dynamics, exploring the intricate connections between these diverse mathematical fields. Symplectic geometry, a fundamental branch of mathematics, provides a natural framework for studying classical mechanics in any space, including the intricate trajectories of billiard balls on a table. I aim to comprehend how the knowledge about billiard trajectories across different tables can impact the type of symplectic geometry and, subsequently, the Hamiltonian dynamics of a related space. Furthermore, I seek to determine if symplectic geometry can aid in resolving open-ended questions regarding the existence of billiard trajectories on complex tables.

Amount invested

1st phase: R$ 100,000.00
2nd phase: R$ 1,000,000.00 (R$ 700,000.00 + R$ 300,000.00 optional bonus for the integration and training of people from underrepresented groups in science)

Open Calls

Chamada 1
  • Topics
  • Billiard theory
  • Contact dynamics
  • Symplectic geometry