Title of the course: Introduction to Contact Geometry and Some Physical Applications
Instructor: Asst. Prof. Özgür Kelekçi
Institution: Türk Hava Kurumu Ü.
Dates: 11-17 September 2023
Prerequisites: Basic Differential Geometry (not a must but preferable)
Level: Graduate, advanced undergraduate
Abstract: Contact geometry was formally born in 1896 in the monumental work of Sophus Lie on Berührungstransformationen (contact transformations). However, the key ideas of contact geometry can be traced back to as early as Huygens’ 1690 formulation of geometric optics. Contact geometry has experienced a surge of interest from various fields of mathematics and physics research community in the last two decades. In the first part of the lecture, we aim to introduce basics of contact geometry such as vector fields and distributions, contact form, contact hyperplane, contact diffeomorphisms and so on. After covering the basic ingredients we will study some physical applications of contact geometry including examples from thermodynamics, Hamiltonian mechanics and electrodynamics.
Language: EN
Textbook:
A. McInerney, “First Steps in Differential Geometry, Riemannian, Contact, Symplectic”. Springer (2013)