Presenter: Dr. Juan Margalef Bentabol, candidate for a tenure-track position in the School of Mathematical and Computational Sciences

Teaching talk: Thursday, April 18, 9:30--10:30 am, Cass Science Hall 101

Research talk: Thursday, April 18, 1:30--2:30 pm, Cass Science Hall 101

Title: "Symplectic Structures in the boundaries of Physics: Bridging the canonical and covariant formalisms"

Abstract:

Symplectic structures play a fundamental role in understanding the dynamics and potential quantization of many physical theories. There are essentially two different ways of endowing a physical theory with such a structure: the canonical and the covariant. While the former relies on the canonical symplectic structure of a cotangent bundle, the latter emerges from variational calculus (differential calculus in infinite-dimensional manifolds) for a given action. Including boundaries in the canonical formalism poses no problem; however, in the covariant formalism, things break apart with the standard methods developed in the 90s.

In this presentation, I will provide concise overviews of both formalisms without boundaries and introduce a novel framework developed to handle boundaries seamlessly. Through this framework, I will prove the equivalence of several gravity theories which were thought to be inequivalent and unveil a recent breakthrough: the establishment of the full equivalence between the canonical and covariant formalisms, resolving a longstanding problem which remained open for nearly four decades.

Teaching and research talks are open to the UPEI campus community.