Spectral Invariants via Contact Instanton Floer Theory in One-Jet Bundles

Spectral invariants are essential tools for studying symplectic and contact rigidity, such as non-squeezing problems and camel problems, as well as Hamiltonian dynamics. These invariants have been constructed through various approaches. In this talk, we focus on the Floer-theoretic construction of Legendrian spectral invariants in one-jet bundles.

Typically, Floer theory on contact manifolds, such as one-jet bundles, involves the use of symplectization. However, in this talk, I will introduce the concept of contact instantons, which enables the construction of Legendrian Floer cohomology and its spectral invariants without relying on symplectization.