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Monday, February 19th 2018

3:30 pm:

I will provide an introductory level overview of recent

applications of resurgent trans-series and Picard-Lefschetz theory to

quantum mechanics and quantum field theory.

Resurgence connects local perturbative data with global topological

structures. In quantum mechanical systems, this program provides a

constructive relation between different saddles. For example, in

certain cases it has been shown that all information around the

instanton saddle is encoded in perturbation theory around the

perturbative saddle. In quantum field theory, such as sigma-models

compactified on a circle, neutral bions provide a semi-classical

interpretation of the elusive IR-renormalon, and fractional kink

instantons lead to the non-perturbatively induced mass gap exactly of

order of the strong scale. I also describe the concept of hidden

topological angle, a phase associated with Lefschetz thimbles.

Hidden topological angle may provide destructive/constructive

interference effects between equally dominant saddles in the Lefschetz

thimble decomposition, providing resolution to some time standing

puzzles in non-perturbative analysis.

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