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Resurgence and transseries in quantum theories

KMI Special Lecture
2014-02-24 13:30
Mithat Unsal
KMI Science Symposia (ES635)

Lecture 1-2) Resurgence, transseries and towards a non-perturbative
continuum definition of QFTs

(This two lecture will mostly discuss  general concepts in the context
of asymptotically free QFTs:
CP(N-1) in two-dimensions, and deformed Yang-Mills and QCD(adj) in
four dimensions.
We will introduce new calculable semi-classical saddles called neutral
and magnetic bions.
It will also discuss semi-classic realization  of  IR renormalons.)

Lecture 3) Analytic continuation,  Lefschetz thimbles  and
introduction to alien calculus

This lecture will cover formal aspects in d=0 dimensional examples
which form prototypes for QFTs.

Lecture 4) Non-perturbative saddles in QFTs and QM  beyond topological

I will address NP saddles in theories  without a homotopy group, and
multiple ways to derive them.
Time permitting,  I will also discuss exotic examples of complex
saddles, (generalized instanton sector)
in multiple context  including QM, and perhaps non-linear ODEs, and
matrix models.