ReNewQuantum

ERC SYNERGY GRANT

UPCOMING ReNewQuantum SEMINAR

Very often in physics and mathematics we have an asymptotic expansion in small parameter which is divergent because the coefficients have factorial growth an ∼ n! exp(O(n)). The property of resurgence means that the Borel transform ∑n anζn/n! admits an analytic continuation, which allows to reconstruct the exact value of the original divergent series.


I will review the theory of resurgence and resummation for the asymptotic expansions of exponential integrals. I will illustrate the theory by finite-dimensional examples (Airy function, Stirling formula for Γ-function), and infinite-dimensional ones (heat kernel, quantum Chern-Simons theory).