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(The colloquium passwordÌýwill be distributed to Princeton University and IAS members. We ask that youÌýdo not share this password. If you would like to be included in the colloquiumÌýand are not a member of either institution, please email the organizer Casey Kelleher (caseyk@princeton.edu) with an email requesting to participate which introduces yourself, your current affiliation and stage in your career.)

Theory of resurgent functions was developed by Jean Écalle starting from early 80-ies.ÌýVery often in physics and mathematics we have an asymptotic expansion in small parameter which is divergentÌýbecause the coefficients have factorial growth anÌý∼ n! exp(O(n)). The property ofÌýresurgenceÌýmeans that the Borel transform ∑nÌýanζn/n! admits an endless analytic continuation, which allows to reconstruct the exact value of the original divergent series.

I will give some examples of resurgent series (classical special functions, Écalle-Voronin theory,Ìýheat kernel, WKB approximation), and propose some new viewpoints (Hodge structures of infinite rank, analytic wall-crossing structures).