BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Non-perturbative quantum geometry\, resurgence and BPS structures 
 - Murad Alim (Universität Hamburg)
DTSTART:20220915T123000Z
DTEND:20220915T133000Z
UID:TALK178136@talks.cam.ac.uk
DESCRIPTION:BPS invariants of certain physical theories correspond to Dona
 ldson-Thomas (DT) invariants of an associated Calabi-Yau geometry. BPS str
 uctures refer to the data of the DT invariants together with their wall-cr
 ossing structure. On the same Calabi-Yau geometry another set of invariant
 s are the Gromov-Witten (GW) invariants. These are organized in the GW pot
 ential\, which is an asymptotic series in a formal parameter and can be ob
 tained from topological string theory. A further asymptotic series in two 
 parameters is obtained from refined topological string theory which contai
 ns the Nekrasov-Shatashvili (NS) limit when one of the two parameters is s
 ent to zero. I will discuss in the case of the resolved conifold how all t
 hese asymptotic series lead to difference equations which admit analytic s
 olutions in the expansion parameters. A detailed study of Borel resummatio
 n allows one to identify these solutions as Borel sums in a distinguished 
 region in parameter space. The Stokes jumps between different Borel sums e
 ncode the BPS invariants of the underlying geometry and are captured in tu
 rn by another set of difference equations. I will further show how the Bor
 el analysis of the NS limit connects to the exact WKB study of quantum cur
 ves. This is based on various joint works with Lotte Hollands\, Arpan Saha
 \, Iv&aacute\;n Tulli and J&ouml\;rg Teschner.
LOCATION:No Room Required
END:VEVENT
END:VCALENDAR