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SUMMARY:The twistor geometry of a family of Schrödinger equations - Timot
 hy Moy (University of Cambridge)
DTSTART:20240904T103000Z
DTEND:20240904T113000Z
UID:TALK219868@talks.cam.ac.uk
DESCRIPTION:Joyce structures were introduced by Bridgeland in work relatin
 g to Donaldson-Thomas invariants and bear resemblance to Frobenius structu
 res. Inspired by the construction of the A2&nbsp\;Joyce structure\, we wil
 l use the Bailey-Eastwood characterisation of complex hyper-K&auml\;hler m
 etrics to construct Joyce structures on particular moduli spaces of meromo
 rphic quadratic differentials on the Riemann sphere. We will observe that 
 the twistor distribution\, which coincides with the span of the isomonodro
 mic flows for a family of 2nd&nbsp\;order linear ODE with rational potenti
 al\, may be obtained as the kernel of a 2-form induced by the intersection
  forms of an associated family of algebraic curves. Important associated d
 ata is simply expressible in terms of periods and intersection products of
  differential forms that appear in WKB analysis of the equation.&nbsp\;\n&
 nbsp\;
LOCATION:Seminar Room 2\, Newton Institute
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