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SUMMARY:Dubrovin Conjecture and Singularities of Painleve-I Tritronquee so
 lution - Saleh Tanveer (Ohio State University)
DTSTART:20221031T140000Z
DTEND:20221031T145000Z
UID:TALK185177@talks.cam.ac.uk
DESCRIPTION:Abstract:&nbsp\; Painleve Equations arise in many context. In 
 particular Grava\, Klein & Dubrovin proposed universality in blow up of fo
 cussing NLS equation that required absence of singularity of Tritronquee s
 olutions of P-I in a sector of width 8 \\pi/5. This conjecture\, usually k
 nown as Dubrovin Conjecture\, remained an important open problem for a whi
 le until it was proved by the authors in 2014. We present the analysis of 
 this proof that require among other results precise asymptotics includuing
  a two scale expansion in a regime where erstwhile exponentially small ter
 ms become $O(1)$ in a manner described for generic ODEs by Costin \\& Cost
 in (2001). There has been more recent work that extends the singularity re
 sults in different directions.&nbsp\;\n&nbsp\;\n*Joint work with Ovidiu Co
 stin & Min Huang
LOCATION:Seminar Room 1\, Newton Institute
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