BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Differential equations and mixed Hodge structures - Matt Kerr (Was
 hington University in St. Louis)
DTSTART:20220621T140000Z
DTEND:20220621T150000Z
UID:TALK174416@talks.cam.ac.uk
DESCRIPTION:We report on a new development in asymptotic Hodge theory\, ar
 ising from work of Golyshev-Zagier and Bloch-Vlasenko\, and connected to t
 he Gamma Conjectures in Fano/LG-model mirror symmetry. &nbsp\;The talk wil
 l focus exclusively on the Hodge/period-theoretic aspects.\n&nbsp\; Given 
 a variation of Hodge structure M on a Zariski open in P^1\, the periods of
  the limiting mixed Hodge structures at the punctures are interesting inva
 riants of M. &nbsp\;More generally\, one can try to compute these asymptot
 ic invariants for iterated extensions of M by "Tate objects"\, which may a
 rise for example from normal functions associated to algebraic cycles. &nb
 sp\;\n&nbsp\; The main point of the talk will be that (with suitable assum
 ptions on M) these invariants are encoded in an entire function called the
  motivic Gamma function\, which is determined by the Picard-Fuchs operator
  L underlying M. &nbsp\;In particular\, when L is hypergeometric\, this is
  easy to compute and we get a closed-form answer (and a limiting motive). 
 &nbsp\;\n&nbsp\; Though that is probably enough for a single talk\, perhap
 s one more thing is worth mentioning in this abstract: &nbsp\;in the next 
 simplest class of cases beyond hypergeometric\, the leading Taylor coeffic
 ient of the motivic Gamma at 1 is given by the special value of a normal f
 unction\, and in one special case this recovers Apery&rsquo\;s irrationali
 ty proof for zeta(3).
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR