BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Rationality of MUMs and 2-functions - Johannes Walcher (Universit
 ät Heidelberg)
DTSTART:20220721T080000Z
DTEND:20220721T090000Z
UID:TALK175652@talks.cam.ac.uk
DESCRIPTION:Points of maximal unipotent monodromy in Calabi-Yau moduli spa
 ce play a central role in mirror symmetry\, and also harbor some interesti
 ng arithmetic. In the classic examples\, suitable expansion coefficients o
 f the (all-genus) prepotential (in polylogarithms) under the mirror map ar
 e integers with an enumerative interpretation on the mirror manifold. This
  correspondence should be expected to extend to periods relative to algebr
 aic cycles capturing the enumerative geometry relative to Lagrangian subma
 nifolds. This expectation is challenged\, however\, when the mixed degener
 ation is not defined over Q. After musing about compatibility with mirror 
 symmetry\, I will discuss two recent results that sharpen these questions 
 further: The first is a theorem proven by Felipe M&uuml\;ller which states
  that the coefficients of rational 2-functions are necessarily contained i
 n an abelian number field. (As defined in the talk\, 2-functions are forma
 l power series whose coefficients satisfy a natural Hodge theoretic superc
 ongruence.) The second are examples worked out in collaboration with B&oum
 l\;nisch\, Klemm\, and van Straten\, of MUMs that are themselves not defin
 ed over Q.
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR