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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Algorithmic study of elliptic modular graph forms
- Martijn Hidding (Uppsala Universitet)
DTSTART;TZID=Europe/London:20220824T111500
DTEND;TZID=Europe/London:20220824T121500
UID:TALK177230AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/177230
DESCRIPTION:Elliptic modular graph forms (eMGFs) are a string-
theory motivated approach to construct higher-dept
h generalizations of Zagier&rsquo\;s single-valued
elliptic polylogarithms. They are generalizations
of modular graph forms (a class of non-holomorphi
c modular forms appearing in genus-one closed stri
ng amplitudes)\, which depend on additional uninte
grated punctures. For example\, eMGFs emerge in th
e non-separating degeneration limit of building bl
ocks of genus two string amplitudes. In this talk\
, we proceed from an algorithmic perspective and f
ocus on general strategies to express eMGFs in ter
ms of a canonical function space which exposes the
ir algebraic / differential relations and their ex
pansion around the cusp. The function space consis
ts of iterated integrals denoted by beta^sv\, whic
h are obtained through a confluence of generating-
series methods and a generalized Sieve algorithm t
hat extends from the case of MGFs. We exemplify at
fixed modular / transcendental weight how our org
anization of eMGFs implies the counting of their i
ndependent representatives.\n(In collaboration wit
h \;Oliver Schlotterer (Uppsala University)\,
Bram Verbeek (Uppsala University))\n \;
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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