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DTSTART;TZID=America/New_York:20230403T100000
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SUMMARY:Kähler-Einstein metrics on families of Fano varieties
DESCRIPTION:Algebraic Geometry in String Theory Seminar \nSpeaker: Chung-Ming Pan\, Institut de Mathématiques de Toulouse \nTitle: Kähler-Einstein metrics on families of Fano varieties \nAbstract: This talk aims to introduce a pluripotential approach to study uniform a priori estimates of Kähler-Einstein (KE) metrics on families of Fano varieties. I will first recall basic tools in the pluripotential theory and the variational approach to complex Monge-Ampère equations. I will then define a notion of convergence of quasi-plurisubharmonic functions in families of normal varieties and extend several classical properties under this context. Last\, I will explain how these elements help to obtain a purely analytic proof of the openness of existing singular KE metrics and a uniform $L^\infty$ estimate of KE potentials. This is joint work with Antonio Trusiani.
URL:https://cmsa.fas.harvard.edu/event/agst-4323/
LOCATION:Virtual
CATEGORIES:Algebraic Geometry in String Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-AGST-Seminar-04.03.2023.png
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SUMMARY:Modular graph forms and iterated integrals in string amplitudes
DESCRIPTION:Algebraic Geometry in String Theory Seminar \nSpeaker: Oliver Schlotterer (Uppsala University) \nTitle: Modular graph forms and iterated integrals in string amplitudes \nAbstract: I will discuss string amplitudes as a laboratory for special functions and period integrals that drive fruitful cross-talk with particle physicists and mathematicians. At genus zero\, integration over punctures on a disk or sphere worldsheet generates multiple zeta values in the low-energy expansion of open- and closed-string amplitudes. At genus one\, closed-string amplitudes introduce infinite families of non-holomorphic modular forms through the integration over torus punctures known as modular graph forms. The latter inspired Francis Brown’s alternative construction of non-holomorphic modular forms in the mathematics literature via iterated integrals\, and I will report on recent progress in clarifying their connection with modular graph forms.
URL:https://cmsa.fas.harvard.edu/event/agst-4723/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Algebraic Geometry in String Theory Seminar
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