Hirosi Ooguri, "Compact Calabi-Yau and Swampland" (No Sound)

Video recording for "Tsinghua-Tokyo workshop on Calabi-Yau," January 15-19, Fuji Kenshujyo (富士研修所), Fujiyoshida, Japan. **This recording is missing audio, unfortunately.**

[workshop webpage] https://indico.ipmu.jp/event/422/
[slides] Some slides are available from https://indico.ipmu.jp/event/422/page/1279-program-titles-and-abstracts
[abstract] In this talk, I will discuss recent applications of Calabi-Yau geometry to make
low-energy predictions of quantum gravity. For the last couple of decades, it has become
increasingly clear that the mathematical consistency of the unification of general relativity and quantum mechanics imposes non-trivial constraints on low-energy physics that
cannot be captured by the standard paradigm of the Wilsonian effective theory. They
are called Swampland conditions. Since many consistent quantum gravity theories can
be constructed by compactifications of string theory on compact Calabi-Yau manifolds,
Calabi-Yau geometry has been used to test Swampland conditions and to discover new
ones. In this talk, I will review the two basic Swampland conditions: the Distance Conjecture and the Weak Gravity Conjecture, and explain how the Hodge structure, the
Gromov-Witten/Donaldson-Thomas invariants and the elliptic genera are used to test
and clarify these conjectures. I will also discuss Swampland conditions in anti-de Sitter
(AdS) space and their derivations using the AdS/CFT correspondence. If time permits, I
will present my recent series of work on the symmetry resolution of the Hilbert spaces of
conformal field theories, which is relevant for the Weak Gravity Conjecture in AdS