Caltech-Tsinghua Joint Colloquium

Tuesday, October 13, 2026

5:00pm to 6:00pm

Online Event

From Calabi–Yau Singularities to 6D Gravitational Anomaly Cancellation

Kai Xu, Assistant Professor, Department of Mathematics, Tsinghua University,

Six-dimensional F-theory compactifications provide a geometric framework for constructing UV complete quantum theory of gravity, in which gauge symmetries and charged matter arise from singularities of elliptically fibered Calabi–Yau threefolds. An important consistency condition on these theories is the cancellation of gravitational anomalies.

I will first review this physical picture and explain how matters localize at singularities, then explain how six-dimensional matter representations can be constructed from the CoHA/BPS cohomology of resolved cDV singularities, equipped with a natural action of the gauge algebra. Finally, I will give a geometric derivation of the 6D gravitational anomaly cancellation condition, reducing it through five-dimensional Coulomb/Higgs branch physics to a local statement about singularities of elliptic Calabi–Yau threefolds.

Zoom Link: https://caltech.zoom.us/j/5181912363?omn=87417799891

For more information, please contact Caltech Mathematics Group by phone at 6263954335 or by email at [email protected].

Event Sponsors

Mathematics More Events from this Sponsor