Middle intersection forms on singular elliptic Calabi-Yau fourfolds, and applications to the standard model and mirror symmetry

Abstract: Recent work with Jefferson and Turner indicates that the intersection form on the vertical part of middle cohomology of singular elliptic Calabi-Yau fourfolds is independent of resolution. This suggests that the intersection structure should have a natural definition even in these singular geometries. The resulting intersection form has a simple block-diagonal structure in terms of Kodaira singularities and the geometry of the base of the elliptic fibration; the talk will describe applications of this intersection form to analysis of chiral matter and standard model constructions in F-theory as well as new insights into mirror symmetry, in particular providing in some cases a complete description of the intersection form on H_4 (X, Z) for a smooth Calabi-Yau fourfold including both vertical and horizontal parts.

differential geometrymetric geometry

Audience: researchers in the discipline

Western Hemisphere colloquium on geometry and physics

Series comments: Description: Biweekly colloquium of geometers and physicists

This weekly online colloquium features geometers and physicists presenting current research on a wide range of topics in the interface of the two fields. The talks are aimed at a broad audience. They will take place via Zoom on alternate Mondays at 3pm Eastern, noon Pacific, 4pm BRT. Each session features a 60 minute talk, followed by 15 minutes for questions and discussion. You may join the meeting 15 minutes in advance. Questions and comments may be submitted to the moderator via the chat interface during the talk, or presented in person during the Q&A session. These colloquia will be recorded and will be available (linked from the website) asap after the event.