UBC Math Department Colloquium: Caleb Suan

Conifold transitions are a mechanism in which a Calabi-Yau 3-fold is deformed into another by contracting curves and smoothing out the resulting conical singularities. Reid's Fantasy conjectures that all Calabi-Yau 3-folds can be linked by a sequence of these transitions. It is further conjectured that these spaces all admit geometries solving a system of PDEs from heterotic string theory. In this talk, I will discuss some results related to these conjectures as well as touch on the 7-dimensional analogue of this problem. Based on joint works with Benjamin Friedman, Sébastien Picard, Henrique N. Sá Earp, and Julieth Saavedra.