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Tristan Collins: Lectures

September 12, 2021
TITLE: Calabi-Yau manifolds through conifold transitions

ABSTRACT: It has been understood for some time that compact Kahler Calabi-Yau manifolds can be “connected” to non-Kahler Calabi-Yau manifolds through the process of conifold transitions.  I will discuss some joint works with S. Picard, S. Gukov, and S.-T. Yau aimed at understanding what geometric structure can be preserved through these transitions, focusing primarily on the case of Hermitian-Yang-Mills connections and special Lagrangians. 

Slides of Lecture

January 10, 2017
TITLE: Sasaki-Einstein metrics and K-Stability

ABSTRACT: I will discuss the connection between Sasaki-Einstein metrics, or conical Ricci flat Kahler metrics, and the algebro-geometric notion of K-stability. In particular, I will give a differential geometric perspective of K-stability which arises from the Sasakian view point, and use K-stability to find infinitely many non-isometric Sasaki-Einstein metrics on the 5-sphere. This is joint work with G. Szekelyhidi.