- 03/16/23: Some aspects of Sasaki-Einstein geometry and AdS/CFT
- 09/12/21: Calabi-Yau manifolds through conifold transitions
- 01/10/17: Sasaki-Einstein metrics and K-Stability
March 16, 2023
TITLE: Some aspects of Sasaki-Einstein geometry and AdS/CFT
ABSTRACT: Sasaki-Einstein manifolds play an important role in the AdS/CFT correspondence. In this talk I will highlight some of the ways that AdS/CFT leads to new results in physics (starting from mathematics) and new conjectures in mathematics (starting from physics). I will focus on:
1) K-stability and its role in field theory
2) Emergent gravity in AdS/CFT
3) Dimension gaps in CFTs.
This talk will discuss joint works with Szekelyhidi, Xie-Yau, Berman-Persson, and Jafferis-Vafa-Xu-Yau.
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.
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.