[GS_M_AG] Fano varieties and Sasaki-Einstein connected sums $(S^2\times S^3)^{\# n}$ and $(S^3\times S^4)^{\# n} $
ABSTRACT
We review the construction of Sasaki--Einstein metrics arising from Fano varieties. In particular, we explain Kollár's construction of such metrics on every connected sum of $S^2\times S^3$. Recent advances in K-stability and the topology of highly connected manifolds have made it possible to investigate the 7-dimensional analogue of Kollár's result, namely the construction of Sasaki--Einstein metrics on connected sums of $S^3\times S^4$. In this talk, we present the 7-dimensional analogue of Kollár's result. This is joint work in progress with D. Jeong, I. Kim, and J. Won.
