Title: Gamma conjecture I: counterexamples and modifications

Abstract: Gamma conjectures were proposed by Galkin, Golyshev and Iritani, and consist of conjecture $\mathcal O$, Gamma conjecture I and II. In this talk, I will introduce the original conjectures and some counterexamples for conjecture $\mathcal O$ and Gamma conjecture I. Then I will talk about some modifications for Gamma conjecture I. Finally, I will discuss an interplay of birational transformations with an extension of Gamma conjecture I over Kahler moduli space.This talk is based on a joint work with S. Galkin, H. Iritani, H. Ke, C. Li and Z. Su.