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Ronan Conlon: Lectures

By Victoria Hain in Lectures on August 29, 2019.

5/15/2024: A family of Kahler flying wing steady Ricci solitons
9/09/2019: Classification results for expanding and shrinking gradient Kähler-Ricci solitons

May 14, 2024
TITLE: A family of Kahler flying wing steady Ricci solitons

ABSTRACT: Steady Kahler-Ricci solitons are eternal solutions of the Kahler-Ricci flow. I will present new examples of such solitons with strictly positive sectional curvature that live on C^n and provide an answer to an open question of H.-D. Cao in complex dimension n>2. This is joint work with Pak-Yeung Chan and Yi Lai.

Slides of Lecture

September 9, 2019
TITLE: Classification results for expanding and shrinking gradient Kähler-Ricci solitons

ABSTRACT: A complete Kahler metric $g$ on a Kahler manifold $M$ is a “gradient Kahler-Ricci soliton” if there exists a smooth real-valued function $f:M\to\mathbb{R}$ with $\nabla f$ holomorphic such that $\operatorname{Ric}(g)-\operatorname{Hess}(f)+\lambda g=0$ for $\lambda$ a real number. I will present some classification results for such manifolds. This is joint work with Alix Deruelle (Université Paris-Sud) and Song Sun (UC Berkeley).