# Stability of algebraic varieties and Kahler geometry

## TL;DR

This survey reviews the interplay between algebraic stability conditions and Kahler geometry, highlighting recent advances and open problems in the field.

## Contribution

It synthesizes recent developments connecting algebraic stability notions with Kahler geometric properties, providing a comprehensive overview for researchers.

## Key findings

- Summarizes key stability criteria in algebraic geometry.
- Highlights links between stability and Kahler metrics.
- Outlines open problems and future directions.

## Abstract

This is a survey article, based on the author's lectures in the 2015 AMS Summer Research Institute in Algebraic Geometry, and to appear in the Proceedings.