# Colloquium abstracts

**Omprokash Das**

TIFR, Mumbai

March 17, 2022

**Some results in 4-dimensional Kähler MMP**: Given two projective varieties X and Y, we say that they are bimeromorphic to each other if they have isomorphic non-empty Zariski open subsets, or equivalently, their function fields are isomorphic as k-algebras, where k is the ground field of the varieties X and Y. This defines an equivalence relation (in the varieties of fixed dimension). The Minimal Model Program (MMP) or Mori Program is a tool which aims to find a `good? and `minimal? representative in each of these equivalence classes. In this talk I will present some new results in Kähler MMP for 4-dimensional Kähler varieties. This is a joint work with Christopher Hacon and Mihai Paun.