In this talk I will discuss the problem of finiteness of log Calabi-Yau varieties and related problems in birational geometry. Some recent results in this direction will be described.

Caucher Birkar is a professor at the University of Cambridge in the United Kingdom. His research area is algebraic geometry. In the International Congress of Mathematicians in 2018, Prof. Caucher Birkar was awarded the Fields medal, the highest honor for mathematicians, for his works on boundedness of Fano varieties and the minimal model program.