Caucher Birkar works in algebraic geometry, in particular, birational geometry. His work involves various topics such as minimal models, Fano and Calabi-Yau and general type varieties, singularity theory, positive characteristic geometry, etc.
In joint work with Paolo Cascini, Christopher Hacon, and James McKernan, Birkar proved the existence of minimal models for varieties of general type and the finite generation of canonical rings. These results have had a major impact on research in algebraic geometry.
In work on Fano varieties Birkar proved the Borisov-Alexeev-Borisov conjecture. This work also has deep applications to complements theory and linear systems, singularity theory, structure of birational automorphism groups, etc, and is expected to find further important applications especially to the minimal model program.
Birkar has received numerous awards including the Philip Leverhulme Prize (2010), the American Mathematical Society Moore research article prize (2016), the London Mathematical Society Whitehead prize (2018), and the Fields Medal (2018).
Professor of Mathematics, Department of Pure Mathematics and Mathematical Statistics, University of Cambridge