Birkar is a main contributor to modern birational geometry. In 2010 he received the Leverhulme Prize in mathematics and statistics for his contributions to algebraic geometry.[2] and, in 2016, the AMS Moore Prize[3] for the article "Existence of minimal models for varieties of log general type," Journal of the AMS (2010) (joint with P. Cascini, C. Hacon and J. McKernan). He was awarded the Fields Medal in 2018, "for his proof of boundedness of Fano varieties and contributions to minimal model problem".