Caucher Birkar

Caucher Birkar serves as Professor of Mathematics at the University of Cambridge since 2015, following roles as University Reader (2010-2015) and University Lecturer (2007-2010). A leading figure in algebraic geometry, his revolutionary work on the minimal model program earned him the 2018 Fields Medal, mathematics' highest honor. He maintains active research in the Department of Pure Mathematics and Mathematical Statistics (DPMMS) at Cambridge.

His academic foundation includes:

• BSc from University of Teheran (2000)
• PhD from University of Nottingham (2004) under advisors I. Fesenko and V. Shokurov

Birkar's research centers on birational geometry with profound contributions to Fano varieties, log canonical singularities, and the minimal model program. His landmark proof of boundedness for Fano varieties resolved fundamental conjectures, while his work extending minimal model theory to positive characteristic opened new research frontiers. He specializes in analyzing singularities through linear systems and log canonical thresholds, developing techniques that transformed classification theory for algebraic varieties.

Recent publications (2016-2017) demonstrate his focus on Mori fibre spaces in positive characteristic, boundedness of Fano varieties, and anti-pluricanonical systems. These works exhibit consistent themes: establishing existence theorems for minimal models, solving boundedness problems through singularity analysis, and advancing the minimal model program beyond characteristic zero. His research shows increasing emphasis on effective methods and explicit bounds in classification problems.

Major recognitions include:

• Fields Medal (2018) for contributions to birational geometry
• Royal Society Research Professorship (2019)
• AMS Moore Prize (2016)
• Leverhulme Prize (2010)
• Royal Society Fellowship (2019)

Birkar advises doctoral students in algebraic geometry though specific names aren't documented in available sources. His Royal Society Research Professorship funds ongoing work on the minimal model program's extension to positive characteristic. While no formal lab structure is mentioned, he collaborates extensively through Cambridge's DPMMS research groups and international geometry networks. Current projects focus on effective Iitaka fibrations and boundedness of polarized pairs.