The Heidelberg Laureate Forum Foundation extends congratulations to 2018’s recipients of the Fields Medal and Nevanlinna Prize!
Fields Medal 2018
For the proof of the boundedness of Fano varieties and for contributions to the minimal model program.
For contributions to the theory of optimal transport and its applications in partial differential equations, metric geometry and probability.
For transforming arithmetic algebraic geometry over p-adic fields through his introduction of perfectoid spaces, with application to Galois representations, and for the development of new cohomology theories.
For his synthesis of analytic number theory, homogeneous dynamics, topology, and representation theory, which has resolved long-standing problems in areas such as the equidistribution of arithmetic objects.
Nevanlinna Prize 2018
For transforming our understanding of the computational complexity of fundamental problems in markets, auctions, equilibria, and other economic structures. His work provides both efficient algorithms and limits on what can be performed efficiently in these domains.