The announcement of the Shaw Prize was posted on 23rd May, reading:
The Shaw Prize in Mathematical Sciences 2017 is awarded in equal shares to János Kollár and Claire Voisin for their remarkable results in many central areas of algebraic geometry, which have transformed the field and led to the solution of long-standing
problems that had appeared out of reach.
The prize is awarded annually to “individuals who are currently active in their respective fields and who have recently achieved distinguished and significant advances, who have made outstanding contributions in academic and scientific research or applications, or who in other domains have achieved excellence”.
The two joint winners this year, Kollár and Voisin, are both professors of algebraic geometry, at Princeton and Collège de France respectively, and have made major contributions to the effort to characterise rational varieties – solution sets of polynomials which differ from a projective space only by a low-dimensional subset.
Kollár’s work relates to the Minimal Model Program, which concerns moduli of higher-dimensional varieties – spaces whose points represent equivalence classes of varieties. These spaces, which Kollár has extensively worked on and developed the field dramatically, have applications in topology, combinatorics and physics. Voisin’s achievements have included solving the Kodaira problem (on complex projective manifolds), developing a technique for showing that a variety is not rational, and even finding a counterexample to an extension of the Hodge conjecture (one of the Clay prize problems), which rules out several approaches to the main conjecture.