Claire Voisin

The Shaw Prize in Mathematical Sciences 2017 is awarded in equal shares to **János Kollár**, Professor of Mathematics, Princeton University, USA and **Claire Voisin**, Professor and Chair in Algebraic Geometry, Collège de France, 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.

Since ancient times, a central theme in mathematics has been the study of polynomials and their solutions. Algebraic geometry is the study of the properties of sets of solutions to polynomial equations in several variables. A simple example of such an equation is *x*^{2} + *y*^{2} + *z*^{2} = 1, the solution set of which is the surface of a sphere of radius 1.

Since ancient times, a central theme in mathematics has been the study of polynomials and their solutions. Algebraic geometry is the study of the properties of sets of solutions to polynomial equations in several variables. A simple example of such an equation is x^{2}+y^{2}+z^{2} = 1, the solution set of which is the surface of a sphere of radius 1.

As this example demonstrates, solution sets of polynomial equations, which are known as varieties, are geometric objects. Examining the interplay between the algebra and the geometry has turned out to be remarkably fruitful, and algebraic geometry is a major branch of mathematics, the study of which has profound consequences not just for algebra and geometry but also for several other areas ranging from number theory to mathematical physics.

**János Kollár** was born in 1956 in Budapest, Hungary and is currently a Professor of Mathematics at Princeton University, USA. He obtained his Bachelor of Science from Eötvös Loránd University, Hungary in 1980 and his PhD from Brandeis University, USA in 1984. He was a Research Assistant at the Hungarian Academy of Sciences (1980–1981) and Junior Fellow at Harvard University, USA (1984–1987). He joined the University of Utah, USA, where he was successively Associate Professor (1987–1990), Professor (1990–1994) and Distinguished Professor (1994–1999). From 1999, he moved to Princeton University, USA as Professor and was appointed Donner Professor of Science since 2009. He is a member of the US National Academy of Sciences and a Fellow of the American Academy of Arts and Sciences.

**Claire Voisin** was born in 1962 in Val-d’Oise, France and is currently Professor, Algebraic Geometry Chair at Collège de France. She obtained a postgraduate teaching diploma in mathematics in 1983 and her PhD from Université Paris-Sud, France in 1986. She joined the Centre National de la Recherche Scientifique (CNRS) immediately after graduation in 1986 and continued her career there until 2016, and she was successively Researcher at the Université Paris-Sud in Orsay and then Senior Researcher and Directrice de recherche at the Institute de Mathematiques de Jussieu (CNRS / UPMC / Université Paris Diderot). She became a Professor at the Collège de France and has held the chair in Algebraic Geometry since 2016. She is a member of the Académie des sciences (France) and foreign associate member of the US National Academy of Sciences.