for his contributions to understanding structure formation in the Universe. With powerful numerical simulations he has shown how small density fluctuations in the early Universe develop into galaxies and other nonlinear structures, strongly supporting a cosmology with a flat geometry, and dominated by dark matter and a cosmological constant.
for conceiving and designing the Laser Interferometer Gravitational-Wave Observatory (LIGO), whose recent direct detection of gravitational waves opens a new window in astronomy, with the first remarkable discovery being the merger of a pair of stellar mass black holes.
for their discovery of the genes and the encoded proteins that recognize one chemical modification of the DNA of chromosomes that influences gene control as the basis of the developmental disorder Rett syndrome.
for his far-reaching contributions to geometry, representation theory and theoretical physics. The fundamental and elegant concepts and techniques that he has introduced have had wide impact and are of lasting importance.