The Royal Swedish Academy of Sciences has announced the recipients of the 2016 Crafoord Prizes in Mathematics and Astronomy. The Crafoord Prize in Mathematics has been awarded to Yakov Eliashberg of Stanford University “*for the development of contact and symplectic topology and groundbreaking discoveries of rigidity and flexibility phenomena.” **T*he 2016 Crafoord Prize in Astronomy has been awarded to Roy Kerr of the** **University of Canterbury, Christchurch, New Zealand and to Roger Blandford of Stanford University *“for fundamental work on rotating black holes and their astrophysical consequences.”* The prize money is 6 million Swedish kronor per prize, and the Crafoord Prize in Astronomy is shared equally between the Laureates.

*The Royal Swedish Academy of Sciences, founded in 1739, is an independent organization whose overall objective is to promote the sciences and to strengthen their influence in society. The Academy states that it “takes special responsibility for the natural sciences and mathematics, but endeavors to promote the exchange of ideas between various disciplines.”*

The Academy awarded the Crafoord Prize for the first time in 1982 after receiving “a considerable donation” from the Lund industrialist Holger Crafoord and his wife Anna-Greta in 1980. This donation forms the basis of the Anna-Greta and Holger Crafoord Fund, whose aims are “to promote pure research in mathematics and astronomy, biosciences (in the first place ecology), geosciences and polyarthritis (rheumatoid arthritis).” These disciplines are chosen so as to complement those for which the Nobel Prizes are awarded.

The prize sum of SEK 6 million makes the Crafoord one of the world´s largest scientific prizes. The international prize is awarded for one field per year in a fixed order to researchers who have made decisive contributions within their fields:

**Year 1:**Astronomy and Mathematics**Year 2:**Geosciences**Year 3:**Biosciences**Year 4:**Astronomy and Mathematics

Since 2012, there have been two separate prizes in astronomy and mathematics awarded at the same time. The prize in polyarthritis is awarded only when a special committee has shown that scientific progress in this field has been such that an award is justified.

The laureates are announced in mid-January each year, and the prize is presented in April/May on “Crafoord Day.” It is received from the hand of His Majesty the King of Sweden. In connection with Crafoord Day, a symposium in the discipline in question is arranged by the Royal Swedish Academy of Sciences.

**2016 Prize Lecture:**Tuesday, May 24, 2016, Lund University, Lund.**2016 Prize symposium**: Wednesday, May 25, 2016, Stockholm registration at http://kva.se/kalendarium.**2016 Prize ceremony**: Thursday, May 26, 2106, Beijer Hall, the Royal Swedish Academy of Sciences, Stockholm.

**The 2016 Crafoord Prize in Mathematics**

The Academy reports that Russian-American mathematician **Yakov Eliashberg** is one of the leading mathematicians of our time. For more than 30 years, he has helped to shape and research a field of mathematics known as symplectic geometry, and one of its branches in particular — symplectic topology.

Eliashberg has solved many of the most important problems in the field and has found new and surprising results. He has further developed the techniques he used in contact geometry, a twin theory to symplectic geometry. While symplectic geometry deals with spaces with two, four or other even dimensions, contact theory describes spaces with odd dimensions. Both theories are closely related to current developments in modern physics, such as string theory and quantum field theory.

Symplectic geometry’s link to physics has old roots. For example, it describes the geometry of a space in a mechanical system, the space phase. For a moving object, its trajectory is determined each moment by its position and velocity. Together, they determine a surface element that is the basic structure of symplectic geometry. The geometry describes the directions in which the system can develop; it describes movement. Physics becomes geometry.

One of Eliashberg’s first, and perhaps most surprising, results was the discovery that there are regions where symplectic geometry is rigid and other regions where it is completely flexible. But where the boundary is between the flexible and the rigid regions, and how it can be described mathematically, is still a question awaiting an answer.

**Yakov Eliashberg** was born in 1946 in St. Petersburg, Russia. He receiced his Ph.D. at Leningrad State University 1972. **Eliashberg** is the Herald L. and Caroline L. Ritch Professor of mathematics at Stanford University.

**The Crafoord Prize in Astronomy **

The Academy explains in a background piece for this year’s prize that black holes are the source of the universe’s most powerful radiation, as well as of jets that can stretch many thousands of light years out into space. **Roger Blandford**’s theoretical work deals with the violent processes behind these phenomena. **Roy Kerr** laid the foundation for this research early on, when he discovered a mathematical description of rotating black holes. This became one of the most important theoretical discoveries in modern cosmology.

The prediction of black holes is one of the perhaps strangest results of the general theory of relativity. When Albert Einstein finally presented his theory, in November 1915, he described gravity as a geometric property of space and time, spacetime. All objects with mass bend spacetime; they create a pit into which smaller objects can fall. The greater the mass, the deeper the pit. The mass of a black hole is so great that nothing that ends up in there can escape, not even light.

It was not until 1963 that mathematician **Roy Kerr** succeeded in solving Einstein’s equations for rotating black holes. That the holes should rotate is feasible because the stars from which they originated should have rotated. At about the same time, astronomers discovered galaxies that emitted light and other electromagnetic radiation that was so strong it outshone several hundred ordinary galaxies. They were named quasars. Nothing other than a black hole could give the quasars their luminosity.

So how is the strong light of rotating black holes created? This question was answered by **Roger Blandford** and his colleagues in the 1970s. Ever since, he has refined and made more realistic models of how gas surrounding a black hole flows towards it, is heated up and transforms some of its gravitational energy to radiation. While this is happening, electrically charged particles are sent millions of kilometers into space in the form of powerful jets. The source of all of this power is the rotational energy of the massive black hole.

Roy Kerr was born in 1934 in Gore, New Zeeland. He received his Ph.D. in 1959 at the University of Cambridge. Kerr is an Emeritus Professor at the University of Canterbury, New Zeeland.

Roger Blandford was born in 1949 in Grantham, Great Britain. He received his Ph.D. in 1974 at the University of Cambridge. Blandford is Luke Blossom Professor in the School of Humanities and Sciences, at Stanford University.

- Learn more about the Crafoord prize: http://www.crafoordprize.se/

- Earlier prizes: http://www.crafoordprize.se/prizesawarded.4.2f692b3510dbfce3396800010039.html
- Watch lectures by Yakov Eliashberg: http://scgp.stonybrook.edu/video_portal/results.php?profile_id=985