
The Canadian Mathematical Society (CMS) has selected Yael Karshon as the recipient of the 2009 KriegerNelson Prize, Stephen Kudla as the recipient of the 2009 JefferyWilliams Prize, and Ravi Vakil as the winner of the 2008 CoxeterJames Prize.
CMS 2009 KriegerNelson Prize:  Dr. Yael Karshon (University of Toronto) 
The KriegerNelson Prize recognizes outstanding research by a female mathematician.
Dr. Yael Karshon is one of Canada's leading experts in symplectic geometry. Symplectic geometry is the geometry underlying classical mechanics, and has close relations with quantum mechanics and quantum field theory. The tools of symplectic geometry appear in algebraic geometry and representation theory, and in connection with convex polytopes. Symplectic spaces arising in physics and mathematics often admit many symmetries.
Dr. Karshon's work has focused on symmetries of symplectic manifolds, formalized as Hamiltonian group actions. She has obtained deep results on the classification of such structures. One of her significant contributions is the idea of "abstract moment maps", which are maps between (not necessarily symplectic) manifolds with group actions, and which generalize moment maps on symplectic manifolds. She is the author (jointly with Guillemin and Ginzburg) of an authoritative monograph that provides new connections between moment maps, cobordisms and Hamiltonian group actions. Some of her recent work is in symplectic topology, involving symplectic capacities and symplectomorphism groups.
Dr. Karshon completed her Ph.D. in 1993 under the supervision of Shlomo Sternberg at Harvard, and then held a C.L.E. Moore Instructorship at MIT. In 1995 she moved to the Hebrew University of Jerusalem, where she obtained tenure. She joined the University of Toronto Mississauga in 2002, and was promoted to Full Professor in 2006. In 2005 she received the University of Toronto's McLean Award, which is given each year to one faculty member in the mathematical or physical sciences or engineering, within 12 years of Ph.D. Dr. Karshon takes pride in the achievements of her Ph.D. students and postdoctoral fellows.
Dr. Karshon will present the 2009 KriegerNelson Prize Lecture at the CMS Summer Meeting in St. John's (June 2009).
CMS 2009 JefferyWilliams Prize:  Dr. Stephen Kudla (University of Toronto) 
The JefferyWilliams Prize recognizes mathematicians who have made outstanding contributions to mathematical research.
Dr. Stephen Kudla has initiated a revolutionary program which reveals surprising, deep connections between two ostensibly disparate areas of mathematics: the theory of automorphic forms and the theory of algebraic cycles on Shimura varieties. The impressive body of established results and farreaching conjectures that has emerged from Kudla's work has come to be referred to as the "Kudla Program". Among the most exciting developments in number theory worldwide in the last decades, Kudla's program has been featured in many research seminars worldwide, including the Séminaire Bourbaki in Paris and the Current Developments in Mathematics series in Boston. Stephen Kudla has been regularly invited to deliver distinguished lectures, such as the Coxeter Lectures at the Fields Institute, the Kuwait Foundation lecture at Cambridge University, the Schur Lecture at Tel Aviv University, and an invited address at the 2002 International Congress of Mathematicians in Beijing. He also received a Sloan Fellowship in 1981 and a Max Planck Research Prize in 2000.
Dr. Kudla received his undergraduate degree from Harvard University in 1971 and completed his doctoral degree at SUNY Stony Brook in 1975. After a period at the Institute for Advanced Study, he served on the Faculty of the University of Maryland from 1976 to 2006, before joining the University of Toronto where he currently holds the Canada Research Chair in Automorphic Forms and Arithmetic Geometry. He has held numerous visiting positions at leading institutions including the University of Cologne, University of Paris VI, Cambridge University, and the Tata Institute for Fundamental Research.
Prior to coming to Toronto, Dr. Kudla served the Canadian mathematical community as an Associate Editor for the Canadian Journal of Mathematics and the Canadian Mathematical Bulletin.
Dr. Kudla will present the 2009 JefferyWilliams Prize Lecture at the CMS Summer Meeting in St. John's (June 2009).
CMS 2008 CoxeterJames Prize:  Dr Ravi Vakil (Stanford University) 
The CoxeterJames Prize recognizes young mathematicians who have made outstanding contributions to mathematical research.
In his short, dynamic career, Dr. Ravi Vakil has become one of the world's leading algebraic geometers. He has made fundamental and lasting contributions in intersection theory, Schubert calculus and in the study of the singularities of moduli spaces. In an early article, for which he was awarded the Society's G. de B. Robinson Prize, Dr. Vakil gave a rigorous derivation of the characteristic numbers for families of plane quartic curves, thereby completing a program in enumerative geometry going back to the first half of the 19th century, which was mentioned by Hilbert in his famous problem list. In two major papers which appeared in the Annals of Mathematics, Ravi Vakil used a clever deformation technique to
solve several classical problems in Schubert Calculus. The most spectacular consequence of this is that any problem involving counting the points in an intersection of Schubert varieties in a (complex) Grassmannian is "totally real". That is, the problem can be solved by restricting to sufficiently general real subspaces of a real Grassmannian. This work also gave a natural geometric interpretation to the "puzzles" of Knutson and Tao. Dr. Vakil's results on the singularities of moduli spaces show that the singular loci of moduli spaces can be as bad as possible.
Dr. Ravi Vakil's outstanding contributions go well beyond his research. He is a model for promoting the overall dissemination of mathematics as well. He has unselfishly contributed his time as an organizer of international meetings, such as the graduate student premeeting before the American Mathematical Society's Summer Symposium in algebraic geometry 2005, a Snowbird Conference in 2006 and most recently, the MSRI jumbo program in algebraic geometry in 2009.
Dr. Vakil is unique in combining his talent for mathematical research with his desire to educate and infuse others with his passion for the subject. Few people combine his abilities and his dedication. Ravi Vakil has been extremely active in organizing workshops and math camps for high school students and undergraduates, and coordinates the William Lowell Putnam competition at Stanford. He is also the coauthor of a book on the Putnam competition.
Dr. Vakil received his B.Sc. from the University of Toronto in 1992 and his Ph.D. from Harvard in 1997. After receiving his degree, he was an instructor at Princeton and a C.L.E. Moore Instructor at MIT. He is now the David Huntington Faculty Scholar and a Professor in the Mathematics Department at Stanford University. In 2005, he won the AndreAisenstadt Prize from the CRM and also received the 200405 Dean's Award for Distinguished Teaching at Stanford. He recently completed an American Mathematical Society Centennial Fellowship, a Frederick E. Terman fellowship, and an Alfred P. Sloan Research Fellowship. He currently holds a National Science Foundation CAREER grant (20032008), and received the Presidential Early Career Award for Scientists and Engineers (PECASE) at the White House in 2004.
Dr. Ravi Vakil will present the 2008 CoxeterJames Prize Lecture at the CMS Winter Meeting hosted by Carleton University in December 2008.
For more information, contact:
Dr. Thomas S. Salisbury President Canadian Mathematical Society Tel: 4167362100 x33921 president@cms.math.ca 
or 
Dr. Graham P. Wright Executive Director Canadian Mathematical Society Tel: (613) 5625702 director@cms.math.ca 