[cmath] THREE HONOURED FOR OUSTANDING RESEARCH ACHIEVEMENTS

[Graham Wright]

THREE HONOURED FOR OUSTANDING RESEARCH ACHIEVEMENTS

The Canadian Mathematical Society (CMS) has selected Lia Bronsard as the 
recipient of the 2010 Krieger-Nelson Prize,  Mikhail Lyubich as the 
recipient of the 2010 Jeffery-Williams Prize, and Patrick Brosnan as the 
winner of the 2009 Coxeter-James Prize.

*********************************************************************K
CMS 2010 Krieger-Nelson Prize: Dr. Lia Bronsard (McMaster University)
*********************************************************************K

The Krieger-Nelson Prize recognizes outstanding research by a female 
mathematician.

Lia Bronsard is one of Canada's leading mathematical analysts, whose 
interests lie in the field of partial differential equations and the 
calculus of variations. She specializes in the study of singular limits of 
solutions of partial differential equations. Her research brings rigorous 
methods of analysis to bear on problems arising in the physical sciences, 
and in particular those involving singular geometrical structures such as 
vortices, phase transition layers, and grain boundaries.

Bronsard was born in Québec in 1963 and received her Baccalauréat ès 
Sciences, in mathematiques from the Université de Montréal in 1983. She 
received her Ph.D. in 1988 from the Courant institute of Mathematical 
Sciences at New York University, working with R. V. Kohn on the De Giorgi 
conjecture connecting singularly perturbed reaction-diffusion equations 
and mean curvature flow. After her degree, she held positions at Brown 
University, the Institute for Advanced Study, and the Center for Nonlinear 
Analysis at Carnegie - Mellon University. In 1992, she moved to McMaster 
University, where she is now a Professor of Mathematics.

During the period after her thesis, Bronsard worked on energy driven 
pattern formation in collaboration with B. Stoth and others. Her paper 
with F. Reitich on the structure of triple-junction layers in grain 
boundaries, from her period at CMU, was the first mathematical analysis of 
these multiphase singular structures and has been highly influential.

In her current research, Bronsard studies the detailed structures of 
vortices in the phenomenon of Bose - Einstein condensation and in the 
Ginzburg - Landau models of superconductivity. In this area, her work, in 
collaboration with S. Alama, T. Giorgi, P. Mironescu, E. Sandier and 
colleague J. Berlinsky from Physics at McMaster University, sets a very 
high standard of quality, and is a model of interdisciplinary research.

*********************************************************************K
CMS 2010 Jeffery-Williams Prize: Dr. Mikhail Lyubich (State University of 
New York at Stony Brook and the University of Toronto)
*********************************************************************K

The Jeffery-Williams Prize recognizes mathematicians who have made 
outstanding contributions to mathematical research.

Mikhail Lyubich is a leader in the field of dynamical systems. He is one 
of the founders of modern real and complex one-dimensional dynamics, 
having in many ways shaped the development of the field.

Lyubich was born in 1959 in Kharkov, Ukraine, then a part of the Soviet 
Union. His interest in dynamics was influenced by his father Yuri Lyubich, 
who was a professor at Kharkov State University where Mikhail studied in 
the period 1975-80.  Soviet political realities (in particular, tacit 
anti-Semitic policies) influenced Lyubich's early career. He was admitted 
to graduate school only in Tashkent, Uzbekistan, where he worked on 
holomorphic dynamics on his own. In his 1984 Ph.D. thesis, he proved 
fundamental results on ergodic theory and structural stability of rational 
maps; in particular, the existence of the measure of maximal entropy of a 
rational map, now known as Lyubich measure.

In 1989 Lyubich was able to leave the Soviet Union together with his 
family. He was invited by John Milnor to join the Institute for 
Mathematical Sciences at Stony Brook, founded at that time.

Lyubich received a Canada Research Chair at the University of Toronto in 
2002, holding a joint appointment with Stony Brook. In 2007 he became 
Director of the Institute for Mathematical Sciences (Stony Brook). Lyubich 
is a sought-after speaker. He gave an invited address at the International 
Congress of Mathematicians in Zurich in 1994, as well as plenary talks at 
the Joint AMS Meeting in 2000 and the first CMS-SMF Mathematics Congress 
in 2003. He was awarded a Sloan Fellowship in 1991 and a Guggenheim 
Fellowship in 2002.

Among Lyubich's fundamental results in one-dimensional dynamics is his 
proof in the 1990s of hyperbolicity of renormalization for unimodal maps 
(conjectured by Feigenbaum and by Coullet and Tresser in the 1970s). 
Renormalization has been one of the main themes in low-dimensional 
dynamics for the past 40 years. Sullivan and later McMullen proved parts 
of the renormalization picture for unimodal maps, and Lyubich completed 
the proof of universality for bounded combinatorics. He later constructed 
a ``full hyperbolic horseshoe'' for the renormalization operator acting on 
real quadratic-like maps.

In earlier work on rigidity of quadratic polynomials, Lyubich resolved 
perhaps the most famous problem in dynamics on the real line by showing 
that hyperbolicity is dense in the real quadratic family. (This result was 
independently obtained by J. Graczyk and G. Świątek.)

One of the most fundamental problems in dynamics, for a parameterized 
family of maps, is to understand the asymptotic behaviour of almost every 
orbit for almost every value of the parameter. Even for the family of 
quadratic interval maps, this question had eluded experts for years. 
Lyubich's construction of the full renormalization horseshoe, together 
with his joint work with M. Martens and T. Nowicki, allowed him to obtain 
the definitive answer: almost every quadratic map is either regular or 
stochastic.

Lyubich's work was a major step towards the celebrated MLC (Mandelbrot set 
is locally connected) conjecture. A series of new breakthroughs has come 
in his recent results with J. Kahn, using the Kahn-Lyubich 
quasi-additivity law in conformal geometry.

*********************************************************************K
CMS 2009 Coxeter-James Prize: Dr Patrick Brosnan (University of British 
Columbia)
*********************************************************************K

The Coxeter-James Prize recognizes young mathematicians who have made 
outstanding contributions to mathematical research.

Patrick Brosnan is a young mathematician of unusual breadth, depth and 
scope; his work has had significant impact in several areas of 
mathematics, including motives, algebraic cycles, Hodge theory, algebraic 
groups, algebraic combinatorics, analytic number theory and mathematical 
physics.

Brosnan was born in Philadelphia, Pennsylvania in 1968 and grew up in 
Corpus Christi, Texas.  He obtained a Bachelor of Arts degree from 
Princeton University in 1991 and a Ph.D. from The University of Chicago in 
1998, studying algebraic cycles under the supervision of Spencer Bloch. 
Prior to joining the University of British Columbia, he held positions at 
Northwestern University, Max-Planck-Institut für Mathematik in Bonn, the 
University of California Irvine, the University of California Los Angeles, 
the State University of New York at Buffalo, and the Institute for 
Advanced Study in Princeton.

In a 2003 Duke Mathematical Journal paper with P. Belkale, Brosnan 
disproved the so-called “spanning tree” conjecture of the 1998 Fields 
medalist M. Kontsevich.  The conjecture, which was motivated by research 
by the physicists D. Broadhurst and D. Kreimer into the number theoretical 
properties of Feynman amplitudes, was supported by a substantial body of 
empirical evidence.  The work of Belkale and Brosnan was, consequently, 
entirely unexpected; and it has had a strong impact on the field.

Recently Brosnan has made important contributions to the theory of 
essential dimension. Brosnan's idea to extend the notion of essential 
dimension to the setting of algebraic stacks paved the way for 
wide-ranging applications of stack-theoretic methods which ultimately led 
to a number of striking developments. One of the applications, to appear 
in a joint Annals of Mathematics paper with Z. Reichstein and A. Vistoli, 
is an unexpectedly strong lower bound on the Pfister number of a quadratic 
form with trivial discriminant and Hasse-Witt invariant.

In a different direction, Brosnan and G. Pearlstein have recently made 
important contributions to Hodge theory. In another paper that will appear 
in the Annals, they show that a non-trivial admissible normal function on 
a curve can have only finitely many zeros. Normal functions are part of a 
conjectured program to prove the Hodge conjecture, one of the outstanding 
open problems in mathematics.



For more information, contact:

Dr. Athony Lau				or	Dr. Graham P. Wright
President 					Executive Director
Canadian Mathematical Society 			Canadian Mathematical Society
780-492-0398					613-733-2662 ext 713
president at cms.math.ca                           director at cms.math.ca