Recent highlights

Some mathematical highlights from the past few years:

• Alan McIntosh's solution of the Kato `square root problem', a conjecture dating back to the 1960s, in joint work with Auscher, Hofmann, Lacey and Tchamitchian. See Annals of Mathematics, 156 (2002), 633-654.
• Terry Tao (who was at ANU in 2001 and 2003) proved the global existence of wave maps in two dimensions, work which was awarded the Bocher prize; see Proceedings of the Centre for Mathematics and its Applications, vol. 40, 2002, 19-48 and Comm. Math. Phys. 224 (2001), 443-544.
• Alan Carey's work with Phillips on index theory, noncommutative geometry and spectral flow; see math.KT/0308161.
• Andrew Hassell's work with Wunsch showing how singularities propagate under the time-dependent Schroedinger equation; see math.AP/0301341.
• Derek Robinson's recent book, Analysis on Lie groups of polynomial growth, with Dungey and ter Elst, summarizing over 10 years of research; Birkhauser, 2003, ISBN 0817632255.
• Rick Loy's work with Laustsen and Read in constructing a Banach space whose algebra of operators has a closed ideal lattice structure not previously encountered; see J. Funct. Analysis 214 (2004), 106-131.
• Alexander Isaev's work with Kruzhilin solving a 10-year old problem on characterising complex n-space by its automorphism group; see Canadian J. Math. 54(2002), 1254-1279.