Pierre Milman
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Dr. Pierre Milman graduated with a B.A. from the University of Moscow in 1967 and obtained his Ph.D. from the University of Tel- Aviv in 1975, after an interlude of several years as Researcher at the Institute of Chemical Physics and then Solid State Physics in Moscow.
In 1975, he came to the University of Toronto as Lecturer and Research Associate, and after holding a Visiting Assistant Professorship at Purdue University from 1978 to 1980, he returned to the University of Toronto, first as an NSERC University Research Fellow until 1985, then as Associate Professor and, since 1986, as Professor.
In 1997, Dr. Milman was elected Fellow of the Royal Society of Canada
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[edit] His Theory
Pierre Milman (University of Toronto) also created a theory of; Standard basis along a Samuel stratum and implicit differentiation. The following is the theory ;
We develop an idea of "formal functions along a subspace", a notion that is related to Grothendieck's "formal completion along a subscheme", but expressed in a concrete analytic terms using "smooth coordinate charts". Formal functions are families of formal power series parametrized by functions from a given class, satisfying natural commutativity relations between formal differentiation and differentiation with respect to the parameters. One of our main results is that, in generic coordinates for a chart U, the standard basis of a local ideal I_{X,a} of a closed subspace X of U (the standard basis is a special set of generators of I_{X,a}) extends as formal functions to generators along the Samuel stratum S of a. (S is the subset of X of points of the same singularity-type as a, as measures by the Hilbert-Samuel function). The simplest example of this phenomenon is "implicit differentiation" in elementary analysis. Our result can be used to reduce resolution of singularities over an infinite field, in general, to a "hypersurface case".
[edit] Recent Awards
In 2000 Pierre was awarded a Killam Research Fellowship.
Dr. Edward Bierstone and Dr. Pierre Milman are honoured jointly for their highly significant work in the study of analytic and geometric properties of singular spaces. They received the Jeffery-Williams Prize in 2005. The Jeffery-Williams Prize recognizes mathematicians who have made outstanding contributions to mathematical research. They received this award because together, they found an amazingly short and ingenious proof of Hironaka's theorem on resolution of singularities, transforming that result from a monument to be admired to a tool to be used, bringing a new dimension of understanding and accessibility to the resolution process, at the same time extending it, and its applications, to a considerably wider range of spaces.
Jointly with Wieslaw Pawlucki, they achieved as well important progress on the classical open problem posed by Whitney about differentiable extensions of functions from subsets to the ambient space.
Dr.'s Bierstone and Milman have also made crucial contributions to the geometry of sub- and semi-analytic sets, exploring their relationship to differentiable functions. Their methods are expected to continue to reveal new and significant features of singular spaces.
[edit] Family
Math runs in the Milman Family. His the father is mathematician David Milman who devised the Krein-Milman theorem. His Mathmatician brother is Vitali Milman.
