John Millson (mathematician)

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John James Millson (born March 11, 1946 in Kingston ) is a Canadian mathematician who studies geometry and topology.

Millson studied mathematics at the Massachusetts Institute of Technology (and 1966/67 in Paris with Laurent Schwartz, among others ) with a bachelor's degree in 1968 and received his doctorate in 1973 with Shiing-Shen Chern and James Simons at the University of California, Berkeley (Chern- Simons Invariants of Constant Curvature Manifolds). As a post-doctoral student , he was at the Institute for Advanced Study . In 1974 he became an assistant professor at Yale University . In 1978 he was in Oxford with a Sloan Research Fellowship . In 1979 he became an Associate Professor at the University of Toronto and from 1980 at the University of California, Los Angeles . From 1989 he was a professor at the University of Maryland in College Park.

Millson proved in 1976 that the standard examples of arithmetic hyperbolic n-manifolds have finite overlays with non-vanishing first Betti numbers. He himself regards this as his best work. From the late 1970s he worked with Stephen S. Kudla on the Weil representation in the theory of theta functions and modular forms and the homology of arithmetic groups. He dealt with the deformation theory of discrete subgroups of Lie groups, partly with William Goldman . He also worked at the University of Maryland with Michael Kapovich on configuration spaces of elementary geometric objects, polygonal linkages in the plane and arrangements of straight lines in the projective plane. They proved a conjecture by William Thurston : for every compact smooth manifold M there is a plane hinge mechanism whose configuration space consists of the disjoint union of a finite number of copies of M.

In 1990 he was invited to speak at the International Congress of Mathematicians in Kyoto (Rational homotopy theory and deformation problems from algebraic geometry).

With Ravi Vakil and two other colleagues, he solved a problem of the classical invariant theory that had been open since 1894. At that time, Alfred Kempe gave the generators for the ring of projective invariants of n ordered points on the projective straight line. The problem of specifying the relations remained open, which was solved by Millson and colleagues in 2009.

Fonts (selection)

Besides the writings cited in the footnotes:

  • Closed geodesics and the eta (η) invariant, Annals of Mathematics , 108, 1978, pp. 1-39
  • Deformation Spaces Associated to Compact Hyperbolic Manifolds, in: Roger Howe (Ed.), Papers in Honor of GD Mostow on His Sixtieth Birthday. Progress in Mathematics, 67, Birkhäuser Verlag 1986
  • with Stephen S. Kudla : The Theta Correspondence and Harmonic Forms. 1 , Mathematische Annalen , Volume 274, 1986, p. 353 online
  • with Michael Kapovich , Bernhard Leeb : The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra, Memoirs, American Mathematical Society AMS, 2008
  • with M. Kapovich: On the moduli spaces of polygons in the Euclidean plane, Journal of Diffential Geometry, Volume 42, 1995, pp. 133-164
  • with M. Kapovich: On the deformation theory of representations of fundamental groups of compact hyperbolic 3-manifolds, Topology, Volume 35, 1996
  • with Ragnar-Olaf Buchweitz : CR-geometry and deformations of isolated singularities, Memoirs, American Mathematical Society, AMS, 1997
  • with M. Kapovich: Moduli spaces of linkages and arrangements, In: J.-L. Brylinski et al. a. (Ed.), Advances in Geometry, Progress in Mathematics, 172, Birkhauser Verlag, 1999, pp. 237-270
  • with Jens Funke: The Geometric Theta (ϑ) Correspondence for Hilbert -Modular Surfaces, Duke Mathematical Journal , 163, 2014, pp. 65–116
  • with Nicolas Bergeron , Colette Moeglin: The Hodge Conjecture and Arithmetic Quotients of Complex Balls, Acta Mathematica , 216, 2016, pp. 1–125.

Web links

Individual evidence

  1. ↑ John Millson in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  2. ↑ J. Millson, On the first Betti number of a constant negatively curved manifold, Annals of Mathematics, 104, 1976, pp. 235-247.
  3. ^ William Goldman, J. Millson: The Deformation Theory of Representations of Fundamental Groups of Compact Kähler Manifolds , Publications mathématiques de l ' IHÉS ISSN  0073-8301 , 67, Springer, 1988, pp. 49-96.
  4. ↑ Kapovich, Millson, Universality theorems for configuration spaces of linkages, Topology, Volume 41, 2002, pp. 1051-1107 full text
  5. ↑ Benjamin Howard, John Millson, Andrew Snowden, Ravi Vakil: The equations for the moduli space of n points on the line, Duke Math. J., Volume 146, 2009, pp. 175-226. Older preprint to this: Benjamin Howard, John Millson, Andrew Snowden, Ravi Vakil: The moduli space of n points on the line is cut out by simple quadrics when n is not six, Arxiv
personal data
SURNAME Millson, John
ALTERNATIVE NAMES Millson, John James (full name)
BRIEF DESCRIPTION Canadian mathematician
DATE OF BIRTH March 11, 1946
PLACE OF BIRTH Kingston