Gilles Pisier
Distinguished Professor
A.G. and M.E. Owen Chair of Mathematics



Research Interests

Ostrowski Prize
Ostrowski Prize 1997
Salem Prize 1979
Stefan Banach Medal 2001
Académie des Sciences de Paris (Member)
Polish Academy of Science (Foreign Member)
Real Academia de Ciencias de Zaragoza (Académico Correspondiente)
Indian National Academy of Science (Foreign Fellow)

Concentration Week on Approximation Properties of Discrete Groups and Operator Spaces

TOPICS  COURSE in Fall 2014 (Math 663/600 planned : TR 9:35-10:50am Blocker 202) : 

Title: Tensor products of C*-algebras and Operator space theory


The course will revolve around the famous Connes-Kirchberg open problem. The various equivalent forms of the problem will be described and the necessary accompanying background will be presented. In addition the general theory of tensor products of C* algebras will be described. The notion of exact C* algebra and operator space will play an important role there, with an emphasis on C* algebras associated to discrete groups. Various forms of the non-commutative Grothendieck theorem will be presented in view of its recent connection with Bell's inequality. An introduction to quantum information theory will be given. Gaussian and unitary random matrices will be used repeatedly to illustrate the estimates by more "concrete" examples.
References: G. Pisier, An introduction to operator space theory, Cambridge Univ. Press, 2003
N. Brown and N. Ozawa, C*-algebras and finite-dimensional approximations, Graduate Studies in Mathematics, 88, American Mathematical Society, Providence, RI, 2008.
N. Ozawa,  About the QWEP conjecture, Internat. J. Math. 15 (2004), 501–530.

Minicourse on Similarity Problems (TAMU July 2005)

  • Minicourse 2005

  • Grothendieck's Theorem, past and present (pdf)
    (where Grothendieck meets Einstein, Bell and the P=NP problem)
    Grothendieck's theorem past and present UNCUT and EXPANDED (pdf)

    Lecture Notes