François Guillemin (1950–2020)

19 April 2013 − − François

Assignment 3 François Séguin

Question 1 First, we have that λ − λ − 2 = (λ + 1)(λ − 2). Therefore, it is true that the eigenvalues of the corresponding adjacency matrix come in pairs of additive inverse. However, notice that ± √ −1 are eigenvalues, and therefore the associated matrix cannot be symmetric (there would only be real eigenvalues). We conclude that no undirected graph can have the above characteristic polynomial...

The Planck mission François

These lecture notes discuss some aspects of the Planck1 mission, whose prime objective was a very accurate measurement of the temperature anisotropies of the Cosmic Microwave Background (CMB). We announced our findings a few months ago, on March 21st , 2013. I describe some of the relevant steps we took to obtain these results, sketching the measurement process, how we processed the data to obt...

Functorial Quantization and the Guillemin–sternberg Conjecture *

We propose that geometric quantization of symplectic manifolds is the arrow part of a functor, whose object part is deformation quantization of Poisson manifolds. The 'quantiza-tion commutes with reduction' conjecture of Guillemin and Sternberg then becomes a special case of the functoriality of quantization. In fact, our formulation yields almost unlimited generalizations of the Guillemin–Ster...

Constructing Involutive Tableaux with Guillemin Normal Form

Involutivity is the algebraic property that guarantees solutions to an analytic and torsion-free exterior differential system or partial differential equation via the Cartan–Kähler theorem. Guillemin normal form establishes that the prolonged symbol of an involutive system admits a commutativity property on certain subspaces of the prolonged tableau. This article examines Guillemin normal form ...