booklet - CUMC - Canadian Mathematical Society

3.2) Le cas Poisson^θ n = ^θ n−1 − ^H −1n−1 ^∇ n−1λ = exp(X ′ β)3.3) La régression logistiqueπ = exp(X′ β)exp(X ′ β)+14) Les machines à vecteurs de support: le cas linéairement séparable, le cas nonséparable,le *kernel trick*.Required Background: math./stat. de 1ère année de baccalauréatBASICS OF THE REPRESENTATION THEORY OF C*-ALGEBRASMAXIMILIAN KLAMBAUERA C*-algebra, A, is a complex algebra equipped with an anti-linear involution, *,and a norm that satisfies the C*-identity: ||x ∗ x|| = ||x|| 2 . A representation of a C*-algebrais a C*-homorphism π : A → B(H), where B(H) denotes the C*-algebra of boundedlinear operators on the Hilbert space H (where the * operation is given by taking adjoints).This talk will cover some of the basic theorems of these representations. A stateon a C*-algebra is a positive linear functional (in the sense that f(x ∗ x) ≥ 0) of norm 1.We will see that every state gives rise to a representation of a C*-algebra via the G.N.S.construction. We will also examine the relation between pure states and irreducible representations.As a consequence, we will also see that every C*-algebra can be faithfullyrealised as a subalgebra of B(H).Required Background: Linear algebra, calculus, basics of ring theorySUDOKU: A FOUR DIMENSIONAL WONDERMELISSA HUGGANMathematical structure behind the world famous Sudoku puzzle is abundant. Througha coordinatization of the 9 by 9 grid, it is possible to use error-correcting codes to buildSudoku solutions, as well as special Sudoku puzzles with additional constraints (symmetricSudokus). Interestingly, affine and projective geometries play a significant rolein constructing orthogonal sets of Sudoku squares. We will explore these beautiful constructions.Required Background: Linear algebra, coding theoryINVESTIGATIONS OF HYPERVISCOUS TURBULENCEMORIAH MAGCALASHyperviscosity is a computational technique that is used in fluid turbulence to improvethe resolution of a fluid model. But are there any other effects of hyperviscosityon the fluid model? And if so, what are those effects? In this talk, an introduction to an38