booklet - CUMC - Canadian Mathematical Society

sufficiently many invariants of that transformation group. For Riemannian manifolds,these invariants can be computed using the Cartan-Karlhede algorithm. To illustratethe method we will consider the local equivalence of 3D Godel spacetimes occurring ingeneral relativity.A METAHEURISTIC APPROACH FOR SOLVING THE UNCONSTRAINED BINARY QUADRATICPROGRAMMING PROBLEMDHANANJAY BHASKARThe unconstrained binary quadratic programming (BQP) problem is known to beNP-hard and has application in many diverse fields, including finance, traffic management,and scheduling. In this talk, we present a metaheuristic approach for solvingthe unconstrained BQP problem. We illustrate the efficiency and robustness of metaheuristicssuch as genetic algorithm and simulated annealing by performing extensivecomputational experiments using test problems from OR-Library.VIBRATING DRUMS, BOUNCING BALLS AND HOW THEY ARE RELATEDDOMINIQUE RATHEL-FOURNIERIf we put sand on a plate vibrating at certain frequencies, it tends to form complexshapes known as "Chladni patterns". This raises the question: can we see sound? Or,as posed by Mark Kac in 1966, "Can one hear the shape of a drum"? We present themathematical model of a vibrating drum, the wave equation, and show how this problemrelates to finding the eigenvalues of the laplace operator. In particular, we showhow the calculus of variations is the basic tool to study these eigenvalues on arbitrarydomains. The second part of the presentation will be devoted to dynamical billiards.We adopt a geometric approach to characterize the trajectory of a billiard ball on simpledomains such as disks and rectangles and show how this can be generalized to morecomplex domains such as ellipses or balls in R n . As a conclusion, we briefly introducean amazing link between spectral geometry and billiards: how do billiard trajectoriesaffect the eigenvalues of the laplacian on a given domain?ON THE PROBLEM OF UNIVERSAL CONSISTENCY OF KNN IN BANACH SPACESDONG YUEKNN classifier is one of the oldest natural classification for labeling data. The classicalStone’s theorem says that this algorithm is universal consistent in finite Euclideanspace. Since then, the result has been generalized in many directions. In particular, itwill show that the algorithm is no longer universal consistent in infinite dimensionalspace. Of certain interest is the problem of universal consistency in more general infinitedimensional–Banach space(the so called functional learning). In this talk, we willsurvey and discuss what is known in this problem.23