## Scientific Lectures

- 14-Jan-08

Sensors, signal processing hardware, and algorithms are under increasing pressure to accommodate ever larger and higher-dimensional data sets; ever faster capture, sampling, and processing rates; ever lower power consumption; communication over ev more››

University of British Columbia

- 10-Jan-08

A bound from below for the temperature in compressible Navier-Stokes equations more››

University of British Columbia

- 13-Dec-07

We consider the well-known edge-disjoint path problem (EDP) where we are given a graph G and pairs of nodes (“demands”) s1t1, s2t2, . . . sktk. A subset F of {1, 2, . . . , k} is routable if there exists |F| edge-disjoint paths in G that conne more››

University of Victoria

- 30-Nov-07

Banach algebras of continuous functions and measures, and their second duals

For every Banach algebra A, there are two products on the second dual space A'' that make A'' into a Banach algebra; they may or may not coincide. A lot of information about the original algebra A comes easily by looking at these second duals. We more››

University of Alberta

- 29-Nov-07

Multi-Banach spaces and Multi-Banach Algebras

The very extensive theories of Banach spaces and Banach algebras, including algebras of operators on Banach spaces, are the foundation stones of much modern analysis. For certain reasons M. Polyakov and I were led to introduce a more more››

University of Alberta

- 23-Nov-07

Efficent smooth GMM through dimension reduction

We propose a new GMM criterion for models defined by conditional moment restrictions that takes into account a number of moment conditions which increases with the sample size. Our criterion allows us to reduce the dimensionality of the conditioni more››

University of Victoria

- 22-Nov-07

Level lowering and Shapiro's conjecture

Let E/Q be an elliptic curve over the rationals. One can associate two rational integers that measure the ramification of this elliptic curve over various primes, the conductor NE and the minimal discriminant ?E. The Szpiro's conjecture states that f more››

University of British Columbia

- 22-Nov-07

Modular methods applied to Diophantine equations

Deep results about elliptic curves, modular forms and Galois representations have successfully been applied to solve FLT and other Diophantine equations. Most of such applications broadly proceed along the following lines. To a hypothetical solution more››

University of British Columbia

- 22-Nov-07

A Paley-Wiener theorem and Arthur's trace formula

Modular forms may be recast and generalized as automorphic representations, which are objects of abstract harmonic analysis. The trace formula is a theorem in harmonic analysis which allows one to compare automorphic representations. The Paley-Wiener more››

University of British Columbia

- 5-Nov-07

A Functional Integral Representation for Many Boson Systems

Functional integrals have long been used, formally, to provide intuition about the behaviour of quantum field theories. For the past several decades, they have also been used, rigorously, in the construction and analysis of those theories. I will more››

University of British Columbia

- 2-Nov-07

Sums of congruent convex bodies

The Minkowski linear combination is a fundamental operation for convex bodies. Further basic structures on the space of convex bodies are the topology induced by the Hausdorff metric, and the operation of the group of rigid motions. Suppose we hav more››

University of British Columbia

- 2-Nov-07

- 1-Nov-07

On Securitization, Market Completion and Equilibrium Risk Transfer

We propose an equilibrium framework within two price financial securities written on non-tradable underlyings such as temperature indices. We analyze a financial market with a finite set of agents whose preferences are described by a convex dynami more››

University of British Columbia

- 1-Nov-07

Asymptotic shapes of random polytopes

We consider random polytopes, generated as intersections of closed halfspaces (containing 0) bounded by the hyperplanes of a Poisson process of hyperplanes (satisfying only some homogeneity property under dilatations). The central question (a very more››

University of British Columbia

- 31-Oct-07

Random projections of regular polytopes and neighborliness

If an N-dimensional regular crosspolytope is projected to a uniform random d-dimensional subspace and N is large, then the projection has strong neighborliness properties, with high probability. Strong results in this direction were recently obtai more››

University of Calgary

- 26-Oct-07

Polytopes and arrangements: diameter and curvature

By analogy with the Hirsh conjecture, we conjecture that the order of the largest total curvature of the central path associated to a polytope is the number of inequalities defining the polytope. By analogy with a result of Dedieu, Malajovich and more››

University of Calgary

- 26-Oct-07

Sums of congruent convex bodies

The Minkowski linear combination is a fundamental operation for convex bodies. Further basic structures on the space of convex bodies are the topology induced by the Hausdorff metric, and the operation of the group of rigid motions. Suppose we hav more››

University of Alberta

- 26-Oct-07

- 25-Oct-07

Klee-Minty cubes and the central path

We consider a family of LO problems over the n-dimensional Klee-Minty cube and show that the central path may visit all of its vertices in the same order as simplex methods do. This is achieved by carefully adding an exponential number of redundan more››

University of Calgary

- 25-Oct-07

Asymptotic shapes of random polytopes

We consider random polytopes, generated as intersections of closed halfspaces (containing 0) bounded by the hyperplanes of a Poisson process of hyperplanes (satisfying only some homogeneity property under dilatations). The central question (a very more››

University of Alberta