## Scientific Lectures

- 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

- 25-Oct-07

Risk Measures with Comonotonic Subadditivity or Convexity and Respecting Stochastic Orders

Taking subadditivity as a main axiom Artzner et.al.(1997, 1999) introduced the coherent risk measures. Song and Yan (2006) introduced risk measures which are comonotonically subadditive or convex. Recently we introduced risk measures which are not more››

University of British Columbia

- 24-Oct-07

Pivot v/s interior point methods: pros and cons

Linear Optimization (Programming) is probably the most successful and most intensively studied model in applied mathematics. First we give a survey of the governing algorithmic principles that lead to design Pivot and Interior Point Methods (IPMs) more››

University of Calgary

- 23-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 Alberta

- 19-Oct-07

Finite element analysis of CAD large assemblies more››

Simon Fraser University

- 15-Oct-07

Nonsmooth, Nonconvex Optimization

There are many algorithms for minimization when the objective function is differentiable or convex, but few options when it is neither. We describe two simple algorithmic approaches for minimization of nonsmooth, nonconvex objectives: BFGS (a new more››

Simon Fraser University

- 13-Oct-07

21st Annual Pacific Northwest Numerical Analysis Seminar

http://www.amath.washington.edu/~pnwnas/2007/ more››

University of Washington