## Scientific Lectures

- 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

- 12-Oct-07

Unsolved for over twenty-five years, a surprisingly difficult conjecture stated that a non-crossing polygonal chain of fixed-length edges in the plane can be continuously opened without crossing. Gunter Rote, Erik Demaine and I proved this Carpent more››

University of Calgary

- 11-Oct-07

Why things don't fall down - Art, geometry and engineering

Why do some geometric shapes hold together, while others are floppy and fall down? An eggshell and a convex dome are rigid, while polygons, with four or more sides of fixed length in the plane, flex. The geometric principles for convex shapes go b more››

University of Calgary

- 11-Oct-07

MITACS Math Finance Seminar 2007

The Mutual Fund Theorem (MFT) is considered in a general semimartingale financial market $ with a finite time horizon T. It is established that: 1) If for given utility functions (i.e. investors) the MFT holds true in all Brown more››

University of British Columbia

- 10-Oct-07

The unfinished revolution: space, time and the quantum

Between 1905 and 1926 Einstein, Bohr and others initiated a scientific revolution by the introduction of quantum mechanics and relativity theory. The revolution is unfortunately still incomplete, because there are major unresolved issues. Th more››

University of British Columbia

- 10-Oct-07

The geometry of rigid and non-rigid structures

Convex triangulated surfaces in three-space are rigid by Cauchy's Theorem. But what about non-convex surfaces? Some interesting recent examples of classes of non-convex surfaces have some convex-like properties, and yet are still rigid. On the oth more››

University of Calgary

- 4-Oct-07

Total Positivity and its Applications

A matrix is called totally positive (resp. totally nonnegative)if all of its minors are positive (resp. nonnegative). This important class of matrices grew out of three separate applications: Vibrating systems, interpolation, and statistics. Since more››

University of Calgary

- 4-Oct-07
- 5-Oct-07

Optimal investment under partial information

We consider the problem of maximizing terminal utility in a model where asset prices are driven by Wiener processes, but where the various rates of returns are allowed to be arbitrary semi-martingales. The only information available to the investo more››

University of British Columbia

- 2-Oct-07

2-Dimensional Lp-Minkowski problem

et S^{n-1}subset R^n be the unit sphere. The L_p-Minkowski problem proposed by Lukwak is a natural generalization of the classical Minkowski problem. Analytically, it is equivalent to find positive solutions of the equation det( more››

University of British Columbia

- 2-Oct-07

Finite Element Analysis of CAD Large Assemblies

In today's product development and engineering process, usage of computer aided design (CAD) platform is obvious. It allows crating of quite realistic models, precisely describing not only the geometry of the developed prototype, but also its phys more››

University of British Columbia