Pacific Institute for the Mathematical Sciences - PIMS

Gauss Sums: Finding the Root of Unity

A Gauss sum over a finite field GF(q) is a sum of q algebraic numbers. It is often useful to evaluate Gauss sums explicitly, for instance, in coding theoretic or cryptographic applications. For small q, the evaluation of Gauss sums can be done nai   more››

Scientific Event

Values and Ideals in Combinatorial Problems

The absolute value of complex numbers is surprisingly useful in the investigation of certain combinatorial problems. The connection often arises from imbedding finite cyclic groups into the complex numbers by sending the group elements to roots of   more››

Scientific Event

Amoebas, Coamoebas, and Tropical Geometry

Given a triangle with side lengths 1, log x, log y and opposite interior angles π-u-v, u, v, the functional determinant ∂(x,y)/∂(u,v) is identically equal to 1. This amusing fact is a special ins   more››

Scientific Event

Time-Frequency Analysis: From Wireless Communications to Abstract Harmonic Analysis

In the talk I will discuss the relation between problems in wireless communications and time-frequency analysis. I will explain the basic principle of OFDM (orthogonal frequency division multiplexing) and its formulation in time-frequency analysis   more››

Scientific Event

Potential energy minimization

Energy minimization can be thought of as a broad generalization of sphere packing. Yudin discovered that harmonic analysis can be applied to prove lower bounds for potential energy. This talk will explain these bounds and show how to use them to p   more››

Scientific Event

Optimality of the Leech lattice

This talk will outline the proof that the Leech lattice is the unique densest lattice in R24. The proof combines linear programming bounds with special algebraic and geometric arguments. This is joint work with Abhinav Kumar.   more››

Scientific Event

Sphere packing and harmonic analysis

Harmonic analysis is one of the fundamental tools in sphere packing, in the form of "linear programming bounds". This talk will give a survey of linear programming bounds and their applications, as well as a brief introduction to semidef   more››

Scientific Event

Random 0/1 polytopes

Scientific Event

Distribution of volume on isotropic convex bodies

Scientific Event

Formal proofs in geometry

Traditional mathematical proofs are written in a way to make them easily understood by mathematicians. Routine logical steps are omitted. An enormous amount of context is assumed on the part of the reader. Proofs, especially in topology and geomet   more››

Scientific Event

Computer-assisted proofs in geometry

In recent years, computer-assisted proofs have become relatively common. For example, in 2002, W. Tucker published a proof of problem 14 (concerning strange attractors) on Smale's list of problems for the new century. Other recent computer-assiste   more››

Scientific Event

Sphere Packings and foams

Kepler's conjecture asserts that the densest possible arrangement of congruent balls in three dimensions is the familiar pyramid arrangement, which is used to stack oranges at the fruit stand. A 300-page proof of this theorem finally appeared in J   more››

Scientific Event

The integral geometry of random sets

In various scientific fields from astro- and high energy physics to neuroimaging, researchers observe entire images or functions rather than single observations. The integral geometric properties, notably the Euler characteristic of the level/excu   more››

Scientific Event

Geophysical Inversion Workshop

The second PIMS GIW will be held on the University of Calgary Campus in August of 2006. Like the first event (2003), the purpose is to bring together mathematicians and geophysicists to focus on a challenging inver   more››

Scientific Event

Canadian Quantum Information Students' Conference

The Canadian Quantum Information Students' Conference (CQISC) offers the ideal environment for graduate students interested in all areas of Quantum Information Theory and Experiment to meet an collaborate. Students of computer science, mathem   more››

Scientific Event

Sixth Canadian Summer School on Quantum Information Processing

The goal of this summer school is to introduce a general audience of computer scientists, physicists, and mathematicians with little or no background in quantum information processing to this exciting and growing field. Quantum information pro   more››

Scientific Event

Canadian Operator Symposium 2006

The 34-th Annual Canadian Operator Symposium (COSy) will take place at the University of Calgary campus from May 29th to June 2, 2006. The meeting will be an occasion to celebrate the 65-th birthday of   more››

Scientific Event

Tax Incentives for Research and Development: Theory and Evidence

R&D differs from other types of investments for several reasons. One is that there are several market failures thought to be associated with R&D – knowledge spillovers, business stealing effects, asymmetric information in financial markets,   more››

Industrial Event