This seminar on Applied Geometry and Algebra aims to explore the arrangement of points in projective spaces to maximize minimum distances. The course covers topics such as fundamental problems in metric geometry, Welsh Bound, Orthonormal Basis, Semidefinite Programming, and Open problems. The teaching method involves discussing applications, surveying the state of the art, and identifying key open problems in the field. This seminar is intended for individuals interested in advanced topics in geometry, algebra, and their applications in various fields.
Overview
Syllabus
Introduction
A Fundamental Problem in Metric Geometry
How to Solve the Problem
Low Dimensions
Welsh Bound
Orthonormal Basis
Best Known Packings
Game of Sloanes
Jasper Prize
Lower Bounds
TarskySeidenberg Theorem
Case Work
Contact Graph
Semidefinite Programming
Suboptimal Cases
Most Important Problem
Seeks
Schrdinger
The emergent feature
Rounding procedure
Stark units
Fixed point theorem
Bingular tight frames
Open problems
Shortcut matrices
Taught by
Society for Industrial and Applied Mathematics
