Using Tensor Diagrams to Represent and Solve Geometric Problems
Sunday, Half Day, 1:30 - 5 pm
matrix notation for algebraic geometry does not adequately
represent some concepts that are important in understanding
and manipulating geometrical quantities. Better notational
tools can be appropriated from the field of mathematical
physics. This course focuses on one such tool, the tensor
diagram (which is related to the Feynman diagram), and
shows how it can improve notational convenience, solve
many geometrical problems that would otherwise be very
complicated, and facilitate understanding of the algebraic
structure of such problems.
Familiarity with homogeneous-coordinate geometry and basic
matrix operations. Distaste for page-long algebraic expressions.
Review of homogeneous-coordinate math. Notational problems
with matrices. Einstein Index notation. How tensor diagrams
represent basic operations. Application of tensor diagrams
to: 1D homogeneous equations (polynomials), 2D homogeneous
equations (curves), 3D homogeneous equations (surfaces).
Unsolved (at least to the knowledge of the speaker) problems.
James F. Blinn