This is the course webpage for the Fall 2024 ``Fields Academy Shared Graduate Course'' - Numerical Algebraic Geometry.
See http://www.fields.utoronto.ca/activities/24-25/SGC-NAG
Documents
Syllabus
Assignments 1 & 2 Solutions
Assignments 3 & 4
Edit/Hint for Q1 - Theory: Whether (x^*,0) is singular is independent of the choice of gamma. Describe when (x^*,0) is a singular point.
Assignments 5 & 6
Assignments 7 & 8
Assignments 9 & 10
Project Ideas
Project Update 1
Project Update 2
Final Project Submission: The directions are essentially the same as Project Update 2. Please polish your papers with respect to my feedback.
Notes
Raw Julia Sessions
September 12 - Julia basics, loading packages, and solving systems (27 lines example)
September 19 - Univariate Homotopy Continuation - A naive implementation with some animations
September 26 - Cauchy Integrals
October 31 - Monodromy Solving
Nov 7 - Monodromy Group of 27 lines
Class Schedule
Resources
Downloading and running HomotopyContinuation.jl in julia
Other numerical algebraic geometry software systems:
Bertini
PHCpack
NAG4M2
HOM4PS
What is Numerical Algebraic Geometry?
The Numerical Solution of Systems of Polynomials Arising in Engineering and Science
Project
This class involves a project: you will write a short (no more than 4 pages) paper summarizing some computational investigation using numerical algebraic geometry. Topic options are below - or you could suggest your own project idea!
Project Ideas
Project ideas
Grading
The project grade is broken down into three parts
Part 1: Proposal - 5% - Due October 1
Suggest a project and outline the 4 page paper as best you can
Part 2: Draft 1 - 5% - Due November 14
Have a complete draft of your paper
Part 3: Final Draft - 10% - Due December 5
Take into account the feedback given and polish the paper.
Assignments
How To Submit Assignments/ProjectUpdates
Email tbrysiew@uwo.ca with the subject NAG-2024-ASSIGNMENTNAME-LASTNAME and the assignments attached.
Example:
To: tbrysiew@uwo.ca
Subject: NAG-2024-Assignments1and2-Smith
Body: Dear Taylor,
Please find attached assignments 1 and 2.
Best,
Shelby Smith
Grading
There are 5 pairs of assignments. Each pair consists of a theory part and a coding part.
The lowest two scores are dropped. The 8 highest scores comprise 60% of the final grade.
Assignment Due Dates
Assignment 1/2 - Due October 1
Assignment 3/4 - Due October 22
Assignment 5/6 - Due November 5
Assignment 7/8 - Due November 19
Assignment 9/10 - Due December 5