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Lecture Notes and/or Slides for the
2019 AMS Short Course on
Sum of Squares: Theory and Applications
Each of the six lectures in the course will be broken into two 45-minute sections. Problem sessions are planned for both days, and speakers and organizers will be available to assist participants with these exercises. Some exercises will be facilitated by numerical software such as Macaulay2, Maple™, MATLAB, or Julia. Participants with a desire to experiment with computations and an interest in applications should find this experience especially stimulating. The speakers will also provide participants with a list of research questions to guide their explorations after the course.
Please bring your laptop to the course, and if possible, download Macauley2 or Julia before the course starts.
This short course is aimed at students with minimal to no background in the theory of SOS polynomials. However, familiarity with properties of polyhedra, convex sets, and polynomials will provide useful background. Appendix A in the book Semidefinite Optimization and Convex Algebraic Geometry, G. Blekherman, P.A. Parrilo and R.R. Thomas (eds.), MOS-SIAM Series on Optimization, SIAM 2012, is recommended as useful preparatory reading. A free pdf of the book can be found at www.mit.edu/~parrilo/sdocag/.
Please look at this file and download the required code:
Getting Started with Sums of Squares: https://sums-of-squares.github.io/sos/
Introduction to Sums of Squares (Slides) (updated)
Exercises
Greg Blekherman, Georgia Tech
Engineering applications of SOS polynomials
Slides
Exercises
Georgina Hall, INSEAD
Lifts of convex sets
Slides
Exercises
Hamza Fawzi, University of Cambridge
Rounding Sum-of-Squares (Lecture 1)
Lower Bounds Against Sum-of-Squares (Lecture 2)
Exercises
Ankur Moitra, MIT
Algebraic geometry through the lens of sums of squares
Slides Part 1
Slides Part 2
Exercises
Mauricio Velasco, Universidad de los Andes
Geometry of Spectrahedra (Slides)
Exercises
Cynthia Vinzant, North Carolina State University
Schedule:
Day 1:
8:30-9:15 Lecture 1 Greg Blekherman
9:25-10:10 Lecture 1, continued
10:10-10:40 Coffee Break
10:40-11:25 Lecture 2 Cynthia Vinzant
11:35-12:20 Lecture 2, continued
12:20-2:00 Lunch
2:00-2:45 Lecture 3 Georgina Hall
2:55-3:40 Lecture 3, continued
3:40-4:10 Coffee Break
4:10-5:30 Problem session
Reception
Day 2:
8:30-9:15 Lecture 4 Mauricio Velasco
9:25-10:10 Lecture 4, continuted
10:10-10:40 Coffee Break
10:40-11:25 Lecture 5 Ankur Moitra
11:35-12:20 Lecture 5, continued.
12:20-2:00 Lunch
2:00-2:45 Lecture 6 Hamza Fawzi
2:55-3:40 Lecture 6, continued
3:40-4:10 Coffee
4:10-5:30 Problem session