Semidefinite Programming for Algebra, Combinatorics and Geometry

The course will take place from Monday, June 19th to Friday, June 23rd and will be given by Lorenzo Baldi and Sebastian Debus. It will be held in presence in room G03-214. We follow the lecture notes by Monique Laurent and Frank Vallentin on Semidefinite Optimization,Tim Netzer on Real Algebra and Geometry and Murray Marshall's book Positive polynomials and sums of squares.


Semidefinite programming is a generalization of linear programming to matrix variables, that has many striking applications in various fields of Mathematics, most notably in Algebra, Geometry, and Combinatorics.

On the first day, we will start discussing the basics of semidefinite programming. For the rest of the week, we will explore how semidefinite programming relates, through sums of squares of polynomials, to real algebra and polynomial optimization, and how it can be used to compute graph parameters such as the independence number and the chromatic number. On Friday, we will present some of our research directions on polynomial optimization, nonnegative polynomials, and sums of squares.


The program is as follows:

Mon, June 19 Tue, June 20 Wed, June 21 Thu, June 22 Fri, June 23
Positive semidefinite matrices and semidefinite programming Sums of Squares and Real Algebra Graphs & Polynomial optimization Spherical packings & Polynomial optimization Research insights
Lecture (07:30-09:00) Lecture (07:30-09:00) Lecture (07:30-09:00) Lecture (07:30-09:00) Lecture (09:15-10:45)
Lecture (13:15-14:45) Lecture (15:00-16:30) Lecture (11:00-12:30) Lecture (11:00-12:30) Lecture (12:15-13:45)
Exercises (15:00-16:30) Exercises (16:45-18:15) Exercises (15:00-16:30) Exercises (13:30-15:00) Exercises (14:00-15:30)

The Jupyter notebook with demonstration of polynomial optimization using MomentTools.jl can be found here.


Not necessary. Please be there in the first lecture.

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