Schedule
01/08/19: Introduction/Tour
01/10/19: Convexity basics: see Barvinok (I.1, II.1-3)
01/15/19: Cones and duality: see Barvinok (IV.1,3,5)
01/17/19: The cone of positive semidefinite matrices: see Barvinok (II.12)
01/22/19: PSD cone (cont'd) and nonnegative polynomials
01/24/19: Convex optimization basics: for more, see Boyd, Vandenberge
01/29/19: Algebraic geometry basics: for more, see Cox, Little, O'Shea
01/31/19: Certifying nonnegativity and the Positivstellensatz: for more, see Blekherman, Parrilo, Thomas, Chapters 3, 4
02/05/19: Sums of squares and SDPs: for more, see Blekherman, Parrilo, Thomas, Chapter 3
02/07/19: The dual perspective: moments: for more, see Blekherman, Parrilo, Thomas, Chapter 3.5
02/12/19: Combinatorial optimization and SDPs (an application to MAXCUT) (Guest lecturer: Dávid Papp)
02/14/19: Combinatorial optimization and SOS (an application to stable sets): for more, see Blekherman, Parrilo, Thomas, Chapter 7
02/19/19: Approximating convex hulls of varieties with theta bodies: for more, see Blekherman, Parrilo, Thomas, Chapter 7
02/21/19: Overview of sums of squares and moments: SOS in M2 (Examples), SOS in Matlab
02/28/19: Matrix completion and spectrahedra: for more, see Barvinok (II.13)
03/01/19: Matrix completion and graph realizability: for more, see Barvinok (II.13,15)
03/05/19: Algebraic boundaries and duality: for more, see Blekherman, Parrilo, Thomas, Chapter 5
03/07/19: Algebraic boundaries and optimization: for more, see Blekherman, Parrilo, Thomas, Chapter 5, (Examples)
03/19/19: Spectrahedra and hyperbolic polynomials: for more, see Pemantle