MA722 - Schedule

Tentative Schedule

Date	Class Schedule	Reading*
January 9, 11, 16, 18,	Algebra-Geometry Dictionary Recall: Groebner basis Solving polynomial systems using multiplication matrices	Lecture Notes 1 Example Combinatorial Nullstellensatz
	Representation of positive dimensional varieties Triangular representation Pseudo-division Wu's method	Lecture Notes 2 Example Example
	Geometric representation Shape Lemma Noether Normalization Lemma Primitive Elements	Lecture Notes 3 Example
	Multipolynomial projective resultants Properties of projective resultants Computation of projective resultants	Lecture Notes 4 Related Problems
	Real closed fields Real Roots of Univariate Polynomials	Lecture Notes 5
	Signature of Hermite and trace matrices Generalization to the multivariate case with examples	Link to Lecture Notes 6 (univariate case) Example Link to Lecture Notes 7 (multivariate case) Example, Example 2
	Positive definite polynomials and sum of squares relaxation Unconstrained optimization of real multivariate polynomials Constrained optimization of real multivariate polynomials Lasserre relaxation	Lecture Notes 8 Lecture Notes 9
April 24, 26	Project presentations
May 1st 8-11am	Final Exam