Additional Useful Resources

There is no required textbook for this course, but the following books and surveys are suggested if you want to deepen your knowledge on the subjects. Throughout the course webpage, we will refer to these resources in the following format: [Authors’ Initials, location in the manuscript]. For instance, to refer to chapter 3 in Ramprasad et al’s survey, we will write [R, Chapter 3].

Commutative Algebra & Algebraic Geometry

• [E]: Eisenbud’s Commutative Algebra with a view towards Algebraic Geometry
• [G]: Gathmann’s Lecture Notes on Commutative Algebra
• [H20]: Hochster’s Introduction to Commutative Algebra
• [GP]: Greuel and Pfister’s A Singular introduction to commutative algebra
• [R1]: Roman’s Field Theory
• [S74]: Seidenberg’s Constructions in algebra
• [BM]: Bayer and Mumford’s What can be computed in Algebraic Geometry
• [CLO1]: Cox, Little, O’Shea’s Ideals, Varieties, and Algorithms
• [CLO2]: Cox, Little, O’Shea’s Using Algebraic Geometry
• [S25]: Schreyer’s An Introduction to Algebraic Geometry

Algebraic Complexity Theory

• [R]: Ramprasad et al’s lower bounds survey and references therein.
• [CKW]: CKW'11 survey on the partial derivative method in algebraic complexity theory. Also here.
• [SY]: SY'10 survey on algebraic complexity theory.
• [S1]: Saxena’s first survey on polynomial identity testing.
• [S2]: Saxena’s second survey on polynomial identity testing.
• [BCS]: Buergisser, Clausen, Shokrollahi’s book on algebraic complexity theory.
• [B]: Buergisser’s book on completeness and reductions in algebraic complexity theory.
• [BCSS]: Blum, Cucker, Shub, Smale, Complexity and Real Computation.
• [BC04]: Bürgisser and Cucker’s 2004 survey.

Related Topics

Complexity Theory

• [W]: Avi Wigderson’s new book, Math and Computation
• [AB]: Arora and Barak’s Computational Complexity: A Modern Approach
• [G]: Goldreich’s Computational Complexity: A Conceptual Perspective
• [P]: Papadimitriou, Computational Complexity
• [RW]: Rudich, Wigderson, Computational Complexity Theory
• [S13]: Sipser, Introduction to the Theory of Computation

Real Algebraic Geometry & Connections

• [BPT] Blekherman, Parrilo, Thomas, Semidefinite Optimization and Convex Algebraic Geometry