Additional Useful Resources

Books:

There is no required textbook for this course, but the following books are suggested if you want to deepen your knowledge on the subject.

• [BCS] Buergisser, Clausen, Shokrollahi Algebraic Complexity Theory
• [CLO'15] Cox, Little, O’Shea Ideals, Varieties and Algorithms
• [CLO'05] Cox, Little, O’Shea Using Algebraic Geometry
• [BC'13] Buergisser, Cucker Condition: the geometry of numerical algorithms
• [S'08] Sturmfels, Bernd Algorithms in Invariant Theory
• [W'17] Wallach, Nolan Geometric Invariant Theory
• [BPT] Blekherman, Parrilo, Thomas, Semidefinite Optimization and Convex Algebraic Geometry

Other web resources:

• Hal Schenck’s webpage contains many sources on hyperplane arrangements and topology for data science
• Ramprasad’s course on Computational Group Theory and Computational Algebra
• Shpilka and Yehudayoff survey on arithmetic circuits
• Madhu Sudan’s 2012 course on Algebra and Computation
• Madhu Sudan’s 1998 course on Algebra and Computation
• Eugene Luks’ 1990 Lectures on Polynomial Time Computation in Groups
• Richard Borcherds’ commutative algebra lectures
• Richard Borcherds’ algebraic geometry lectures

Further reading:

• Avi Wigderson’s new book, Math and Computation
• Ramprasad Saptharishi’s survey, Lower Bounds in Algebraic Complexity
• Chen, Kayal Wigderson’s survey Partial Derivatives in Arithmetic Complexity