Tuesday and Thursday 3:00 - 4:15pm in 1218 SAS Hall
Instructor: Cynthia Vinzant (3260 SAS, email)
Offce Hours: Tuesday, Wednesday 11am-noon or by appointment
Syllabus
Description: Real algebraic geometry is the study of solutions to polynomial equalities and inequalities over the real numbers. It provides powerful tools to understand the geometry behind many problems in optimization and develop new methods for solving them. This class will introduce basic notions and techniques in real algebraic geometry, convexity, and conic optimization. Further topics include semidefinite programming, sums of squares, moment problems, hyperbolic and stable polynomials, and several applications in polynomial and combinatorial optimization.
Final Project
Students will write a final paper (due Tuesday, May 7) on a topic
related to real algebraic geometry and convex optimization and give a
presentation in class at the end of the semester. (More details.)
Homework
Homework 1 (.pdf .tex) due Thursday, January 24
Homework 2 (.pdf .tex) due Thursday, February 7
Homework 3 (.pdf .tex) due Friday, February 22
Homework 4 (.pdf .tex) due Thursday, March 7
Oral Presentations
Thurs. April 11
Jane Coons on
Geometry of maximum likelihood estimation in Gaussian graphical
models, after Uhler
Cash Bortner, Owen Coss, Ben Hollering on
Gaussian
Graphical Models: An Algebraic and Geometric Perspective, after
Uhler
Tues. April 16
Christian Smith on Cuts, matrix completions and graph
rigidity, after Laurent
Wesley Nelson on Nonnegative Polynomials and Circuit
Polynomials, after Wang
Thurs. April 18
Saran Ahluwalia, Geneva Collins, Jonathan Dunay on
Typical and Generic Ranks in
Matrix Completion, after Bernstein, Blekherman, and Sinn
Ella Pavlechko on A
Riemannian approach to convex optimization, after Mishra, Meyer, and Sepulchre
Tues. April 23
Eric Geiger on Symmetry
groups, semidefinite programs, and sums of
squares, after Gatermann and Parrilo
Jordan Almeter on Symmetric
Sums Of Squares Over k-Subset Hypercubes after Raymond, Sanderson,
Singh and Thomas
Thurs. April 25
Georgy Scholten on The Chow of
Reciprocal Linear Space, after Kummer and Vinzant
Katherine Harris on The Euclidean Distance Degree of an
Algebraic Variety, after Draisma, Horobet, Ottaviani,
Sturmfels, and Thomas