## CS 506, Computational Geometry, Spring 2024 |

- Jared Saia
- Email: "last name" at cs.unm.edu.
- Office: FEC 3120, The best way to reach me for this class is generally via Piazza. I check it once a day, usually around noon.
- Office Hours: By appointment.
- Note: I will always be available in my office during office hours. At other times, if my door is open, feel free to come in. If the door is closed, I'm probably at work on a paper, grant or research problem. Please come by another time or make an appointment via email.

- Convex Hull
- My Convex Hull Notes
- Jeff Erickson's Convex Hull Notes
- Convex Crepes!
- High Dimensional Convex Hull; See also Quickhull
- Duality
- My Halfplane Intersection and Convex Hull Notes
- UFL lecture notes on Duality
- U. Maryland Notes, Pages 41-44 give a good connection between convex hulls, and upper/lower envelopes, Lecture 8 gives good connection between envelopes and linear programming. Lecture 16 gives good connections between convex hulls and Voronoi diagrams, and Delaunay triangulations
- Voronoi Diagrams, Delaunay Triangulations and More Dual Transformations
- My notes on Voronoi Diagrams, Delaunay Triangulations and More Dual Transformations
- Many of these problems have deep connections to each other via Projections and Duality Transformations
- Linear Programming
- My notes on Linear Programming and High-Dimensional Convex Hulls
- Linear Programming: Gupta's notes, Lecture 17
- Higher Dimensional Spaces and Johnson-Lindenstrauss
- My notes on High Dimensional Properties and the Johnson-Lindenstrauss Projection
- Arora Notes on Johnson-Lindenstrauss Projection
- You can embed an arbitrary metric into Euclidean space with O(log n) distortion (via Bourgain's theorem, see also here). Then, you can use Johnson-Lidenstrauss to project onto R^d where d = O(log n).
- Arora Notes on SVD (re low-rank approximation)
- Arora Notes on SVD (Part 2)
- SVD Low-rank Approximation
- My notes on the Singular Value Decomposition
- Arora Notes on SVD (re low-rank approximation)
- Arora Notes on SVD (Part 2)
- Convex Optimization
- My notes on Multiplicative Weights (MW)
- Multiplicative Weights by Aaron Roth.
- Survey Paper on Multiplicative Weights by Arora et al.
- Online Convex Optimization via MW (Section 3.9 of the Arora survey paper)
- Arora Lecture on Gradient Descent and Stochastic Gradient Descent
- Andrew Ng video on Intuition of Gradient Descent
- Another interesting video on gradient descent
- Combinatorial Topology
- Distributed Computing Through Combinatorial Topology (UNM Library has the ebook)
- Maurice Herlihy's slides
- Class Summary