CO 750: Local-to-Global Phenomena in Optimization

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Course Information

Institution: University of Waterloo
Dates: Spring 2026
Time: Tuesdays and Thursdays, 1:00pm-2:20pm
Room: QNC 1506

Evaluation Criteria

Every student must scribe 2 lectures. Scribing must be rigorous and fill in informal or ommitted details from lecture (within reason - don't spend time fleshing out proofs of facts that are tangential to the material; simply quote them). Each scribe will also be given additional extensions/variations of the lecture content to prove. You have 3 weeks to finish scribing the lecture. You will be evaluated on the level of mathematical maturity displayed in your scribe notes (with an eye towards research ability).

Topics and References

Part I: Max-Cut Integrality Gap Graph as an example of a highly connected graph with Local structure

Goemans-Williamson algorithm and optimal Max-Cut integrality gap from discretizing the isoperimetric inequality over the sphere

Reference: Gartner-Matousek SDP book

Part II: Expander graphs and Constructions; Relation to Fourier Analysis
Hoory Linial Wigderson Expander survey
Davidoff, Sarnak, Valette Ramanujan Graphs Book

Part III: High Dimensional Expanders, Agreement Testing
Kaufman-Oppenheim Construction
Local-to-Global phenomenon in HDXs

Part IV: Error Correcting Codes: Tanner Codes, Locally Testable Codes, Sheaf Codes
Locally testable codes

Part V: PCP Theory and connection to Expansion
Dor Minzer's PCP Course Notes
Prasad Raghavendra's thesis
PCP from Coset Complexes (O'Donnell, Singer)