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title: Great Theory Hits
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# Raghu Meka: CS289: Great Theory Hits of 21st Century Winter 2023

| [HOME](http://www.raghumeka.org) | [RESEARCH](http://raghumeka.github.io/research.html) | [TEACHING](http://raghumeka.github.io/courses.html) |
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## Introduction

We will cover a handful of groundbreaking results across the entire gamut of theoretical computer science discovered in the 21st century! A tentative list of topics can be found below; the topics may change based on student interest as well.

**Prerequisites**: You **need** background in linear algebra, probability theory, and algorithms (all at a typical undergraduate upper-division level) to make the class fun and interesting for you as well as for me. Check your prerequisites by testing yourself with these problems [assignment](https://ucla.box.com/s/zra5139k5625a68g09anv7jkfjnc7y4r). You can also check last years' [notes](https://hackmd.io/F_qqEjKqTxS3S2_JYZrurg) to get an idea.

Undergrads are welcome! I will allow PTEs as long as you can assure yourself that you have the prerequisites. If in doubt, please contact me by email.

**Lectures: M-W 10-11:50. BOELTER 5422**. Office hours are by appointment (quite flexible). [Zoom link](https://ucla.zoom.us/j/93361419541). (Zoom interactions won't count toward class participation.)

**edStem:** We will use edStem for communication and announcements (including for links to video recordings) - please register [here](https://edstem.org/us/join/V6qgdE).

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## Course Work

We will have three take-home midterms worth 30% each.

- Midterm 1: February 1. Due in 48 hours.
- Midterm 2: February 27. Due in 48 hours.
- Midterm 3: March 20th. Due in 48 hours.

10% credit is for class participation (asking questions in class). If you can't attend class live, then talk to me and we will figure out a suitable fix.

The best resources will be the original papers. The transcipt of the lectures will be available on Scribble. You can also access last year's notes (and other details) on previous years' course webpage [here](https://hackmd.io/F_qqEjKqTxS3S2_JYZrurg).

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## Notes

:::spoiler **Course notes**: We will use [ScribbleTogether](https://scribbletogether.com/).
- Note that each lecture is on a different sheet within the files.
- [Notes on extension complexity](https://scribbletogether.com/whiteboard/6C452FDF-4AE9-47C4-9589-8431B27B39EA)
- [Notes on information complexity](https://scribbletogether.com/whiteboard/9E530A3D-95EC-4C29-A34C-C9676BD36FFE)
- [Notes for Sunflower](https://scribbletogether.com/whiteboard/A355971E-3A0D-4776-9E0B-DD9A81B7E5D7).
- [Notes for Parts 1, 2](https://scribbletogether.com/whiteboard/7BD725CA-A417-4CD0-92DE-78C3304FC58B).

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## Syllabus

The syllabus is flexible and we can cover diverse topics based on your interest. The following is a tentative list of topics to be covered. For each of the specific results, we will use it as an excuse to learn some essential tools in theory of computing.

- SL = L: Undirected connectivity in Logspace (4 lectures). Refs: [This chapter](https://people.seas.harvard.edu/~salil/pseudorandomness/expanders.pdf) and [the original paper](https://omereingold.files.wordpress.com/2014/10/sl.pdf). This excellent (and award winning) survey on [expander graphs](https://www.ams.org/journals/bull/2006-43-04/S0273-0979-06-01126-8/) for further topics.
- Sensitivity conjecture (2 lectures)
- Improved bounds on sunflower conjecture (3 lectures)
- Information Complexity and Applications (4 lectures)
- Quantum LDPC Codes (5 lectures)