| 01 | 1/23 | Introduction [PDF] [TEX]
randomized algorithms, statistical distance, pseudorandom distributions | Gautam Prakriya |
| 02 | 1/28 | Pseudorandom Generators and Extractors [PDF] [TEX]
definition, use, connection with hardness, finite fields | Nick Pappas |
| 03 | 1/30 | Error Correcting Codes [PDF] [TEX]
Hamming code, Hadamard code, Reed-Solomon code, code concatenation | Xi Wu |
| 04 | 2/4 | k-Wise Uniform Generators [PDF] [TEX]
definition, connection with ECCs, construction | Alexi Brooks |
| 05 | 2/6 | Applications of k-Wise Uniform Generators [PDF] [TEX]
Chebyshev's inequality, concentration bounds, list decoding the Hadamard code, hashing | Lubos Krcal |
| 06 | 2/11 | Small-Bias Generators [PDF] [TEX]
definition, connection with ECCs, construction, PRGs for low-degree polynomials | Kevin Kowalski |
| 07 | 2/13 | Harmonic Analysis [PDF] [TEX]
Fourier transform, Parseval's equality, list decoding the Hadamard code | Gautam Prakriya |
| 08 | 2/18 | Applications of Small-Bias Generators [PDF] [TEX]
almost k-wise uniform generators, hardness of approximation | Gautam Prakriya |
| 09 | 2/20 | Expanders [PDF] [TEX]
vertex expansion, edge expansion, quasi-randomness,
rapid mixing, spectral expansion | Adam Everspaugh |
| 10 | 3/4 | Expander Constructions [PDF] [TEX]
Cayley graph, Schreier graph, replacement product, zig-zag product | Xi Wu |
| 11 | 2/25-27 | Applications of Expanders [PDF] [TEX]
deterministic and randomness-efficient confidence boosting, Chernoff bound | Mahnaz Akbari and Nick Pappas |
| 12 | | - | |
| 13 | 3/6 | Derandomized Squaring [PDF] [TEX] (draft from Jul 19, 8:43pm) | Alexi Brooks |
| 14 | 3/11 | Undirected Connectivity in Logarithmic Space [PDF] [TEX] (draft from Jul 16, 4:09pm)
Random walk algorithm, iterared derandomized squaring, INW-generator for undirected connectivity | Adam Everspaugh |
| 15 | 3/13 | Pseudorandomness for Logarithmic Space [PDF] [TEX] (draft from Jul 16, 4:09pm)
Branching programs, INW generator, Nisan's generator | Gautam Prakriya |
| 16 | 3/18 | BPL in L^1.5 [PDF] [TEX] (draft from Jul 16, 4:26pm)
Random perturbation, Rounding, Saks & Zhou | Lubos Krcal |
| 17 | 3/20 | Randomness Extractors [PDF] [TEX] (draft from Aug 2, 2:33pm)
Extractors, Seeded Extractors, Existence | Mahnaz Akbari |
| 18 | 4/1 | Construction of Extractors [PDF] [TEX] (draft from Apr 15, 9:44pm)
Expander walk extractor, GUV-extractor | Kevin Kowalski |
| 19 | 4/3 | Extractor-based PRGs [PDF] [TEX] (draft from Apr 8, 7:32am)
Extractor-based INW generator | Alexi Brooks |
| 20 | 4/8 | Pseudorandomness for Regular Branching Programs [PDF] [TEX] (draft from Feb 27, 11:43pm) | Nick Pappas |
| 21 | 4/10 | Randomness and Space [PDF] [TEX] (draft from Apr 26, 11:34am)
NZ-generator | Adam Everspaugh |
| 22 | 4/15 | Pseudorandomness from Average-Case Hardness [PDF] [TEX] (draft from Apr 29, 8:04am) | Mahnaz Akbari |
| 23 | 4/17 | Pseudorandomness from Worst-Case Hardness [PDF] [TEX] (draft from Apr 22, 12:00pm) | Kevin Kowalski |
| 24 | 4/22 | Pseudorandomness for Bounded-Depth Circuits [PDF] [TEX] (draft from Apr 26, 11:32am)
Local list decoding, Reed-Muller code | Xi Wu |
| 25 | 4/24 | Shrinkage [PDF] [TEX] (draft from May 1, 6:38pm)
Random restrictions, concentration bounds for k-wise independence | Lubos Krcal |
| 26 | 4/29 | Pseudorandomness from Shrinkage [PDF] [TEX] (draft from May 22, 8:09pm) | Gautam Prakriya |
| 27 | 5/1 | Pseudorandomness for Half-spaces [PDF] [TEX] (draft from May 6, 12:59pm)
Sandwiching technique, invariance principle | Alexi Brooks |
| 28 | 5/6 | Pseudorandomness for Half-spaces [PDF] [TEX] (draft from May 9, 7:41am) | Nick Pappas |
| 29 | 5/8 | PRGs from Communication Complexity [PDF] [TEX] (draft from Oct 22, 11:38am) | Xi Wu |
