All of the readings are from the draft monograph Pseudorandomness.
|
Date |
Title |
Reading/Reference |
Jan 24 |
Introduction (Course overview)
|
Ch. 1 |
Jan 26 |
Class cancelled |
|
|
The Power of Randomness
|
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|
Jan 31 |
Randomized Algorithms and Complexity
Classes |
Sec. 2.1-2.3.1 |
Problem Set 1 (due 2/11) |
Probs. 2.2, 2.5, 2.6, 2.7 [pdf] |
|
|
Feb 2 |
Sampling and Approximation Problems |
Sec. 2.3.2-2.4 |
Basic Derandomization Techniques |
||
Feb 7 |
Enumeration, Nonuniformity, Nondeterminism |
Sec. 3.1-3.3 |
Feb 9 |
Conditional Expectations, Pairwise Independence |
Sec. 3.4-3.5 |
Problem Set 2 (due 2/25) |
[pdf] |
|
Expander Graphs |
||
Feb 14 |
Measures of Expansion, Existence |
Sec. 4.1 |
Feb 16 |
Random Walks on Expanders, Algebraic Constructions |
Sec. 4.2-4.3.1 |
Feb 21 |
No class (Presidents' Day) |
|
Feb 23 |
Explicit Constructions, USTCONN in L |
Sec. 4.3.2-4.4 |
Problem Set 3 (due 3/11) |
[pdf] |
|
List-Decodable Codes |
||
Feb 28 |
Definition & Existence |
Sec. 5.1 |
Mar 2 |
List-Decoding Algorithms |
Sec. 5.2 |
Mar 7 |
List-Decoding View of Samplers & Expanders |
Sec. 5.3-5.4 |
Problem Set 4 (due 4/1) |
[pdf] |
|
Randomness Extractors |
||
Mar 9 |
Definition & Existence |
Sec. 6.1 |
Mar 14 & 16 |
No Class (Spring Break) |
|
Mar 21 |
Connections to Other Pseudorandom Objects, Block Sources |
Sec. 6.2-6.3.2 |
Mar 23 |
Condensers, Constructing Extractors |
Sec. 6.3.3-6.5 |
Mar 28 & 30 |
No Class (Theory of Cryptography Conference) |
Sec. 6.2-6.3.2 |
Problem Set 5 (due 4/22) |
[pdf] |
|
Pseudorandom Generators |
||
Apr 4 |
Motivation & Definition, Cryptographic PRGs |
Sec. 7.1-7.2 |
Apr 6 |
Hybrid Arguments, Average-Case Hardness |
Sec. 7.3-7.4.1 |
Apr 11 |
The Nisan-Wigderson Generator |
Sec. 7.4.2-7.4.3 |
Apr 13 |
Worst-case/Average-case Connections & Locally Decodable Codes |
Sec. 7.5 |
Apr 18 |
Local List Decoding & PRGs from Worst-Case Hardness |
Sec. 7.6 |
Apr 20 |
Connections to other Pseudorandom Objects |
Sec. 7.7 |
Problem Set 6 (due 5/6) |
[pdf] |
|
Conclusions and Beyond |
Ch. 8 |
|
Apr 25 |
The Unified Theory of Pseudorandomness & Additional Topics |
|
Algebraic Pseudorandomness |
|
|
Apr 27 |
Small-bias Spaces, Cayley Expanders, and Linear Codes |
|
May 2 |
PRGs for Polynomials and Gowers Uniformity |
|
May 4 |
Non-abelian Cayley Expanders and Representation Theory |
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