Plan for Lectures
Topics to be Covered
- Computational Models & Complexity Classes (1 lectures)
- Complete Polynomials (2 lectures)
- Basic structural results: universal circuits, homogenization, division elimination (1 lecture).
- Partial derivatives (1 lecture)
- Factoring (2 lectures)
- Depth reduction (3 lectures)
- Polynomial identity testing, randomized algorithms for matching problems (1 lecture).
- Derandomizing Polynomial Identity Testing (2 lectures).
- Lower Bounds (2 lectures)
- Hardness vs Randomness (1 lecture)
- Matrix Multiplication, Tensors & Border Rank (1 Lecture)
- Circuit Reconstruction/Learning (1 Lecture)
- Barriers to Lower Bounds (1 Lecture)
- Proof Complexity (1 Lecture)
- Conclusion (1 Lecture)
Lecture Schedule
|
Date |
Topics |
Notes |
| Lecture 0 |
May 6th |
Introduction & Overview |
PDF |
| Lecture 1 |
May 6th |
Computational Models & Complexity Classes |
|
| Lecture 2 |
May 8th |
Complete Polynomials I |
|
| Lecture 3 |
May 13th |
Complete Polynomials II |
|
| Lecture 4 |
May 15th |
Basic Structural Results |
|
| Lecture 5 |
May 21st |
Computing First-Order Partial Derivatives |
|
| Lecture 6 |
May 22nd |
Factoring I |
|
| Lecture 7 |
May 27th |
Factoring II |
|
| Lecture 8 |
May 29th |
Depth Reduction I |
|
| Lecture 9 |
June 10th |
Depth Reduction II |
|
| Lecture 10 |
June 12th |
Depth Reduction III |
|
| Lecture 11 |
June 17th |
Polynomial Identity Testing (PIT) |
|
| Lecture 12 |
June 19th |
Derandomizing PIT |
|
| Lecture 13 |
July 3rd |
Derandomizing PIT |
|
| Lecture 14 |
July 8th |
Lower Bounds I |
|
| Lecture 15 |
July 10th |
Lower Bounds II |
|
| Lecture 16 |
July 15th |
Hardness vs Randomness |
|
| Lecture 17 |
July 17th |
Matrix Multiplication, Tensors, Border Rank |
|
| Lecture 18 |
July 17th |
Circuit Reconstruction/Learning |
|
| Lecture 19 |
July 22nd |
Barriers to Lower Bounds |
|
| Lecture 20 |
July 24th |
Algebraic Proof Complexity |
|
| Lecture 21 |
July 29th |
Conclusion |
|
| Lecture 22 |
August 7th |
Final Presentations |
|
| Lecture 23 |
August 8th |
Final Presentations |
|
| Lecture 24 |
August 9th |
Final Presentations |
|
Suggested Reading
|
Topics |
Suggested Reading |
| Lecture 0 |
Introduction & Overview of Course |
PDF |
| Lecture 1 |
Computational Models & Complexity Classes |
[R, Chapter 3], [B, Chapter 1, 2], [BCS, Chapter 21] |
| Lecture 2 |
Complete Polynomials I - Determinant |
[R, Chapter 3], [BCS, Chapter 21] |
| Lecture 3 |
Complete Polynomials II - Permanent |
[R, Chapter 3], [B, Chapter 2], [BCS, Chapter 21] |
| Lecture 4 |
Basic Structural Results |
[SY, Chapter 2.1, 2.2, 2.3] |
| Lecture 5 |
Computing First-Order Partial Derivatives |
[SY, Chapter 2.3] |
| Lecture 6 |
Factoring I |
|
| Lecture 7 |
Factoring II |
|
| Lecture 8 |
Depth Reduction I |
|
| Lecture 9 |
Depth Reduction II |
|
| Lecture 10 |
Depth Reduction III |
|
| Lecture 11 |
Polynomial Identity Testing (PIT) |
|
| Lecture 12 |
Derandomizing PIT |
|
| Lecture 13 |
Derandomizing PIT |
|
| Lecture 14 |
Lower Bounds I |
|
| Lecture 15 |
Lower Bounds II |
|
| Lecture 16 |
Hardness vs Randomness |
|
| Lecture 17 |
Matrix Multiplication, Tensors, Border Rank |
|
| Lecture 18 |
Circuit Reconstruction/Learning |
|
| Lecture 19 |
Barriers to Lower Bounds |
|
| Lecture 20 |
Algebraic Proof Complexity |
|
| Lecture 21 |
Conclusion |
|