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)
- Lower Bounds (2 lectures)
- Polynomial identity testing, randomized algorithms for matching problems (1 lecture).
- Hardness vs Randomness (1 lecture)
- Derandomizing Polynomial Identity Testing (2 lectures).
- 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 | |
| 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 | Lower Bounds I | |
| Lecture 12 | June 19th | Nitin’s Distinguished Lecture | |
| Lecture 13 | July 3rd | Lower Bounds II | |
| Lecture 14 | July 8th | Polynomial Identity Testing (PIT) | |
| Lecture 15 | July 10th | Derandomizing PIT | |
| Lecture 16 | July 15th | Hardness vs Randomness | |
| Lecture 17 | July 17th | Matrix Multiplication, Tensors, Border Rank | |
| Lecture 18 | July 22nd | Circuit Reconstruction/Learning | |
| Lecture 19 | July 24th | Barriers to Lower Bounds | |
| Lecture 20 | July 29th | Final Presentations | |
| Lecture 21 | August 5th | Final Presentations | |
| Lecture 22 | August 7th | Final Presentations |
Suggested Reading
| Topics | Suggested Reading | |
|---|---|---|
| Lecture 0 | Introduction & Overview of Course | |
| 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 | paper 1 paper 2 |
| Lecture 7 | Factoring II | Kaltofen Trager |
| Lecture 8 | Depth Reduction I | [R, Chapter 5.3], [SY, Chapter 2.4] |
| Lecture 9 | Depth Reduction II | [R, Chapter 5.3], [SY, Chapter 2.4] |
| Lecture 10 | Depth Reduction III | [R, Chapter 5.3], [SY, Chapter 2.4] |
| Lecture 11 | Lower Bounds I | [R, Chapters 6, 9], [SY, Chapters 3.2, 3.5] |
| Lecture 12 | Nitin’s Distinguished Lecture | |
| Lecture 13 | Lower Bounds II | [R, Chapter 19] |
| Lecture 14 | Polynomial Identity Testing (PIT) | [SY, Chapters 4.1-4.4] |
| Lecture 15 | Derandomizing PIT | [SY, Chapters 4.1-4.4, 4.8] |
| Lecture 16 | Hardness vs Randomness | [SY, Chapter 4.3] |
| Lecture 17 | Matrix Multiplication, Tensors, Border Rank | [BCS Chapter 15], [BI18, Chapters 14, 15] |
| Lecture 18 | Circuit Reconstruction/Learning | [SY, Chapter 5], [ BSV paper], [ PSV paper], [ BS paper] |
| Lecture 19 | Barriers to Lower Bounds | [ EGOW paper] |