SCHEDULE
No. | Date | Topic | Remarks | 1 | Wed Feb 8 | Hermite, Laguerre and Jacobi: the uniquitious triad and the moment problem | [Syllabus][PSet1] |
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2 | Mon Feb 13 | Joint element and eigenvalue density for the Hermite Ensemble | |
3 | Wed Feb 15 | Joint element and eigenvalue density for the Laguerre Ensemble, Demonstration of Julia's Power! | PSet1 Due [PSet 2] |
Fri Feb 17 | Introduction to Jack Polynomials | Extra Research Class | |
4 | Mon Feb 20 | |
MIT Holiday |
Tue Feb 21 | Jacobi Ensemble: angle between subspaces, gsvd, CS decomposition and all that | ||
5 | Wed Feb 22 | Computer Free Random Matrix Factorization | PSet 2 Due [PSet 3][PS3 Supp] |
Fri Feb 24 | More on Jack Polynomials | Extra Research Class | |
6 | Mon Feb 27 | Guest lecture | |
7 | Wed Feb 29 | Matrix Jacobians with Wedge product | |
8 | Mon Mar 5 | How to do integration over the Orthogonal group and Why is it important? | |
9 | Wed Mar 7 | Cauchy-Binet formula and its consequence | [PSet 4] [Chapter 11] |
Fri Feb 17 | Group Representation and Zonal Polynomials | Extra Research Class | |
10 | Mon Mar 12 | Tracy-Widom Law I | |
11 | Wed Mar 14 | Tracy-Widom Law II | |
12 | Mon Mar 19 | Eigenvalue Spacing Distribution and Random Polynomials | |
13 | Wed Mar 21 | More on Spacing Distribution | [Suggested Projects List] |
Mon Mar 26 | Spring Break | ||
Wed Mar 28 | Spring Break | ||
14 | Mon Apr 2 | Random Gowth Model | |
15 | Wed Apr 4 | Aztec Diamond and Longest Increasing Subsequence | |
16 | Mon Apr 9 | Longest Increasing Subsequence, Young Tableaux and Schensted Correspondence | |
17 | Wed Apr 11 | ||
Mon Apr 16 | Patriots Day | ||
18 | Wed Apr 18 | Free Probability I | |
19 | Mon Apr 23 | Free Probability II | |
20 | Wed Apr 25 | Free Probability III | |
21 | Mon Apr 30 | Free Probability IV | |
22 | Wed May 2 | Free Probability V | |
23 | Mon May 7 | Project Presentation | |
Yufei Zhao, Spectrual Distributions of Random Graphs | [slides][report] | ||
Yi Sun, Virasoro Constraints and the Tracy-Widom Law | [slides][report] | ||
24 | Wed May 9 | Project Presentation | |
Chenhui Hu, Spectral Perturbation of Small-World Networks | [slides][report] | ||
25 | Mon May 14 | Project Presentation | |
26 | Wed May 16 | Project Presentation |