| No. |
Date |
Topic |
Remarks |
| 1 | Wed Feb 3 | Hermite, Laguerre and Jacobi ensemble: the ubiquitous triad | Syllabus |
| 1* | Fri Feb 5 | Spiked (deformed) Random Matrix Models | 11-12:30 2-139, [Donoho et al., 2013][Johnstone, 2001] |
| 1* | Fri Feb 5 | Optional Julia Tutorial by Steven Johnson (if possible, try the instructions) | 5pm, 4-270 |
| 2 | Mon Feb 8 | Guest Lecture: Michael La Croix | |
| 3 | Wed Feb 10 | Jacobi Ensemble: angles between subspaces, gsvd and CS decomposition | [PS 1] |
| 3* | Fri Feb 12 | IDSS Seminar: Principla Components Analysis in Light of the Spiked Model (David Donoho) | |
| Mon Feb 15 | no lecture | Presidents Day |
| 4 | Tue Feb 16 | Semicircle, Quartercircle, Circular and other infinite RMT Laws | |
| 5 | Wed Feb 17 | Cauchy-Binet Formula and its consequences | |
| 6 | Mon Feb 22 | Tracy-Widom Law | [PS 2] |
| 7 | Wed Feb 24 | Tracy-Widom Law, Fredholm Determinant and Determinantal Point Processes | |
| 8 | Mon Feb 29 | Numerical Computation of RMT Laws (Bornemann's Toolbox) | |
| 9 | Wed Mar 2 | Orthogonal Polynomials, Tridiagonal Matrices, Gaussian Quadratures, Lanczos and all that | |
| 10 | Mon Mar 7 | Riemann-Hilbert problem I | |
| 11 | Wed Mar 9 | Riemann-Hilbert problem II | |
| 12 | Mon Mar 14 | Eigenvalue Perturbation Theory and Dyson-Brownian Motion | [PS 3] |
| 13 | Wed Mar 16 | From Gaussian Ensembles to Stochastic Operators | |
| Mon Mar 21 | no lecture | Spring Break |
| Wed Mar 23 | no lecture | Spring Break |
| 14 | Mon Mar 28 | $\beta$-ensembles and Orthogonal Polynomial Ensembles | |
| 15 | Wed Mar 30 | Jack Polynomials, Multivariate Orthogonal Polynomials and their applications I | |
| 16 | Mon Apr 4 | Jack Polynomials, Multivariate Orthogonal Polynomials and their applications II | |
| 17 | Mon Apr 6 | Random Growth models, Aztec Diamond and Longest Increasing Subsequence (LIS) | |
| 18 | Mon Apr 11 | LIS, Group Representation and Baik-Deift-Johansson theorem | |
| 19 | Mon Apr 13 | Ghost and Shadows | |
| * | Mon Apr 18 | no lecture | Patriots Day |
| 20 | Wed Apr 20 | Free Probability I | |
| 21 | Mon Apr 25 | Free Probability II | |
| 22 | Wed Apr 27 | Free Probability III | |
| 23 | Mon May 2 | Project Presentation | |
| 24 | Wed May 4 | Project Presentation | |
| 25 | Mon May 9 | Project Presentation | |
| 26 | Wed May 11 | Project Presentation | |
