We are meeting on every Friday at 5pm in the department of mathematics. I am maintaing a google group for the participants. Please write to me at rajeshkannan1.m@gmail.com, if you interested in joining the group.
We shall discuss some of the basic properties of nonnegative matrices.
| Date | Contents |
|---|---|
| 02/02/2018 | A quick overview of positive semidefinite matrices, nonnegative(entrywise) matrices and cones. |
| 09/02/2018 | A crash course on positive semidefinite matrices - I. |
| 16/02/2018 | A crash course on positive semidefinite matrices - II. |
| From March 8 to March 17, there is a short term course on Topics in Advanced Linear Algebra. We shall continue our seminar after March 17. | |
| 23/03/2018 | Introduction to nonnegative matrices - I (Perron's theorem, irreducible matrices and Perron-Frobenius theorem). |
| 06/04/2018 | Introduction to nonnegative matrices - II (Matrix norms and proof of Perron's theorem). |
| 13/04/2018 | Introduction to nonnegative matrices - III (Irreducible matrices and Perron-Frobenius theorem) |
| 11/05/2018 | Introduction to nonnegative matrices - IV (Proof of Perron-Frobenius theorem continued.) |
| 25/05/2018 | Introduction to nonnegative matrices - V (Primitive matrices) |
We shall start the weekly seminar of this semester with a series of talks by Dr Sanand on "Optimization, matrix manifolds and dynamical systems."
| Date | Contents |
|---|---|
| 02/08/2018 | Matrix eigenvalue methods |
| 10/08/2018 | Optimization and dynamical systems |
| 17/08/2018 | Rayleigh quotients on symmetric matrices and gradient flows |
| 23/08/2018 | Projective, Grassmann spaces and Power method |
| From August 27 to August 31, there is a short term course on Grobner basis and its applications by Prof J. K. Verma from IIT Bombay. We shall meet on 07/09/2018 . | |
| 07/09/2018 | Projective spaces, power method and Riccati equations |
| 28/09/2018 | A problem in control involving graphs and matrices |
| Date | Contents |
|---|---|
| 05/10/2018 | Low rank approximation of matrices. |
We shall start the weekly seminar of this semester with a series of talks on "Adjacency and Laplacian matrices of graphs". I will discuss topics from the (mostly)following books: Graphs and matrices by R. B. Bapat, Spectra of graphs by Andries E. Brouwer and Willem H. Haemers.
| Date | Contents |
|---|---|
| 18/01/2019 | Properties of adjacency matrices, eigenvalues of adjacency matrices graphs, indecompsability complete graph on 10 vertices in to 3 copies of petersen graph |
| 25/01/2019 | Spring Fest - no lecture |
| 01/02/2019 | Spectral properties of bipartite graphs |
| 08/02/2019 | Mathematics Colloqium talk (Determinant of adjacency matrices of graphs and inverses of trees) Slides |
| 12/02/2019 | CALDAM talk (Adjacency matrices of complex unit gain graphs) Slides |
| 15/02/2019 | existance of inverse of a tree, formula for the inverse of a tree |
| 22/02/2019 | inverses of trees(continued) |
Dr Prateep Chakraborty will deliver a series of lectures on Simplicial complexes.
| Date | Contents |
|---|---|
| 01/03/2019 | Triangulation of Surfaces, Simplicial Complex, Geometric Realization |
| 08/03/2019 | Basics of Simplicial complexes |
| 15/03/2019 | f-vector, Kruskal-Katona theorem |
| 29/03/2019 | Proof of Kruskal-Katona theorem |
| 12/04/2019 | Shellable simplicial complex, face ring |
| 18/04/2019 | Face ring, Hilbert series, Krull dimension, Regular sequence. |
Mr Arnab Maiti will deliver a series of lectures on algorithms for vertex cover problem.
| Date | Contents |
|---|---|
| Jan-Feb 2020 | Prateep continued his lectures on Simplicial complexes. |
| 05/03/2020 | Groups of oriented chains, boundary operators and simplicial homology groups of a topological space. |