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Seminar on "Graphs, matrices and applications"

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.


January - April 2018

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)

August - November 2018

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

Dr. Swanand Khare will deliver a series of lectures on on low rank approximation of matrices and inverse eigenvalue problems.

Date Contents
05/10/2018 Low rank approximation of matrices.

January - April 2019

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.

August - November 2019

Mr Arnab Maiti will deliver a series of lectures on algorithms for vertex cover problem.

January - April 2020

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.