The Advanced Training in Mathematics Schools (ATM Schools) were launched by the National Board for Higher Mathematics (NBHM) in May 2004. The purpose of these schools is to provide training in core subjects in Mathematics to Ph.D. students, young researchers and teachers. The emphasis in these schools is on learning mathematics by doing it. IIT Bombay and TIFR have jointly established the National Centre for Mathematics (NCM) in 2011. The instructional schools and workshops which were earlier planned by an NBHM committee on ATM Schools are now being organized under the supervision of the Apex Committee of the NCM.
Matrix theory is a fundamental branch of mathematics having incredibly diverse and far-reaching applications in various fields, including engineering, statistics, computer science, and finance. Its use is critical to many areas of modern science and technology.
The workshop on matrix theory will feature three mini courses from some prominent mathematicians and leading experts in the area. This one-week long event will focus on various aspects of matrix theory, and its connections with Fourier analysis, real and complex analysis and numerical linear algebra to solve problems related to matrices, matrix factorizations and their applications, and the theory of functions that preserve matrix positivity. The programme is aimed at Ph.D. students, post-doctoral fellows and researchers interested in matrix theory and related areas.
Dates: 18 Dec 2023 to 23 Dec 2023
For more details please click : https://www.atmschools.org/school/2023/NCMW/mt
| Name of the Speakers with their affiliation. | No. of Lectures | Detailed Syllabus |
| Professor Rajendra Bhatia Department of Mathematics Ashoka University, Haryana | 6 hrs | Use of Fourier Analysis to solve some problems of matrix theory: Computation of norms of some infinite matrices like the Hilbert matrix, Cesaro matrix, etc. as well as of the Toeplitz and Hankel matrices. Some generalizations of these that are useful in number theory. Solutions of the Sylvester Equation using Fourier analysis. Positive definite sequences and functions, and their use in deriving matrix inequalities. |
| Professor Peter Semrl Institute of Mathematics, Physics and Mechanics, Slovenia, | 3 hrs | TBA |
| Professor Shreemayee Bora Department of Mathematics IIT, Guwahati | 9 hrs | LU factorization: Gaussian Elimination as an LU factorization of a matrix; Existence and uniqueness of LU factorization; computing LU factors; variants of LU factorization; Cholesky factorization of positive definite matrices: Positive definite matrices and their properties; existence and uniqueness of Cholesky factorization of positive definite matrices and its relationship with LU factorization; computing Cholesky factors;QR factorizations of matrices: Existence and uniqueness of QR factorizations of matrices; computing QR factors; applications of QR factorizations; relationship of QR factorizations with other factorizations;Polar decompositions of matrices: Existence of polar decompositions; relationship with other decompositions; their applications;Singularvaluedecompositionsofmatrices:Existenceanduniqueness, properties and applications. Relationship with other decompositions. Decompositions related to the matrix eigenvalue problem:Diagonalizability; Jordan canonical form (in brief);Schur’sTheorem (real and complex versions); spectral theorems; a brief introduction to computing eigenvalues and eigenvectors for dense matrices. |
| Dr. Apoorva Khare Associate Professor Department of Mathematics IISC, Bangalore | 4.5 hrs | Entrywise positivity preservers: Theory of functions preserving matrix positivity. Positivity and total positivity of matrices, classical results of Schoenberg and Karlin; inertia of matrices; classical results on entrywise powers as well as some recent developments on positivity |
| Dr. Tanvi Jain Associate Professor Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, New Delhi. | 4.5 hrs |
Convener(s)
| Name: | Dr. Tanvi Jain | Dr. Jagjit Singh |
| Mailing Address: | Associate Professor Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, New Delhi. | Assistant Professor University Institute of Engineering and Technology Panjab University, Chandigarh |
| Email: | tanvi at isid.ac.in | matharuj at pu.ac.in |
