Speaker: Charles Johnson, William and Mary

Title: Determinantal Inequalities: Ancient History and Recent Advances

Abstract: In 1893, Hadamard showed that the determinant of a positive definite matrix was bounded above by the product of its diagonal entries, a result he wanted for the analysis of solutions to PDE's. A generalization due to Fischer in 1908 was followed at wartime by a broad result due to Koteljanskii.

In modern times there has been a push to understand all inequalities involving ratios of products of principal minors in special classes of matrices such as positive definite, M-matrices and totally positive matrices. We survey both the classical results and recent developments, as well as the ideas behind them.. Motivation comes from combinatorics, geometry of numbers and number theory, as well as PDE's and matrix theory.

Place: Science and Technology Building I, Room 242

Refreshments will be served before the talk at 3:00 p.m. in Room 222.

Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
http://math.gmu.edu/
Tel. 703-993-1460, Fax. 703-993-1491