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# Thomas Lam : Total positivity, Toeplitz matrices, and loop groups

A real matrix is totally nonnegative if every minor in it is nonnegative. The classical Edrei-Thoma theorem classifies totally nonnegative infinite Toeplitz matrices, and is related to problems in representation theory, combinatorics and probability. I will discuss progress towards two variations on this theorem to block-Toeplitz matrices, and to finite Toeplitz matrices. Both of these variations connect the classical theory to loop groups.

**Category**: Presentations**Duration**: 01:34:48**Date**: January 28, 2009 at 4:25 PM-
**Tags:**seminar, Department of Mathematics Seminar

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