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Introduction to Total Positivity

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Lauren Williams, UC Berkeley

The classical theory of total positivity is the study of real n
by n matrices such that all minors are positive (or nonnegative). Such
matrices appear in various areas of mathematics such as graph theory,
algebraic geometry, stochastic processes, game theory, matroids, and
representation theory. They also appear in various areas of study in the
natural sciences, including brownian motion and electrical networks. In
this talk we will survey some of the classical results about total
positivity. Additionally, we will present some recent work on totally
nonnegative real flag varieties.