Diagonally symmetric polynomials and applications

The logo

The logo presents three objects related to diagonally symmetric polynomials.

The drawing at the top right corner shows a cubic curve cut by a straight line at three points, and the tangents to the curve at these three points. This illustrates Gordan's geometric explanations (1894) of the construction of Brill's covariant, whose vanishing characterizes the curves that degenerate into union of lines.

The table at the center of the logo presents the simplest non-trivial of the 52 tables (written on 53 pages) of conversion between linear bases of diagonally symmetric polynomial computed by Junker in 1896.

The picture at the down left corner illustrates the "compactification moves" used to expand a monomial function in the basis of "compact diagrams" (Bergeron and Lamontagne, 2004).