In 1933 Lincoln Kirstein, co-founder and editor of Hound & Horn, wrote Tate, the Southern editor, that he "would like very much to know what all you people think could be done in relation to black and white." . . . Was the friction "inevitably racial, or accidentally economic?" Why were sexual relations between a white man and a black woman tolerated but not the reverse? Tate stated that there was "absolutely no 'solution' to the race problem in the South. That is, there is no solution that will remove the tension and the oppression that the negro must feel. . . . When two such radically different races live together, one must rule. I think the negro race is an inferior race." The key was social order, which served not social justice but "legal justice for the ruled race. . . . Liberal agitators" deprived "the negro of even the legal justice." Liberal policy was like "that of the Reconstruction, . . . a steady campaign against the Southern social system . . . to crush absolutely the remaining power of independent agriculture." As for the sexual question, "it is upon the sexual consent of women that the race depends for the future. . . . Under the industrial capitalist regime . . . women are no longer the very center of the social system. . . . What is to be done about all this I do not know; and I am inclined to think no one else knows."
Many systems are modellable using polynomials, and solving systems ofpolynomial equations is a fundamental task in their study. A staplemethod for polynomial system solving is homotopy continuation, whichconstructs an easy start system and deforms it to the difficult targetsystem whilst keeping track of the solutions along the way. To do thisoptimally requires an accurate estimate of the number of solutions,which is generally a very difficult task. Fortunately, polynomialsystems in many applications can be assumed to be generic instancesinside a bigger family of polynomial systems. We refer to their numberof solutions as the generic root count of the family.In this talk, we explain how the variation of polynomial systemswithin a family can be exploited tropically in order to encode theirgeneric root count in a tropical intersection number. We furtherdiscuss how this tropical intersection number can be computed, andhighlight the role of matroids in their computation. The maintheoretic result is a tropical generalisation of Bernstein's Theoremto families of properly intersecting schemes. Main applications arethe steady states of chemical reaction networks, as well as theDuffing and Kuramoto model for dampened and coupled oscillators,respectively. 781b155fdc