24 citations · 30 across the 8 of their papers we have counts for
4 papers · 1 filter
Classifying real polynomial pencils
Julius Borcea, Boris Shapiro
Let $\bP^n$ be the space of all homogeneous polynomials of degree in two variables with real coefficients. The standard discriminant $\D_{n+1}\subset \bP^n$ is Whitney stratifi…
Counting real rational functions with all real critical values
B. Shapiro, A. Vainshtein
We study the number of real rational degree n functions (considered up to linear fractional transformations of the independent variable) with a given set of 2n-2 distinct real crit…
Simply-laced Coxeter groups and groups generated by symplectic transvections
Boris Shapiro, Michael Shapiro, Alek Vainshtein +1
Let W be an arbitrary Coxeter group of simply-laced type (possibly infinite but of finite rank), u,v be any two elements in W, and i be a reduced word (of length m) for the pair (u…
Algebras of curvature forms on homogeneous manifolds
Alexander Postnikov, Boris Shapiro, Mikhail Shapiro
Let C(X) be the algebra generated by the curvature 2-forms of the standard hermitian line bundles over the complex homogeneous manifold X=G/B. We calculate the Hilbert polynomial o…