Rational functions and real Schubert calculus

By Alexandre Eremenko, Andrei Gabrielov, Michael Shapiro, A. Vainshtein. 2004

50 citations recorded by the source corpus.

We single out some problems of Schubert calculus of subspaces of codimension 2 that have the property that all their solutions are real whenever the data are real. Our arguments explore the connection between subspaces of codimension 2 and rational functions of one variable.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/3e90463ca312d0089050efe768813cbd2e4f0cc8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. V. Tarasov
2. A. Varchenko
3. Alexandre Eremenko
4. Andrei Gabrielov
5. E. Mukhin
6. Bin Xu
7. Valerio Toledano Laredo
8. P. Boalch

In Computational Theory and Mathematics

1. V. Tarasov
2. Andrei Gabrielov

In Discrete Mathematics and Combinatorics

1. V. Tarasov
2. E. Mukhin
3. A. Varchenko
4. Alexandre Eremenko
5. Andrei Gabrielov

Citations in the corpus

• Conformal metrics with constant curvature one and finitely many conical singularities on compact Riemann surfaces (2013, background): “[Eremenko and Gabrielov 2002; Eremenko et al. 2006] proved that there exists a real rational function in each equivalence class if each point in the support of D is real.”
• The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz (2005, methodology): “The conjecture, its supporting evidence, and applications are discussed in [EG1]–[EG3], [ EGSV ], [ESS], [KS], [RSSS], [S1]–[S6].”
• Metrics with conic singularities and spherical polygons (2014, methodology): “We recall that equivalence classes of real rational functions with real critical points are counted by chord diagrams [5], [6], [8].”