Results 1 to 10 of about 6,601 (98)
Pieri rule for the affine flag variety [PDF]
, 2015 We prove the affine Pieri rule for the cohomology of the affine flag variety conjectured by Lam, Lapointe, Morse and Shimozono. We study the cap operator on the affine nilHecke ring that is motivated by Kostant and Kumar's work on the equivariant ...
Lee, Seung Jin
core +5 more sources
Double transitivity of Galois Groups in Schubert Calculus of Grassmannians [PDF]
, 2014 We investigate double transitivity of Galois groups in the classical Schubert calculus on Grassmannians. We show that all Schubert problems on Grassmannians of 2- and 3-planes have doubly transitive Galois groups, as do all Schubert problems involving ...
Sottile, Frank, White, Jacob
core
$k$-Schur functions and affine Schubert calculus
, 2013 This book is an exposition of the current state of research of affine Schubert calculus and $k$-Schur functions. This text is based on a series of lectures given at a workshop titled "Affine Schubert Calculus" that took place in July 2010 at the Fields ...
Lam, Thomas +5 more
core +1 more source
A primal-dual formulation for certifiable computations in Schubert calculus [PDF]
, 2015 Formulating a Schubert problem as the solutions to a system of equations in either Pl\"ucker space or in the local coordinates of a Schubert cell typically involves more equations than variables. We present a novel primal-dual formulation of any Schubert
Hauenstein, Jonathan D. +2 more
core
Permutation actions on equivariant cohomology [PDF]
, 2007 This survey paper describes two geometric representations of the permutation group using the tools of toric topology. These actions are extremely useful for computational problems in Schubert calculus.
Tymoczko, Julianna S.
core
On the works of Euler and his followers on spherical geometry [PDF]
, 2014 We review and comment on some works of Euler and his followers on spherical geometry. We start by presenting some memoirs of Euler on spherical trigonometry. We comment on Euler's use of the methods of the calculus of variations in spherical trigonometry.
Papadopoulos, Athanase
core
Quantum state transformations and the Schubert calculus
, 2004 Recent developments in mathematics have provided powerful tools for comparing the eigenvalues of matrices related to each other via a moment map. In this paper we survey some of the more concrete aspects of the approach with a particular focus on ...
Bennett +28 more
core +2 more sources
An update of quantum cohomology of homogeneous varieties [PDF]
, 2014 We describe recent progress on QH(G/P) with special emphasis of our own work.Comment: 18 pages.
Changzheng Li, Leung, Naichung Conan
core
Lucretia - intersection type polymorphism for scripting languages
, 2015 Scripting code may present maintenance problems in the long run. There is, then, the call for methodologies that make it possible to control the properties of programs written in dynamic languages in an automatic fashion.
Benke, Marcin +2 more
core +2 more sources
Maximally inflected real rational curves [PDF]
, 2003 We introduce and begin the topological study of real rational plane curves, all of whose inflection points are real. The existence of such curves is a corollary of results in the real Schubert calculus, and their study has consequences for the important ...
Kharlamov, Viatcheslav, Sottile, Frank
core +4 more sources