Results 11 to 20 of about 220,490 (165)
Numerical Schubert Calculus [PDF]
Journal of Symbolic Computation, 1997 We develop numerical homotopy algorithms for solving systems of polynomial equations arising from the classical Schubert calculus. These homotopies are optimal in that generically no paths diverge. For problems defined by hypersurface Schubert conditions
Sottile, F. +5 more
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Persistence module and Schubert calculus [PDF]
A multiplication on persistence diagrams is introduced by means of Schubert calculus. The key observation behind this multiplication comes from the fact that the representation space of persistence modules has the structure of the Schubert decomposition ...
Hiraoka, Yasuaki +2 more
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Schubert Calculus according to Schubert
, 2006 We try to understand and justify Schubert calculus the way Schubert did it.
Felice Ronga
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Arkiv för Matematik, 2010 We describe T -equivariant Schubert calculus on G(k, n), T being an n-dimensio- nal torus, through derivations on the exterior algebra of a free A-module of rank n, where A is the T-equivariant cohomology of a point.
SANTIAGO T. +2 more
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Crystal approach to affine Schubert calculus [PDF]
International Mathematics Research Notices, 2014 We apply crystal theory to affine Schubert calculus, Gromov-Witten invariants for the complete flag manifold, and the positroid stratification of the positive Grassmannian.
Jennifer Morse +3 more
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Numerical Schubert Calculus by the Pieri Homotopy Algorithm [PDF]
SIAM Journal on Numerical Analysis, 2010 Based on Pieri's formula on Schubert varieties, the Pieri homotopy algorithm was first proposed by Huber, Sottile, and Sturmfels [J. Symbolic Comput., 26 (1998), pp.
Li, Tien-yien; Wang, Xiaoshen; 吳孟年; Wu, Meng-nien
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Probabilistic Schubert Calculus: Asymptotics [PDF]
Arnold Mathematical Journal, 2020 AbstractIn the recent paper Bürgisser and Lerario (Journal für die reine und angewandte Mathematik (Crelles J), 2016) introduced a geometric framework for a probabilistic study of real Schubert Problems. They denoted by $$\delta _{k,n}$$ δ k ,
Lerario, Antonio, Mathis, Léo
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Soergel Calculus and Schubert Calculus [PDF]
Bulletin of the Institute of Mathematics Academia Sinica NEW SERIES, 2018 We reduce some key calculations of compositions of morphisms between Soergel bimodules ("Soergel calculus") to calculations in the nil Hecke ring ("Schubert calculus"). This formula has several applications in modular representation theory.
He, X., Williamson, G.
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Probabilistic Schubert calculus [PDF]
Journal für die reine und angewandte Mathematik (Crelles Journal), 2018 Abstract We initiate the study of average intersection theory in real Grassmannians. We define the expected degree edeg
Bürgisser, Peter, Lerario, Antonio
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Generalized Permutahedra and Schubert Calculus
Arnold Mathematical Journal, 2022 We connect generalized permutahedra with Schubert calculus. Thereby, we give sufficient vanishing criteria for Schubert intersection numbers of the flag variety. Our argument utilizes recent developments in the study of Schubitopes, which are Newton polytopes of Schubert polynomials. The resulting tableau test executes in polynomial time.
Avery St. Dizier, Alexander Yong
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