Results 61 to 70 of about 12,587 (151)
Schubert calculus and singularity theory
, 2011 Schubert calculus has been in the intersection of several fast developing areas of mathematics for a long time. Originally invented as the description of the cohomology of homogeneous spaces it has to be redesigned when applied to other generalized ...
Akyildiz +35 more
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Persistence Module and Schubert Calculus
Abstract 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 of a flag.
Hiraoka, Yasuaki +2 more
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Degree bounds in quantum Schubert calculus [PDF]
Proceedings of the American Mathematical Society, 2003 Fulton and Woodward have recently identified the smallest degree of $q$ that appears in the expansion of the product of two Schubert classes in the (small) quantum cohomology ring of a Grassmannian. We present a combinatorial proof of this result, and provide an alternative characterization of this smallest degree in terms of the rim hook formula for ...
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Schubert polynomials and Arakelov theory of symplectic flag varieties
, 2013 Let X be the flag variety of the symplectic group. We propose a theory of combinatorially explicit Schubert polynomials which represent the Schubert classes in the Borel presentation of the cohomology ring of X.
Tamvakis, Harry
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Affine Hecke algebras and the Schubert calculus
European Journal of Combinatorics, 2004 Using a combinatorial approach which avoids geometry, this paper studies the ring structure of K_T(G/B), the T-equivariant K-theory of the (generalized) flag variety G/B. Here the data is a complex reductive algebraic group (or symmetrizable Kac-Moody group) G, a Borel subgroup B, and a maximal torus T, and K_T(G/B) is the Grothendieck group of T ...
Stephen Griffeth, Arun Ram
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Schubert Calculus, Schubert Cell, Schubert Cycle, and Schubert Polynomials
, 2001 We briefly describe each of the four topics: Schubert Calculus, Schubert Cell, Schubert Cycle, and Schubert Polynomials.
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Advanced Studies in Pure Mathematics, 2018 These are notes for four lectures given at the Osaka summer school on Schubert calculus in 2012, presenting the geometry from the unpublished arXiv:1008.4302 giving an extension of the puzzle rule for Schubert calculus to equivariant $K$-theory, while eliding some of the combinatorial detail.
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Schubert puzzles and integrability I: invariant trilinear forms
, 2020 The puzzle rules for computing Schubert calculus on $d$-step flag manifolds, proven in [Knutson Tao 2003] for $1$-step, in [Buch Kresch Purbhoo Tamvakis 2016] for $2$-step, and conjectured in [Coskun Vakil 2009] for $3$-step, lead to vector ...
Knutson, Allen, Zinn-Justin, Paul
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On some invariants of cubic fourfolds. [PDF]
Eur J Math, 2023 Gounelas F, Kouvidakis A.
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Retained Ureteral Stent Encrustation After Stent Removal: A Case Report. [PDF]
Cureus, 2023 Johnson K +3 more
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