Flag varieties and schubert calculus

Author: dllc

August undefined, 2024

WebAug 1, 2015 · In the context of Schubert calculus we present the integral cohomology $H^{\ast }(G/T)$by a minimal system of generators and relations. MSC classification … WebIn particular, I am interested in flag varieties and related configuration spaces, cluster algebras and toric varieties. On the combinatorial side side, I use ideas from Schubert calculus, matroids, lattice point enumeration and Coxeter groups.

Lectures on the Geometry of Flag Varieties SpringerLink

WebIn particular, I am interested in equivariant K-theory, cohomology, and Chow groups, as well as problems related to flag varieties, Schubert calculus, and some related combinatorics. A complete list of my published research papers and preprints, as well as a more detailed description of my research interests, is available on my research page . WebIn mathematics, a generalized flag variety (or simply flag variety) is a homogeneous space whose points are flags in a finite-dimensional vector space V over a field F.When F is … order lanyards australia

David Speyer U-M LSA Mathematics - University of Michigan

WebFor example, Schubert calculus and Kazhdan-Lusztig theory both obtain information about the representation theory of Hecke algebras and their specializations by studying the geometry of the flag variety. Basically, Schubert calculus is the study of the ordinary cohomology of the Schubert varieties on a flag variety, while Kazhdan-Lusztig theory ... WebWe present a partial generalization to Schubert calculus on flag varieties of the classical Littlewood-Richardson rule, in its version based on Schuetzenberger's jeu de taquin. … WebWe establish an equivariant quantum Giambelli formula for partial flag varieties. The answer is given in terms of a specialization of universal double Schubert polynomials. Along the way, we give new proofs of the pres… ireland citizen information

William Graham - UGA

Schubert calculus is a formal calculus in enumerative geometry, which geometrically reduces to the combinatorics and intersection theory of so-called Schubert cells in Grassmannians. Schubert calculus is concerned with the ring structure on the cohomology of flag varieties and Schubert varieties. … See more WebSchubert Varieties A Schubert variety is a member of a family of projective varieties which is deﬁned as the closure of some orbit under a group action in a … ireland citizenship through great grandparentWebIn this thesis, we explore various lattice models using this perspective as guidance. We first describe how both the torus fixed point basis and the basis of Schubert classes in the equivariant cohomology of the flag variety are manifest in the "Frozen Pipes" lattice model of Brubaker, Frechette, Hardt, Tibor, and Weber. ireland city breaks 2022

"WebThere will be an initial focus on Schubert calculus of Grassmannians and full flag varieties; this is the study of the ring structure of the cohomology ring of these varieties. There is then a possibility of extending this study to the equivariant/quantum Schubert calculus, or moving in a different direction and investigating Springer theory ... " - Flag varieties and schubert calculus

Flag varieties and schubert calculus

Schubert Varieties and Schubert Calculus - Brown …

WebJan 19, 2015 · There are quantum, noncommutative and infinite-dimensional generalizations. Flag varieties have rich combinatorial and geometric structure and play an important role in representation theory and integrable systems. Related concepts. Grassmannian. coset space. coadjoint orbit. building. Schubert variety. Schubert calculus WebSchubert calculus as a method for counting intersections of subspaces, an im-portant problem historically in enumerative geometry. After introducing basic objects of study such as Schubert cells and Schubert varieties in the Grass-mannian - and showing how intersections of these varieties can express the

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WebFeb 26, 2024 · Section 14.7. Schubert Calculus. Example 14.7.7. This is a standard example to use the Schubert calculus to deal with some simple algebraic geometry problems and we write this as a model. Note that the first step is to deduce the relations of Schubert relations as Example 14.7.2. In mathematics, Schubert calculus is a branch of algebraic geometry introduced in the nineteenth century by Hermann Schubert, in order to solve various counting problems of projective geometry (part of enumerative geometry). It was a precursor of several more modern theories, for example characteristic classes, and in particular its algorithmic aspects are still of current interest. The phrase "Schubert calculus" is sometimes used to mean the enumerative geometry of linear sub…

WebMy research centers on geometry of flag varieties, with focus on Quantum (K) Schubert Calculus (i.e. the study of quantum cohomology, and quantum K theory), and the … WebJan 22, 2024 · Variation 2 (Sect. 5) repeats this story for the complete flag variety (in place of the Grassmannian), with the role of Schur functions replaced by the Schubert polynomials. Finally, Variation 3 (Sect. 6) explores Schubert calculus in the “Lie type B” Grassmannian, known as the orthogonal Grassmannian.

WebPart 1. Equivariant Schubert calculus 2 1. Flag and Schubert varieties 2 1.1. Atlases on ﬂag manifolds 3 1.2. The Bruhat decomposition of Gr(k; Cn) 4 1.3. First examples of Schubert calculus 6 1.4. The Bruhat decomposition of ﬂag manifolds 7 1.5. Poincare polynomials of ﬂag manifolds 8´ 1.6. Self-duality of the Schubert basis 9 1.7. WebMar 30, 2012 · The Schubert calculus or Schubert enumerative calculus is a formal calculus of symbols representing geometric conditions used to solve problems in enumerative …

WebIn the area of algebraic geometry, the book gives a detailed account of the Grassmannian varieties, flag varieties, and their Schubert subvarieties. Many of the geometric results …

WebThese varieties include the flag variety and related objects such as Schubert varieties, nilpotent orbits and Springer fibres. Here I have worked on problems such as positivity in … order large photo printWebJun 13, 2024 · There is a new direction in Schubert calculus, which links the Yang-Baxter equation, the central equation in quantum integrable systems, to problems in representation theory that have their origin in … order lat flow govWebcomplex projective space and may be canonically expressed as toric varieties. We discuss their cell structure by analogy with the classical Schubert decompo-sition, and detail the implications for Poincar´e duality with respect to double cobordism theory; these lead directly to our main results for the Landweber– Novikov algebra. order laminate countertopsWeb1.1 Flag varieties and Schubert polynomials The ﬂag variety Fl n is the smooth projective algebraic variety classifying full ﬂags inside an n-dimensional complex vector space Cn. The cohomology ring H∗(Fl n) was determined by Borel [Bor53]: it is the quotient of the polynomial ring Q[x1,...,x n] by the ideal generated by symmetric ... order laser business checksWebW. Graham: Positivity in equivariant Schubert calculus, Duke Math. J. 109 (2001), 599–614. CrossRef Google Scholar ... S. Ramanan and A. Ramanathan: Projective normality of flag varieties and Schubert varieties, Invent. Math. 79 (1985), 217–224. CrossRef Google Scholar ireland citizenship through investmentWebDISSERTATION GRASSMANN, FLAG, and SCHUBERT VARIETIES in APPLICATIONS. Submitted by Timothy P. Marrinan Department of Mathematics; On Schubert Varieties in the Flag Manifold of Sl(N, •) K-Orbits on the Flag Variety and Strongly Regular Nilpotent Matrices; Domains of Discontinuity in Oriented Flag Manifolds Arxiv:1806.04459V1 … order lasix without prescription dr. smithWebBook excerpt: This text grew out of an advanced course taught by the author at the Fourier Institute (Grenoble, France). It serves as an introduction to the combinatorics of symmetric functions, more precisely to Schur and Schubert polynomials. Also studied is the geometry of Grassmannians, flag varieties, and especially, their Schubert varieties. order lat flow test online