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Complete intersections in spherical varieties
Let G be a complex reductive algebraic group. We study complete intersections in a spherical homogeneous space G / H defined by a generic collection...
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The Geometry of Gaussoids
A gaussoid is a combinatorial structure that encodes independence in probability and statistics, just like matroids encode independence in linear...
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Fitness, Apprenticeship, and Polynomials
This article discusses the design of the Apprenticeship Program at the Fields Institute, held 21 August–3 September 2016. Six themes from...
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CONVEXITY AND THIMM’S TRICK
In this paper we study topological properties of maps constructed by Thimm's trick with Guillemin and Sternberg's action coordinates on a connected...
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Computing Toric Degenerations of Flag Varieties
We compute toric degenerations arising from the tropicalization of the full flag varieties...
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Convex bodies and multiplicities of ideals
We associate convex regions in ℝ n to m-primary graded sequences of subspaces, in particular m-primary graded sequences of ideals, in a large class...
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Related Topics
In this chapter, we give a brief account of some of the topics that are related to flag and Grassmannian varieties.
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Minuscule Schubert Varieties: Poset Polytopes, PBW-Degenerated Demazure Modules, and Kogan Faces
We study a family of posets and the associated chain and order polytopes. We identify the order polytope as a maximal Kogan face in a Gelfand-Tsetlin...
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Surface defects and instanton partition functions
We study the superconformal index of five-dimensional SCFTs and the sphere partition function of four-dimensional gauge theories with eight...
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ON THE GEOMETRY OF SPHERICAL VARIETIES
This is a survey article on the geometry of spherical varieties.
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On the Expected Number of Zeros of Nonlinear Equations
This paper investigates the expected number of complex roots of nonlinear equations. Those equations are assumed to be analytic, and to belong to...
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Completions of convex families of convex bodies
The paper discusses the existence of a continuous extension of functions that are defined on subsets of ℝ n and whose values are convex bodies in ℝ ...
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Algebraic Equations and Convex Bodies
The well-known Bernstein–Kushnirenko theorem from the theory of Newton polyhedra relates algebraic geometry and the theory of mixed volumes....
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Intersection theory and Hilbert function
Birationally invariant intersection theory is a far-reaching generalization and extension of the Bernstein-Kushnirenko theorem. This paper presents...
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Moment polytopes, semigroup of representations and Kazarnovskii’s theorem
Two representations of a reductive group G are spectrally equivalent if the same irreducible representations appear in both of them. The semigroup of...