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The Notion of Space in Grothendieck
In this essay we give a general picture about the evolution of Grothendieck’s ideas regarding the notion of space. Starting with his fundamental work...
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When is a Locally Convex Space Eberlein–Grothendieck?
The weak topology of a locally convex space (lcs) E is denoted by w . In this paper we undertake a systematic study of those lcs E such that ( E , w ) is...
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Weak and almost Grothendieck operators in Banach lattices
In this paper, we introduce and study a weak version of Grothendieck operators that we will call weak Grothendieck operators, these are operators...
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Tilted biorthogonal ensembles, Grothendieck random partitions, and determinantal tests
We study probability measures on partitions based on symmetric Grothendieck polynomials. These deformations of Schur polynomials introduced in the...
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Grothendieck Ring of Pairs of Quasi-Projective Varieties
AbstractWe define a Grothendieck ring of pairs of complex quasi-projective varieties (consisting of a variety and a subvariety). We describe
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Weighted Tutte–Grothendieck Polynomials of Graphs
In this paper, we introduce the notion of weighted chromatic polynomials of a graph associated to a weight function f of a certain degree, and...
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Additive Grothendieck Pretopologies and Presentations of Tensor Categories
We study how tensor categories can be presented in terms of rigid monoidal categories and Grothendieck topologies and show that such presentations...
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Equivariant Grothendieck ring of a complete symmetric variety of minimal rank
We describe the G -equivariant Grothendieck ring of a regular compactification X of an adjoint symmetric space G / H of minimal rank. This extends the...
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Grothendieck Enriched Categories
In this paper, we introduce the notion of Grothendieck enriched categories for categories enriched over a sufficiently nice Grothendieck monoidal...
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Free-fermions and skew stable Grothendieck polynomials
We present a free-fermionic presentation of the skew (dual) stable Grothendieck polynomials. A direct proof of their determinantal formulas is given...
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The Grothendieck property from an ordered point of view
In this note, we consider several notions related to the Grothendieck property. Among them, we introduce the notion of the unbounded Grothendieck...
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Grothendieck spaces: the landscape and perspectives
In 1973, Diestel published his seminal paper Grothendieck spaces and vector measures that drew a connection between Grothendieck spaces (Banach...
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Mathematical Practice as Philosophy, with Galois, Riemann, and Grothendieck
The primary aim of this chapter is to consider mathematicians’ working philosophy of mathematics as emerging in and defining actual mathematical...
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Mathematical Practice as Philosophy, with Galois, Riemann, and Grothendieck
The primary aim of this chapter is to consider mathematicians’ working philosophy of mathematics as emerging in and defining actual mathematical...
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“That Which a Minority Construct”: Abelian Mathematics in Abel, Galois, Noether, and Grothendieck
This chapter considers the nature of radical transformations of mathematics, enabled by minority mathematics. It will be particularly concerned with...
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Toroidal Grothendieck rings and cluster algebras
We study deformations of cluster algebras with several quantum parameters, called toroidal cluster algebras, which naturally appear in the study of...
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“That Which a Minority Construct”: Abelian Mathematics in Abel, Galois, Noether, and Grothendieck
This chapter considers the nature of radical transformations of mathematics, enabled by minority mathematics. It will be particularly concerned with...