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Relative growth rate and contact Banach–Mazur distance
In this paper, we define non-linear versions of Banach–Mazur distance in the contact geometry set-up, called contact Banach–Mazur distances and...
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On Liu morphisms in non-Archimedean geometry
We define Liu morphisms and quasi-Liu morphisms between Berkovich analytic spaces. We show that Liu morphisms and quasi-Liu morphisms behave exactly...
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The tensor embedding for a Grothendieck cosmos
While the Yoneda embedding and its generalizations have been studied extensively in the literature, the so-called tensor embedding has only received...
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Soergel Calculus with Patches
We adapt the diagrammatic presentation of the Hecke category to the dg category formed by the standard representatives for the Rouquier complexes. We...
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Perverse Sheaves
Perverse sheaves are fundamental objects of study in topology, algebraic geometry, analysis and differential equations, with a plethora of...
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Perverse schobers and Orlov equivalences
A perverse schober is a categorification of a perverse sheaf proposed by Kapranov–Schechtman. In this paper, we construct examples of perverse...
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Equivariant Oka theory: survey of recent progress
We survey recent work, published since 2015, on equivariant Oka theory. The main results described in the survey are as follows. Homotopy principles...
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Framed and MW-transfers for homotopy modules
In the paper we use the theory of framed correspondences to construct Milnor–Witt transfers on homotopy modules. As a consequence we identify the...
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On BV supermanifolds and the super Atiyah class
We study global and local geometry of forms on odd symplectic BV supermanifolds, constructed from the total space of the bundle of 1-forms on a base...
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Differential equations and Lie group representations
We discuss the role of differential equations in Lie group representation theory. We use Kashiwara’s pentagon as a reference frame for the real...
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HOMFLY-PT HOMOLOGY OF COXETER LINKS
A Coxeter link is a closure of a product of two braids, one being a quasi-Coxeter element and the other being a product of partial full twists. This...
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A Stacky Approach to Crystals
Inspired by a theorem of Bhatt–Morrow–Scholze, we develop a stacky approach to crystals and isocrystals on “Frobenius-smooth” schemes over...
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A Note on Real Line Bundles with Connection and Real Smooth Deligne Cohomology
We define a Real version of smooth Deligne cohomology for manifolds with involution which interpolates between equivariant sheaf cohomology and...
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Introduction
In this chapter, we give background of Donaldson-Thomas theory, and motivations of considering categorical DT theory. The categorical DT theory is...
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Categorical DT Theory for Local Surfaces
In this chapter, for a quasi-smooth and QCA derived stack $$\mathfrak...
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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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A Topological View of Sheaf Cohomology
In Sect. 9.3 we introduced algebraic topology informally, as the way to associate to topological...