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The derived Brauer map via twisted sheaves
Let X be a quasicompact quasiseparated scheme. The collection of derived Azumaya algebras in the sense of Toën forms a group, which contains the...
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Quantum parameters of the geometric Langlands theory
Fix a smooth, complete algebraic curve X over an algebraically closed field k of characteristic zero. To a reductive group G over k , we associate an...
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Diffeological principal bundles and principal infinity bundles
In this paper, we study diffeological spaces as certain kinds of discrete simplicial presheaves on the site of cartesian spaces with the coverage of...
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Descent of dg cohesive modules for open covers on complex manifolds
We study the descent problem of cohesive modules on complex manifolds. For a complex manifold X we can consider the Dolbeault dg-algebra
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Weighted limits in an \((\infty ,1)\)-category
We introduce the notion of weighted limit in an arbitrary quasi-category, suitably generalizing ordinary limits in a quasi-category, and classical...
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Bifurcations of Orbits Homoclinic and Heteroclinic to Hyperbolic Equilibria
In this chapter, we will study global bifurcations corresponding to the appearance of homoclinic or heteroclinic orbits connecting hyperbolic...
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Twisted smooth Deligne cohomology
Deligne cohomology can be viewed as a differential refinement of integral cohomology, hence captures both topological and geometric information. On...
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A Note on a Local Combinatorial Formula for the Euler Class of a PL Spherical Fiber Bundle
We present a local combinatorial formula for the Euler class of an n-dimensional PL spherical fiber bundle as a rational number eCH associated to a...
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Maurer–Cartan Moduli and Theorems of Riemann–Hilbert Type
We study Maurer–Cartan moduli spaces of dg algebras and associated dg categories and show that, while not quasi-isomorphism invariants, they are...
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A topological origin of quantum symmetric pairs
It is well known that braided monoidal categories are the categorical algebras of the little two-dimensional disks operad. We introduce involutive...
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Coxeter Groups, Artin Groups, Buildings
The basic notion in this chapter is a Coxeter system...
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Other Cohomologies
The chapter begins by comparing the \(\mathsf {D}\)...
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Weak cartesian properties of simplicial sets
Many special classes of simplicial sets, such as the nerves of categories or groupoids, the 2-Segal sets of Dyckerhoff and Kapranov, and the...
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Topological Equivalence, Bifurcations, and Structural Stability of Dynamical Systems
In this chapter, we introduce and discuss the following fundamental notions that will be used throughout the book: topological equivalence of...
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