Related papers: Bounded G-theory with fibred control
It is well known that numerical quantities arising from the theory of D-modules are related to invariants of singularities in birational geometry. This paper surveys a deeper relationship between the two areas, where the numerical…
We realize higher-form symmetries in F-theory compactifications on non-compact elliptically fibered Calabi-Yau manifolds. Central to this endeavour is the topology of the boundary of the non-compact elliptic fibration, as well as the…
In this paper we consider non-abelian 1-cohomology for groups with coefficients in other groups. We prove versions of the `five lemma' arising from this situation. We go on to show that a connected unipotent algebraic group Q acted on…
While non-abelian groups are undoubtedly the cornerstone of Grand Unified Theories (GUTs), phenomenology shows that the role of abelian and discrete symmetries is equally important in model building. The latter are the appropriate tool to…
A new notion of controllability, eigenstate controllability, is defined for finite-dimensional bilinear quantum mechanical systems which are neither strongly completely controllably nor completely controllable. And a quantum control…
We consider the algebraic K-theory of a truncated polynomial algebra in several commuting variables, K(k[x_1, ..., x_n]/(x_1^a_1, ..., x_n^a_n)). This naturally leads to a new generalization of the big Witt vectors. If k is a perfect field…
The standard techniques of variational calculus are geometrically stated in the ambient of fiber bundles endowed with a (pre)multisymplectic structure. Then, for the corresponding variational equations, conserved quantities (or, what is…
We prove a version of Quillen's stratification theorem in equivariant homotopy theory for a finite group $G$, generalizing the classical theorem in two directions. Firstly, we work with arbitrary commutative equivariant ring spectra as…
We develop vertex and factorisation algebra analogues of the theory of quasitriangular bialgebras. Analogously to the classical theory, we prove their categories of representations are controlled by spectral R-matrices. In the vertex…
We introduce bivariant K-theory for nonarchimedean bornological algebras over a complete discrete valuation ring $V$. This is the universal target for dagger homotopy invariant, matricially stable and excisive functors, similar to bivariant…
We use a Heegaard splitting of the topological 3-sphere as a guiding principle to construct a family of its noncommutative deformations. The main technical point is an identification of the universal C*-algebras defining our quantum…
In this paper, we introduce a variation of the notion of topological phase reflecting metric structure of the position space. This framework contains not only periodic and non-periodic systems with symmetries in Kitaev's periodic table but…
A duality is discussed for Lie group bundles vs. certain tensor categories with non-simple identity, in the setting of Nistor-Troitsky gauge-equivariant K-theory. As an application, we study C*-algebra bundles with fibre a fixed-point…
In the example of complex grassmannians, we demonstrate various techniques available for computing genus-0 K-theoretic GW-invariants of flag manifolds and more general quiver varieties. In particular, we address explicit reconstruction of…
A central question in equivariant algebraic K-theory asks whether there exists an equivariant K-theory machine from genuine symmetric monoidal G-categories to orthogonal G-spectra that preserves equivariant algebraic structures. We answer…
The geometry of elliptic fibrations translates to the physics of gauge theories in F-theory. We systematically develop the dictionary between arithmetic structures on elliptic curves as well as desingularized elliptic fibrations and…
We explore the structure of $\text{Fil}$, the category of filters and germs of admissible partial functions. In particular, we show that $\text{Fil}$ is a nonsymmetric closed category, as defined elsewhere by this and other authors.
Quantum control is traditionally expressed through bilinear models and their associated Lie algebra controllability criteria. But, the first order approximation are not always sufficient and higher order developpements are used in recent…
The coprimary filtration is a basic construction in commutative algebra. In this article, we prove the existence and uniqueness of coprimary filtration of modules (not necessarily finitely generated) over a Noetherian ring. Moreover, we…
Directed Algebraic Topology is beginning to emerge from various applications. The basic structure we shall use for such a theory, a 'd-space', is a topological space equipped with a family of 'directed paths', closed under some operations.…