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Among several ideas which arose as consequences of modular localization there are two proposals which promise to be important for the classification and construction of QFTs. One is based on the observation that wedge-localized algebras may…
We compute the transgressed forms of some modularly invariant characteristic forms,which are related to the twisted elliptic genera. We study the modularity properties of these secondary characteristic forms and relations among them. We…
In this paper, we define the notion of a mapping on soft classes and study several properties of images and inverse images of soft sets supported by examples and counterexamples. Finally, these notions have been applied to the problem of…
Many-body localization (MBL) is understood theoretically through the existence of an extensive number of local integrals of motion (LIOMs). These conserved quantities are related to the microscopic quantum degrees of freedom that are…
Isotropic Quot schemes parameterize rank $r$ isotropic subsheaves of a vector bundle equipped with symplectic or symmetric quadratic form. We define a virtual fundamental class for isotropic Quot schemes over smooth projective curves. Using…
Let M be a manifold carrying the action of a Lie group G, and A a Lie algebroid on M equipped with a compatible infinitesimal G-action. Out of these data we construct an equivariant Lie algebroid cohomology and prove for compact G a related…
In this paper, we focus on the variable selection techniques for a class of semiparametric spatial regression models which allow one to study the effects of explanatory variables in the presence of the spatial information. The spatial…
Localization principle is a powerful analytic tool in supersymmetric gauge theories which enables one to perform supersymmetric path integrals explicitly. Many important formulae have been obtained, and they led to a major breakthrough in…
We derive a canonical form for skew-symmetric endomorphisms $F$ in Lorentzian vector spaces of dimension three and four which covers all non-trivial cases at once. We analyze its invariance group, as well as the connection of this canonical…
In this paper, we will demonstrate how Manhattan structure can be exploited to transform the Simultaneous Localization and Mapping (SLAM) problem, which is typically solved by a nonlinear optimization over feature positions, into a model…
In this part of the series, we shall investigate Deligne-Mumford semistable reductions from the point of view of numerical invariants. As an application, we obtain two numerical criterions for a base change to be stabilizing, and for a…
Pairs $\aa \subset \bb$ of local quantum field theories are studied, where $\aa$ is a chiral conformal \qft and $\bb$ is a local extension, either chiral or two-dimensional. The local correlation functions of fields from $\bb$ have an…
For random quantum spin models, the strong disorder perturbative expansion of the Local Integrals of Motion (LIOMs) around the real-spin operators is revisited. The emphasis is on the links with other properties of the Many-Body-Localized…
Given a compatible vector field on a compact connected almost-complex manifold, we show in this article that the multiplicities of eigenvalues among the zero point set of this vector field have intimate relations. We highlight a special…
We study large partial sums, localized with respect to the sums of variances, of a sequence of centered random variables. An application is given to the distribution of prime factors of typical integers.
We put forward an interpretation of scalar quantum field theory as relativistic quantum mechanics by curing well known problems related to locality. A probabilistic interpretation of quantum field theory similar to quantum mechanics is…
Let Y be a divisor on a smooth algebraic variety X. We investigate the geometry of the Jacobian scheme of Y, homological invariants derived from logarithmic differential forms along Y, and their relationship with the property that Y is a…
There has been a recent interest in imitation learning methods that are guaranteed to produce a stabilizing control law with respect to a known system. Work in this area has generally considered linear systems and controllers, for which…
We construct rigid supersymmetric theories for interacting vector and tensor multiplets on six-dimensional Riemannian spin manifolds. Analyzing the Killing spinor equations, we derive the constraints on these theories. To this end, we…
The fixed point set under a natural torus action on projectivized moduli spaces of simple representations of quivers is described. As an application, the Euler characteristic of these moduli is computed.