相关论文: Applications of Kawamata's positivity theorem
Contribution to Light Cone 2019: This contribution discusses some of the advantages and unique properties of relativistic quantum theories with kinematic light-front symmetries.
A review of Heavy Quark Effective Theory and Non Relativistic Quantum Chromondynamics is given. Some applications are discussed.
This review article deals with some case studies of relativistic and correlation effects in atomic systems. After a brief introduction to relativistic many-electron theory, a number of applications ranging from correlation energy to parity…
In this article we use our constructions from "Enlargements of Categories" (Theory and Applications of Categories, 14:357-398) to lay down some foundations for the application of A. Robinson's nonstandard methods to modern Algebraic…
A simple mathematical extension of quantum theory is presented. As well as opening the possibility of alternative methods of calculation, the additional formalism implies a new physical interpretation of the standard theory by providing a…
A smooth scheme X over a field k of positive characteristic is said to be strongly liftable, if X and all prime divisors on X can be lifted simultaneously over W_2(k). In this paper, we give some concrete examples and properties of strongly…
Newton's identities provide a way to express elementary symmetric polynomials in terms of power polynomials over fields of characteristic zero. In this article, we study the failure of this relation in positive characteristic and what can…
Using the combinatorics of $\alpha$-unimodal sets, we establish two new results in the theory of quasisymmetric functions. First, we obtain the expansion of the fundamental basis into quasisymmetric power sums. Secondly, we prove that…
We derive new positivity bounds for scattering amplitudes in theories with a massless graviton in the spectrum in four spacetime dimensions, of relevance for the weak gravity conjecture and modified gravity theories. The bounds imply that…
The aim of this paper is to show further results following those published in [5], and to relate the Riemann zeta function to the relativistic cosmology.
The aim of this article is to promote the use of probabilistic methods in the study of problems in mathematical general relativity. Two new and simple singularity theorems, whose features are different from the classical singularity…
We investigate positivity properties in quantum field theory (QFT). We provide evidence,and in some case proofs, that many building blocks of scattering amplitudes, and in some cases the full amplitudes, satisfy an infinite number of…
Symmetry plays a central role in quantum field theory. Recent developments include symmetries that act on defects and other subsystems, and symmetries that are categorical rather than group-like. These generalized notions of symmetry allow…
We prove a compactness theorem for metrics with Bounded Integral Curvature on a fixed closed surface $\Sigma$. As a corollary, we obtain a compactification of the space of Riemannian metrics with conical singularities, where an accumulation…
We review the classical and quantum singularity structure of a broad class of spacetimes with asymptotically power-law behavior near the origin. Quantum considerations "heal" a large class of scalar curvature singularities.
We study properties related to nice enumerability of countably categorical structures and properties related to extreme amenability of automorphism groups of these structures. The text substantially differs from the previous version. In…
We use double categories to obtain a single theorem characterizing certain exponentiable morphisms of small categories, topological spaces, locales, and posets.
In previous work, we have introduced delta-forms on the Berkovich analytification of an algebraic variety in order to study smooth or formal metrics via their associated Chern delta-forms. In this paper, we investigate positivity properties…
We study the weighted spectrum and vanishing cohomology for several classes of isolated hypersurface singularities, and how they contribute to the limiting mixed Hodge structure of a smoothing. Applications are given to several types of…
Let $E$ be a holomorphic vector bundle endowed with a singular Hermitian metric $H$. In this paper, we develop the harmonic theory on $(E,H)$. Then we extend several canonical results of J. Koll\'{a}r and K. Takegoshi to this situation. In…