Related papers: Applications of Kawamata's positivity theorem

We prove Tamura's theorem on partitions of the set of positive integers (a generalization of the more famous Rayleigh-Beatty theorem) using the positive $\mathbb{S}^1$-equivariant symplectic homology.

We derive extensions of the monomialization theorems for morphisms of varieties in our earlier work. In this note we show that a local monomialization can be found which satisfies stronger local conditions. Some comments are made about how…

We introduce a notion of singular hermitian metrics (s.h.m.) for holomorphic vector bundles and define positivity in view of $L^2$-estimates. Associated with a suitably positive s.h.m. there is a (coherent) sheaf 0-th kernel of a certain…

The PCT theorem is shown to be valid in quantum field theory formulated on noncommutative spacetime by exploiting the properties of the Wightman functions defined in such a set up.

This is a survey article on $F$-singularities and their applications.

Within the context of piecewise linear manifolds we establish reflection positivity with a Hilbert action given in terms of the Regge curvature and a cosmological term. Using this positivity a Hilbert space for a quantum theory is…

We derive norm bounds that imply the convergence of perturbation theory in fermionic quantum field theory if the propagator is summable and has a finite Gram constant. These bounds are sufficient for an application in renormalization group…

We first prove a Cauchy's integral theorem and Cauchy type formula for certain inhomogeneous Cimmino system from quaternionic analysis perspective. The second part of the paper directs the attention towards some applications of the…

We prove a positivity result in (T-)equivariant quantum cohomology of the homogeneous space G/P, generalizing Graham's positivity in equivariant cohomology.

I shall discuss some "conditions of possibility" of a quantum theory of gravity, stressing the need for solutions to some of fundamental problems confronting any attempt to apply some method of quantization to the field equations of general…

In this work, we elaborate on a measure-theoretic approach to negative probabilities. We study a natural notion of contextuality measure and characterize its main properties. Then, we apply this measure to relevant examples of quantum…

Some aspects and applications of $ \sigma$-models in particle and condensed matter physics are briefly reviewed.

Let $G$ be a subgroup of a discrete (countable) group $\Gamma$. We introduce a notion of relative inner amenability of $G$ in $\Gamma$, we prove some equivalent conditions and provide examples as well as counter-examples. We also discuss…

The concept of convex compactness, weaker than the classical notion of compactness, is introduced and discussed. It is shown that a large class of convex subsets of topological vector spaces shares this property and that is can be used in…

In this work an observation concerning a positivity property of the quantum anharmonic oscillator is made. This positivity property is suggested by the BMV conjecture.

We generalise the Caristi Fixed Point Theorem to the mappings of the complete semi-metric spaces.

Contrary to recent claims in the literature, a simple test for reflection positivite, which we call perturbative reflection positivity in the coincidence limit, is shown to be satisfied for nonlocal field theories. Particular attention is…

The paper studies differentially positive systems, that is, systems whose linearization along an arbitrary trajectory is positive. We illustrate the use of differential positivity on compact forward invariant sets for the characterization…

Via elementary examples it is demonstrated that the singularities of classical physics (sampled by the Big Bang in cosmology) need not necessarily get smeared out after quantization. It is proposed that the role of quantum singularities can…

We survey some recent topics on singularities, with a focus on their connection to the minimal model program. This includes the construction and properties of dual complexes, the proof of the ACC conjecture for log canonical thresholds and…