Related papers: An abundance theorem for generalised pairs

We study the behavior of infinite systems of coupled harmonic oscillators as t->infinity, and generalize the Central Limit Theorem (CLT) to show that their reduced Wigner distributions become Gaussian under quite general conditions. This…

We prove a general duality theorem for tangle-like dense objects in combinatorial structures such as graphs and matroids. This paper continues, and assumes familiarity with, the theory developed in [6]

This paper presents simple, syntactic strong normalization proofs for the simply-typed lambda-calculus and the polymorphic lambda-calculus (system F) with the full set of logical connectives, and all the permutative reductions. The…

We develop a technique for normalization for $\infty$-type theories. The normalization property helps us to prove a coherence theorem: the initial model of a given $\infty$-type theory is $0$-truncated. The coherence theorem justifies…

We prove normalization for MTT, a general multimodal dependent type theory capable of expressing modal type theories for guarded recursion, internalized parametricity, and various other prototypical modal situations. We prove that deciding…

We prove that the abundance conjecture holds on a variety $X$ with mild singularities if $X$ has many reflexive differential forms with coefficients in pluricanonical bundles, assuming the Minimal Model Program in lower dimensions. This…

In a recent paper, Amini et al. introduce a general framework to prove duality theorems between special decompositions and their dual combinatorial object. They thus unify all known ad-hoc proofs in one single theorem. While this…

There is a difficulty in finding an estimate of variance of the profile likelihood estimator in the joint model of longitudinal and survival data. We solve the difficulty by introducing the ``statistical generalized derivative''. The…

Regarding the conjugacy representation on symmetric groups, we initiate a normalized measure emerging from this representation, namely the conjugacy measure. A central limit theorem for character ratios of random representations of the…

In the present article, real number representations, that are generalizations of classical positive and alternating representations of numbers, are introduced and investigated. The main metric relation, properties of cylinder sets are…

The "unit theorem" to which the present mini-course is devoted is a theorem from algebra that has a combinatorial flavour, and that originated in fact from algebraic combinatorics. Beyond a proof, the course also addresses applications, one…

Let $(X,B)$ be a projective log canonical pair such that $B$ is a $\Q$-divisor, and that there is a surjective morphism $f\colon X\to Z$ onto a normal variety $Z$ satisfying: $K_X+B\sim_\Q f^*M$ for some $\Q$-divisor $M$, and the augmented…

We propose a sufficient condition of the convergence of a generalized power series formally satisfying an algebraic (polynomial) ordinary differential equation. The proof is based on the majorant method.

We discuss two approaches to producing generalized parity proofs of the Kochen-Specker theorem. Such proofs use contexts of observables whose product is $I$ or $-I$; we call them constraints. In the first approach, one starts with a fixed…

We extend the main vanishing theorem in a paper of de Fernex and Ein to singular varieties without assuming locally complete intersection.

What singles out quantum mechanics as the fundamental theory of Nature? Here we study local measurements in generalised probabilistic theories (GPTs) and investigate how observational limitations affect the production of correlations. We…

We give a new proof of a classical theorem on approximation of continuous functions on totally real sets

We prove two generalisations of the Binomial theorem that are also generalisations of the q-binomial theorem. These generalisations arise from the commutation relations satisfied by the components of the co-multiplications of non-simple…

We define a class of singularity on arbitrary pairs of a normal variety and an effective $\mathbb{R}$-divisor on it, which we call pseudo-lc in this paper. This is a generalization of the usual lc singularity of pairs and log canonical…

We show that the dualizing sheaves of reduced simple normal crossings pairs have a canonical weight filtration in a compatible way with the one on the corresponding mixed Hodge modules by calculating the extension classes between the…