Related papers: Counter-examples to the minimal model theory in ch…

We prove the finiteness of relative log pluricanonical representations in the complex analytic setting. As an application, we discuss the abundance conjecture for semi-log canonical pairs within this framework. Furthermore, we establish the…

Random matrix theory (RMT) is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Most of the proposed generalizations keep the first assumption and violate the second. Recently, several authors presented…

We construct the counter-example for polynomial version of Sarnak's conjecture for minimal systems, which assets that the M\"obius function is linearly disjoint from subsequences along polynomials of deterministic sequences realized in…

We prove Behrend's conjecture on the rationality of the canonical reduction of principal bundles and reductive group schemes for classical groups and give new bounds for the conjecture for exceptional groups. However we find a…

This paper introduces small-gain sufficient conditions for $2$-contraction of feedback interconnected systems, on the basis of individual gains of suitable subsystems arising from a modular decomposition of the second additive compound…

Cox's well-known theorem justifying the use of probability is shown not to hold in finite domains. The counterexample also suggests that Cox's assumptions are insufficient to prove the result even in infinite domains. The same…

We discuss the log minimal model theory for log surfaces. We show that the log minimal model program, the finite generation of log canonical rings, and the log abundance theorem for log surfaces hold true under assumptions weaker than the…

We show that many statements of the Minimal Model Program, including the cone theorem, the base point free theorem and the existence of Mori fibre spaces, fail for 1-foliated surface pairs $(X,\mathcal{F})$ with canonical singularities in…

In this short note we present a family of counterexamples to the King's conjecture.

We show that the local and deterministic mode of description is not only in conflict with the quantum theory, but also with relativity. We argue that elementary relativistic properties of spacetime lead to the emergence of a…

We discuss the birational geometry of singular surfaces in positive characteristic. More precisely, we establish the minimal model program and the abundance theorem for Q-factorial surfaces and for log canonical surfaces. Moreover, in the…

We find new "reasons" for a class of models for not having a universal model in a cardinal $\lambda$. This work, though it has consequences in model theory, is really in combinatorial set theory. We concentrate on a prototypical class which…

Let L/K be a separable field extension of degree 6. An 1867 theorem of P. Joubert asserts that if char(K) is different from 2 then L is generated over K by an element whose minimal polynomial is of the form t^6 + a t^4 + b t^2 + ct + d for…

According to Bell's theorem a large class of hidden-variable models obeying Bell's notion of local causality conflict with the predictions of quantum mechanics. Recently, a Bell-type theorem has been proven using a weaker notion of local…

We present another proof for the well-known {\em small model property} of two-variable logic. As far as we know, existing proofs of this property rely heavily on model theoretic concepts. In contrast, ours is purely combinatorial and uses…

The "Modularity Conjecture" is the assertion that the join of two nonmodular varieties is nonmodular. We establish the veracity of this conjecture for the case of linear idempotent varieties. We also establish analogous results concerning…

The $N=2$ minimal superconformal model can be twisted yielding an example of topological conformal field theory. In this article we investigate a Lie theoretic extension of this process.

We give an example of a countable theory T such that for every cardinal lambda >= aleph_2 there is a fully indiscernible set A of power lambda such that the principal types are dense over A, yet there is no atomic model of T over A. In…

For an arbitrary integer N that is at least 2, this paper gives a construction of a strictly stationary, N-tuplewise independent sequence of (non-degenerate) bounded random variables such that the Central Limit Theorem fails to hold. The…

A natural construction of the logarithmic extension of the M(2,p) minimal models is presented, which generalises our previous model [0708.0802] of percolation (p=3). Its key aspect is the replacement of the minimal model irreducible modules…