Related papers: Fermats Last Theorem on Topological Fields
The induced fractional fermion number at zero temperature is topological (in the sense that it is only sensitive to global asymptotic properties of the background field), and is a sharp observable (in the sense that it has vanishing rms…
Fermat Last Theorem, which inspired mathematicians during 300 years, is proved by Andrew Wiles. Even among mathematicians there is a narrow circle of specialists, who can read this proof and understand all details. Is it a reason for…
In this paper, we construct a new topological quantum field theory of cohomological type and show that its partition function is a crossing number.
This chapter is divided into two parts. The first part is a survey of some recent results on nests and the orderability problem. The second part consists of results, partial results and open questions, all viewed in the light of nests. From…
We give a short review on the status of research on the theoretical foundations of $f(T)$ gravity theories. We discuss recent results on perturbative and non-perturbative approaches, causality and degrees of freedom, and discuss future…
In this paper we study the number of finite topologies on an $n$-element set subject to various restrictions.
We prove various results on the size and structure of subsets of vector spaces over finite fields which, in some sense, have too many mutually orthogonal pairs of vectors. In particular, we obtain sharp finite field variants of a theorem of…
We study the automorphism group of the algebraic closure of a substructure A of a pseudo-finite field F. We show that the behavior of this group, even when A is large, depends essentially on the roots of unity in F. For almost all…
Two singularity theorems can be proven if one attempts to let a Lorentzian cobordism interpolate between two topologically distinct manifolds. On the other hand, Cartier and DeWitt-Morette have given a rigorous definition for quantum field…
We construct a version of Hamiltonian Floer Homology based on the notion of a semi-infinite cycle. As an application, we provide a new proof for the existence of critical points of the action functional.
In this paper we prove another pairing theorem for bordered Floer homology. Unlike the original pairing theorem, this one is stated in terms of homomorphisms, not tensor products. The present formulation is closer in spirit to the usual…
We discuss a few selected topics in finite temperature field theory.
We prove finiteness results on integral points on complements of large divisors in projective varieties over finitely generated fields of characteristic zero. To do so, we prove a function field analogue of arithmetic finiteness results of…
We introduce a number field analogue of the Mertens conjecture and demonstrate its falsity for all but finitely many number fields of any given degree. We establish the existence of a logarithmic limiting distribution for the analogous…
We construct a topology on a given algebraically closed field with a distinguished subfield which is also algebraically closed. This topology is finer than Zariski topology and it captures the sets definable in the pair of algebraically…
We prove an analogue of the prime number theorem for finite fields.
A classical theorem of Frucht states that any finite group appears as the automorphism group of a finite graph. In the quantum setting the problem is to understand the structure of the compact quantum groups which can appear as quantum…
It is an original method based on systems of prameters represented by reals which obey to an infinite descent (convergent sequences). We define calculus of quotients and they conduct quickly to a consequent result. Our own scepticism made…
A convenient technique for calculating completed topological tensor products of functional Frechet and DF spaces is developed. The general construction is applied to proving kernel theorems for a wide class of spaces of smooth and entire…
We resolve an open problem concerning finite logical implication for path functional dependencies (PFDs).