Related papers: The present state of the capitulation problem
We reduce the classification of finite extensions of function fields (of curves over finite fields) with the same class number to a finite computation; complete this computation in all cases except when both curves have base field…
An overview of quantum computing and in particular the Hidden Subgroup Problem are presented from a mathematical viewpoint. Detailed proofs are supplied for many important results from the literature, and notation is unified, making it…
For congruence subgroups commensurable with $\operatorname{SL}_2$ over number fields, we study cusp counts with certain multiplicities. We prove that the ratio of the total weighted cusp count to the group index is bounded by a negative…
This article is an overview of the vanishing cycles method in number theory over function fields. We first explain how this works in detail in a toy example, and then give three examples which are relevant to current research. The focus…
This survey paper aims at giving the state of the art in the study of string C-group representations of almost simple groups. It also suggest a series of problems and conjectures to the interested reader.
I discuss the concept of quasi-state decompositions for ground states and equilibrium states of quantum spin systems. Some recent results on the ground states of a class of one-dimensional quantum spin models are summarized and new work in…
A review of the current status of SUSY/SUGRA/String phenomenology is given.
We generalize Iwasawa's theorem on class group over $\Z_p$-extensions to all $\Z_p^d$-extensions.
A general question is posed to the quantum community. Partial results are formulated in a self-contained way. In particular, the title question is answered affirmatorily in two cases: 1) The case of spin/ angular momentum of a partcle; 2) A…
We show that there is a canonical, order preserving map $\psi$ of lattices of subgroups, which maps the lattice $\Sub(A)$ of subgroups of the ideal class group of a galois number field $\K$ into the lattice $\Sub(\KH/\K)$ of subfields of…
The subgroup commutativity degree of a group G has been defined in [6] as the probability that two subgroups of G commute, or equivalently that the product of two subgroups is again a subgroup. Problem 4.3 of [6] asks whether there exist…
We study the famous mathematical puzzle of prisoners and hats. We introduce a framework in which various variants of the problem can be formalized. We examine three particular versions of the problem (each one in fact a class of problems)…
The purpose of this short paper is to identify the mathematical essence of the superiorization methodology. This methodology has been developed in recent years while attempting to solve specific application-oriented problems. Consequently,…
We present a general theorem for distributed synthesis problems in coordination games with $\omega$-regular objectives of the form: If there exists a winning strategy for the coalition, then there exists an "essential" winning strategy,…
We present a short review of the existing evidence in favor of neutrino mass and neutrino oscillations which come from different kinds of experiments. We focus our attention in particular on solar neutrinos, presenting a global updated…
In this paper we formalize some foundation concepts and theorems of group theory in a variant of type theory called the Calculus of Constructions with Definitions. In this theory we introduce definition of a group, which is both general and…
Building on Bosca's method, we extend to tame ray class groups the results on capitulation of ideals of a number field by composition with abelian extensions of a subfield first studied by Gras. More precisely, for every extension of number…
Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…
Over a large class of function fields, we show that the solutions of some linear equations in the topological closure of a certain subgroup of the group of units in the function field are exactly the solutions that are already in the…
We attempt to survey the field of combinatorial representation theory, describe the main results and main questions and give an update of its current status. We give a personal viewpoint on the field, while remaining aware that there is…