Related papers: The Kempf-Ness theorem and Invariant Theory
This article introduces three invariance principles under which P is different from NP. In the second part a theorem of convergence is proven. This theorem states that for any language L there exists an infinite sequence of languages from…
We study invariant Seifert surfaces for strongly invertible knots, and prove that the gap between the equivariant genus (the minimum of the genera of invariant Seifert surfaces) of a strongly invertible knot and the (usual) genus of the…
We describe recent advances in the study of random analogues of combinatorial theorems.
For a class of stationary regularly varying and weakly dependent time series, we prove the so-called complete convergence result for the corresponding space-time point processes. As an application of our main theorem, we give a simple proof…
Lectures on Poincare invariant quantum theory presented at TJNAF.
The theory of singularities and its broad ramifications, especially catastrophe theory, have found fertile ground in some areas of physics (e.g., caustics, wave optics) for their applications. In the context of quantum many-body theory,…
The study of the number of photons leads to a new way of characterizing curves and to a novel integral invariant over curves.
Using a diagrammatic reformulation of Bayes' theorem, we provide a necessary and sufficient condition for the existence of Bayesian inference in the setting of finite-dimensional $C^*$-algebras. In other words, we prove an analogue of…
It is often claimed that Bayesian methods, in particular Bayes factor methods for hypothesis testing, can deal with optional stopping. We first give an overview, using elementary probability theory, of three different mathematical meanings…
We review some recent results of the theory of Lie systems in order to apply such results to study Ermakov systems. The fundamental properties of Ermakov systems, i.e. their superposition rules, the Lewis-Ermakov invariants, etc., are found…
The purpose of this article is to introduce the concept of invariance and its properties. These properties can be used to check the primality of a number. Combining these properties with the Euler theorem, it is possible to generalize this…
We use correspondences to define a purely topological equivariant bivariant K-theory for spaces with a proper groupoid action. Our notion of correspondence differs slightly from that of Connes and Skandalis. We replace smooth K-oriented…
Counterparts of several classical results of number theory are proven for the ring of polynomials with coefficients in a number field. A theorem of Milnor that determines the Witt ring of a function field is applied to prove an analogue of…
We study a random dynamical system such that one transformation is randomly selected from a family of transformations and then applied on each iteration. For such random dynamical systems, we consider estimates of absolutely continuous…
Recently, a new definition for quantum $f$-divergences was introduced based on an integral representation. These divergences have shown remarkable properties, for example when investigating contraction coefficients under noisy channels. At…
We give a detailed and unified survey of equivariant $KK$-theory over locally compact, second countable, locally Hausdorff groupoids. We indicate precisely how the "classical" proofs relating to the Kasparov product can be used almost…
We study distribution of zeros of a complex polynomial whose coefficients has been modified. We give a new proof of the theorem of Rubinstein, and with similar method we prove a new theorem that is not generalization of the previous…
We establish some new theorems on pentagon and pentagram.
We give a sheaf-theoretic version of the universal coefficient theorem.
The goal of invariant theory is to find all the generators for the algebra of representations of a group that leave the group invariant. Such generators will be called \emph{basic invariants}. In particular, we set out to find the set of…