Related papers: The Kempf-Ness theorem and Invariant Theory
These lectures centered around the Kempf-Ness theorem, which describes the equivalence between notions of quotient in symplectic and algebraic geometry. The text also describes connections to invariant theory, such existence of invariants…
A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.
We give in the present work a new methodology that allows to give isoperimetric proofs, for Kneser's Theorem and Kemperman's structure Theory and most sophisticated results of this type. As an illustration we present a new proof of Kneser's…
The assumptions needed to prove Cox's Theorem are discussed and examined. Various sets of assumptions under which a Cox-style theorem can be proved are provided, although all are rather strong and, arguably, not natural.
In this paper, we define an invariant, which we believe should be the substitute for total K-theory in the case when there is one distinguished ideal. Moreover, some diagrams relating the new groups to the ordinary K-groups with…
For linear actions of real reductive Lie groups we prove the Kempf-Ness Theorem about closed orbits and the Kirwan-Ness Stratification Theorem of the null cone. Since our completely self-contained proof focuses strongly on geometric and…
A very short proof of Kneser's theorem via transversal is given.
We give a new proof of the theorem of Kronecker-Weber based on Kummer theory and Stickelberger's theorem.
The fundamental problem of knot theory is to know whether two knots are equivalent or not. As a tool to prove that two knots are different, mathematicians have developed various invariants. Knots invariants are just functions that can be…
In this note, we consider applications of Ratner's theorem to constructions of families of polynomials with dense values on the set of primitive integer points from the viewpoint of invariant theory.
Using an equivariant version of Connes' Thom Isomorphism,w}e prove that equivariant $K$-theory is invariant under strict deformation quantization for a compact Lie group action.
We give a proof of the Marker-Steinhorn Theorem which fills a gap in previous proofs of the result.
In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.
We explain how structures analogous to those appearing in the theory of stability conditions on abelian and triangulated categories arise in geometric invariant theory. This leads to an axiomatic notion of a central charge on a scheme with…
We prove an analytic KAM-Theorem, which is used in [1], where the differential part of KAM-theory is discussed. Related theorems on analytic KAM-theory exist in the literature (e. g., among many others, [7], [8], [13]). The aim of the…
Many novel quantum phenomena emerge in non-equilibrium relativistic quantum matter under extreme conditions such as strong magnetic fields and rotations. The quantum kinetic theory based on Wigner functions in quantum field theory provides…
The Poincare-Hopf Theorem is one of the most used in other areas of science. There are applications of the Poincare-Hopf Theorem in physics, chemistry, biology and even in economics, psychology, etc ... The Poincare-Hopf Theorem connects an…
An technically interesting proof of a known theorem.
The Linearization Theorem for proper Lie groupoids organizes and generalizes several results for classic geometries. Despite the various approaches and recent works on the subject, the problem of understanding invariant linearization…
The theorem is proved that generalizes the Gelfand generalization of the Paley-Wiener tauberian theorem to general abelian topological semigroups with invariant measure. Several corollaries of this theorem are given.