相关论文: Algebraic proof of explicit formulas of basic rela…

This paper deals with holomorphic self-maps of the complex projective plane and the algebraic relations among the eigenvalues of the derivatives at the fixed points. These eigenvalues are constrained by certain index theorems such as the…

The aim of this paper is to use the methods and results of symplectic homogenization (see [V4]) to prove existence of periodic orbits and invariant measures with rotation number depending on the differential of the Homogenized Hamiltonian.…

The purpose of this paper is to investigate coefficient matrices of functional equations of zeta functions associated with homogeneous cones, which are given explicitly in the previous paper, in detail. We prove that the coefficient matrix…

The positive linear maps $\ad_s$ which send matrices $x$ to $s^*xs$ play important roles in quantum information theory as well as matrix theory. It was proved by Marciniak [Linear Multilinear Alg. 61 (2013), 970--975] that the map $\ad_s$…

We establish effective versions of Oppenheim's conjecture for generic inhomogeneous quadratic forms. We prove such results for fixed shift vectors and generic quadratic forms. When the shift is rational we prove a counting result which…

Assuming local one-sided units exist, I give an elementary proof of Wodzicki excision for cyclic homology. The proof is also constructive and provides an explicit inverse excision map. As far as I know, the latter is new.

For a pair of quadratic forms with rational coefficients in at least $10$ variables, we prove an asymptotic formula for the number of common zeros under the assumption that the two forms determine a projective variety with exactly two…

In this work we state a version of the double extension for homogeneous quadratic Lie super algebras that includes even and odd cases. We prove that any indecomposable, non-simple and homogeneous quadratic Lie super algebra is obtained by…

We consider actions of non-compact simple Lie groups preserving an analytic rigid geometric structure of algebraic type on a compact manifold. The structure is not assumed to be unimodular, so an invariant measure may not exist. Ergodic…

Let X be a complex surface with no nontrivial 2-forms. Then we show that Bloch's conjecture is true (i.e. the Albanese map in this case is injective) if and only if any homologically trivial idempotent in the ring of correspondences…

Hilbert's ternary quartic theorem states that every nonnegative degree 4 homogeneous polynomial in three variables can be written as a sum of three squares of homogeneous quadratic polynomials. We give a linear-algebraic approach to…

We study a new type of normal form at a critical point of an analytic Hamiltonian. Under a Bruno condition on the frequency, we prove a convergence statement to the normal form. Using this result, we prove the Herman invariant tori…

Let $M$ be an irreducible smooth projective variety, defined over an algebraically closed field, equipped with an action of a connected reductive affine algebraic group $G$, and let ${\mathcal L}$ be a $G$--equivariant very ample line…

This is an expository paper in which we explain how basic, standard, results about simple Lie algebras can be obtained by geometric arguments, following ideas of Cartan, Richardson and others.

Let k be a field. We show that all homogeneous noncommutative curves of genus zero over k are noncommutative P^1-bundles over a (possibly) noncommutative base. Using this result, we compute complete isomorphism invariants of homogeneous…

In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].

In this work we study, in greater detail than before, J.H. Conway's topographs for integral binary quadratic forms. These are trees in the plane with regions labeled by integers following a simple pattern. Each topograph can display the…

In the $(G,H)$-isomorphism game, a verifier interacts with two non-communicating players (called provers) by privately sending each of them a random vertex from either $G$ or $H$, whose aim is to convince the verifier that two graphs $G$…

Let G be an arbitrary simple graph. The main results are explicit representations of the edge cone of G as a finite intersection of closed halfspaces. If G is bipartite and connected we determine the facets of the edge cone and present a…

We first give a new proof and also a new formulation for the Abhyankar-Gurjar inversion formula for formal maps of affine spaces. We then use the reformulated Abhyankar-Gurjar formula to give a more straightforward proof for the equivalence…