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The mixed Littlewood conjecture for pseudo-absolute values
Littlewood conjecture measure rigidity linear forms in logarithms
2011/1/17
In this paper we prove the mixed Littlewood conjecture for a p−adic absolute value and any pseudo-absolute value with bounded ratios. More precisely we show that if p is a prime and D is a pseud...
Thom polynomials and the Green-Griffiths conjecture
Thom polynomials the Green-Griffiths conjecture
2010/11/24
In the first part of this paper we apply equivariant localization techniques to prove the Green-Griffiths conjecture for a generic projective hypersurface of dimension n and degree >2^{8nlogn}. In th...
Complete solution to a conjecture on the maximal energy of unicyclic graphs
Complete solution conjecture unicyclic graphs
2010/11/24
For a given simple graph $G$, the energy of $G$ denoted by $E(G)$, is defined as the sum of the absolute values of all eigenvalues of its adjacency matrix. Let $P_n^{\ell}$ be the unicyclic graph obt...
Proof of the Borwein-Broadhurst conjecture for a dilogarithmic integral arising in quantum field theory
the Borwein-Broadhurst conjecture dilogarithmic integral arising quantum field theory
2010/11/8
Borwein and Broadhurst, using experimental-mathematics techniques, in 1998 identified numerous hyperbolic 3-manifolds whose volumes are rationally related to values of various Dirichlet L series $\te...
Holomorphic Morse inequalities and the Green-Griffiths-Lang conjecture
Holomorphic Morse inequalities the Green-Griffiths-Lang conjecture
2010/11/22
The goal of this work is to study the existence and properties of non constant entire curves f drawn in a complex irreducible n-dimensional variety X, and more specifically to show that they must sati...
Let A be a finite dimensional associative algebra over an algebraically closed field with a simple module S of finite projective dimension. The strong no loop conjecture says that this implies Ext(S,...
On a Generalization of the Flag Complex Conjecture of Charney and Davis
Coxeter group Charney-Davis Conjecture Flag Complex Conjecture
2010/11/30
The Flag Complex Conjecture of Charney and Davis states that for a simplicial complex S which triangulates a (2n − 1)-generalized homology sphere as a flag complex one has (−1)nP2S⣵...
Algorithms to disprove the Poincare Conjecture。
Deformations of algebras over operads and Deligne's conjecture
Deformations algebras operads Deligne's conjecture
2010/11/1
In present paper we develop the deformation theory of operads and algebras over operads. Free resolutions (constructed via Boardman-Vogt approach) are used in order to describe formal moduli spaces o...