Related papers: The Heyde Theorem on a-adic Solenoids
In this note, we prove an analog of the Valiron-Titchmarsch Theorem for Positive Temperatures
This paper provides a new simple proof of Hesse's theorem in projective geometry for any dimension.
We introduce the notion of skew-holomorphic Lie algebroid on a complex manifold, and explore some cohomologies theories that one can associate to it. Examples are given in terms of holomorphic Poisson structures of various sorts.
We give a short proof of Kaledin's theorem on the degeneration of the noncommutative Hodge-to-de Rham spectral sequence. Our approach is based on topological Hochschild homology and the theory of cyclotomic spectra. As a consequence, we…
This note contains a complete proof of the Abhyankar-Moh-Suzuki theorem (in characteristic zero case).
In this paper, we generalize the \textit{Clock Theorem} of Formal Knot Theory to knotoids in $S^2$. The clock theorem implies that clock states of a knotoid diagram form a lattice under transpositions. These states form the basis of many…
We prove a new q-analogue of Nicomachus's Theorem about the sum of cubes and some related results.
We prove the Aharoni Berger Conjecture
We prove a second main theorem for elliptic projective planes.
The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].
We give a new proof of a theorem of Mansour and Sun by using number theory and Rothe's identity.
We derive the Gallai-Edmonds Structure Theorem from Hall's Theorem.
We outline the construction of the holonomy groupoid of a locally Lie groupoid and the monodromy groupoid of a Lie groupoid. These specialise to the well known holonomy and monodromy groupoids of a foliation, when the groupoid is just an…
Due to a result by Mackenzie, extensions of transitive Lie groupoids are equivalent to certain Lie groupoids which admit an action of a Lie group. This paper is a treatment of the equivariant connection theory and holonomy of such…
The purpose of this article is to present a "Groupoid proof" to the Lefschetz fixed point formula for elliptic complexes. We shall define a "relative version" of tangent groupoid, describe the corresponding pseudodifferential calculi and…
Here we give a short survey of our new results. References to the complete proofs can be found in the text of this article and in the litterature.
Suppose that Y is a cyclic cover of projective space branched over a hyperplane arrangement D, and that U is the complement of the ramification locus in Y. The first theorem implies that the Beilinson-Hodge conjecture holds for U if certain…
We prove the real integral Hodge conjecture for several classes of real abelian threefolds. For instance, we prove the property for real abelian threefolds $A$ whose real locus $A(\mathbb R)$ is connected, and for real abelian threefolds…
In this paper, we prove a Liouville theorem for the $2$-Hessian equation on the Heisenberg group $\mathbb{H}^n$. The result is obtained by choosing a suitable test function and using integration by parts to derive the necessary integral…
A description of solutions of some integral equations has been obtained. A two-radii theorem is obtained as well.