Related papers: Finitude g\'eom\'etrique en g\'eom\'etrie de Hilbe…
The paper is centered around a new proof of the infinitesimal rigidity of convex polyhedra. The proof is based on studying derivatives of the discrete Hilbert-Einstein functional on the space of "warped polyhedra" with a fixed metric on the…
We develop a notion of formal groups in the filtered setting and describe a duality relating these to a specified class of filtered Hopf algebras. We then study a deformation to the normal cone construction in the setting of derived…
We discuss the local and global problems for the equivalence of geometric structures of an arbitrary order and, in later sections, attention is given to what really matters, namely the equivalence with respect to transformations belonging…
In this note we fill a gap in the proof of the main theorem (Theorem 1.2) of our paper 'Surfaces in 4-manifolds', Math. Res. Letters 4 (1997), 907-914.
In this paper we investigate some algebraic and geometric consequences which arise from an extremal bound on the Hilbert function of the general hyperplane section of a variety (Green's Hyperplane Restriction Theorem). These geometric…
Given a finite subgroup G of SL(2,C) we define an additive 2-category H^G whose Grothendieck group is isomorphic to an integral form of the Heisenberg algebra. We construct an action of H^G on derived categories of coherent sheaves on…
This thesis deals with the geometric and integrable aspects associated with random matrix models. Its purpose is to provide various applications of random matrix theory, from algebraic geometry to partial differential equations of…
A new method is presented for Fourier decomposition of the Helmholtz Green Function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of…
This paper is the supplement to the section 2 of the paper "Floating bundles and their applications" (math.AT/0102054). Below we construct the denumerable set of extensions of the formal group of geometric cobordisms $F(x\otimes 1,1\otimes…
This manuscript, a revised version of arXiv:0811.3168v1, was inadvertently submitted as a separate paper. It can now be accessed, including some final corrections for the published version, as arXiv:0811.3168v2.
This note complements our paper "Categoricity-like properties in the first order realm" (Journal for the Philosophy of Mathematics, 2024).
Results concerning recurrence and ergodicity are proved in an abstract Hilbert space setting based on the proof of Khintchine's recurrence theorem for sets, and on the Hilbert space characterization of ergodicity. These results are carried…
An extension of algebras is a homomorphism of algebras preserving identities. We use extensions of algebras to study the finitistic dimension conjecture over Artin algebras. Let $f: B \to A$ be an extension of Artin algebras. We denote by…
In this paper, we give a finiteness result on the diffeomorphism types of curvature-adapted equifocal hypersurfaces in a simply connected compact symmetric space. Furthermore, the condition curvature-adapted can be dropped if the symmetric…
We consider the numerical computation of finite-range singular integrals $$I[f]=\intBar^b_a f(x)\,dx,\quad f(x)=\frac{g(x)}{(x-t)^m},\quad m=1,2,\ldots,\quad a<t<b,$$ that are defined in the sense of Hadamard Finite Part, assuming that…
We prove a couple of new endpoint geodesic restriction estimates for eigenfunctions. In the case of general 3-dimensional compact manifolds, after a $TT^*$ argument, simply by using the $L^2$-boundedness of the Hilbert transform on $\R$, we…
This article presents a geometric approach to some similarity problems involving metric arguments in the non-positively curved space of positive invertible operators of an operator algebra and the canonical isometric action by invertible…
We close a gap appearing at the same time in the author's thesis "Iterated rings of bounded elements and generalizations of Schm\"udgen's theorem" [1] and in the author's article "Iterated rings of bounded elements and generalizations of…
This note refers to our previous paper "The emergence of torsion in the continuum limit of distributed edge-dislocations". It identifies and fixes an error in the notion of convergence of Weitzenb\"ock manifolds defined in the paper, and in…
This paper gives a quick overview of the author's recent result that all finitely presented groups are QSF.