Related papers: Symmetry of Derived Delooping Level
We survey the role of symmetry in diffeomorphic registration of landmarks, curves, surfaces, images and higher-order data. The infinite dimensional problem of finding correspondences between objects can for a range of concrete data types be…
An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with…
We present new techniques for removing arrows of bound quiver algebras, reducing thus the Finitistic Dimension Conjecture $\mathsf{(FDC)}$ for a given algebra to a smaller one. Unlike the classic arrow removal operation of…
We present a local and constructive differential geometric description of finite-dimensional solvable and transitive Lie algebras of vector fields. We show that it implies a Lie's conjecture for such Lie algebras. Also infinite-dimensional…
We give two proofs to the following theorem and its generalization: if a finite dimensional algebra $A$ is derived equivalent to a smooth projective scheme, then any derived equivalence between $A$ and another algebra $B$ is standard, that…
This is a survey of the existing literature, the state of the art, and a few minor new results and open questions regarding the essential dimension of central simple algebras and finite sequences of such algebras over fields whose…
We describe dimensional entropies introduced in a previous work list some of their properties and give some new proofs. These entropies allowed the definition of entropy-expanding maps. We introduce a new notion of entropy-hyperbolicity for…
Given a compact pseudo-metric space, we associate to it upper and lower dimensions, depending only on the metric. Then we construct a doubling metric for which the measure of a dillated ball is closely related to these dimensions.
In this paper we investigate homologically finite-dimensional objects in the derived category of a given small dg-enhanced triangulated category. Using these we define reflexivity, hfd-closedness, and the Gorenstein property for…
It has been suggested that higher-derivative gravity theories coupled to a scalar field with shift symmetry may be an important candidate for a quantum gravity. We show that this class of gravity theories are renormalizable in D = 3 and 4…
We consider the question of whether the injective modules generate the unbounded derived category of a ring as a triangulated category with arbitrary coproducts. We give an example of a non-Noetherian commutative ring where they don't, but…
Recollements of derived module categories are investigated, using a new technique, ladders of recollements, which are mutation sequences. The position in the ladder is shown to control whether a recollement restricts from unbounded to…
The paper proposes and motivates a conjecture on the invariance of cohomological support loci under derived equivalence. It contains a proof in the case of surfaces, and explains further developments and consequences.
Symmetry under a particular class of non-strictly canonical transformation may be used to identify, and subsequently excise degrees of freedom which do not contribute to the closure of the algebra of dynamical observables. Such redundant…
We study a combinatorial notion where given a set of lattice points one takes the set of all sums of subsets of a fixed size, and we ask if the given set comes from a convex lattice polytope whether the resulting set also comes from a…
In this paper we give a detailed measure theoretical analysis of what we call sum-level sets for regular continued fraction expansions. The first main result is to settle a recent conjecture of Fiala and Kleban, which asserts that the…
We study the pointwise dimension for a new class of projection measures on arbitrary fractal limit sets without separation conditions. We prove that the pointwise dimension exists a.e. for this class of measures associated to equilibrium…
We give a proof, based on the rigidity of tilting complexes, that the class of self-injective finite-dimensional algebras over an algebraically closed field is closed under derived equivalence.
A conjecture due to Y. Han asks whether that Hochschild homology groups of a finite dimensional algebra vanish for sufficiently large degrees would imply that the algebra is of finite global dimension. We investigate this conjecture from…
A detailed presentation of the results obtained during my Ph.D. research. The main investigations concern explicit descriptions of classes of finite dimensional pointed Hopf algebras and their quasi-isomorphism types.