arXiv research

Study mixed commutator lengths in wreath products and their relation to general ranks.

The fundamental ideas of aplicability of Levi-Malcev Theorem for Bol algebras, which plays a basic role in structural theory are outlined

New spectral theory for non-associative algebras with applications to Moufang dynamics.

Explicit BCH series radii found for special Banach-Malcev shift algebras.

Infinitesimal calculations link fundamental groups to Lie algebras.

Proves properties of Torelli Lie algebra for surfaces.

Extends foliation results to singular cases.

A Levi-Malcev type decomposition for $2$-step solvable Lie algebras with a complex structure

We represent the coordinate ring of algebraic hulls (which are generalizations of the Malcev completions of nilpotent groups for solvable groups) of solvmanifolds $G/Γ$ by using Miller's exponential iterated integrals (which are extensions of Chen's iterated integrals) of invariant differential forms.

We introduce a notion of a Fox pairing in a group algebra and use Fox pairings to define automorphisms of the Malcev completions of groups. These automorphisms generalize to the algebraic setting the action of the Dehn twists in the group algebras of the fundamental groups of surfaces. This work is inspired by the Kawa…

We show that the Malcev Lie algebra of the fundamental group of a compact $2n+1$-dimensional Sasakian manifold with $n\ge 2$ admits a quadratic presentation by using Morgan's bigradings of minimal models of mixed-Hodge diagrams. By using bigradings of minimal models, we also simplify the proof of the result of Cappelle…

Extends Floquet-Bloch theory to nilpotent groups for geometric applications.

Given a smooth manifold $M$ equipped with a properly and discontinuous smooth action of a discrete group $G$, the nerve $M_{\bullet}G$ is a simplicial manifold and its vector space of differential forms $\operatorname{Tot}_{N}\left(A_{DR}(M_{\bullet}G)\right)$ carry a $C_{\infty}$-algebra structure $m_{\bullet}$. We sh…

Paper proves non-triviality of Johnson kernel torsion subgroup.

Let S be a compact connected oriented surface with one boundary component. We extend each of Johnson's and Morita's homomorphisms to the Ptolemy groupoid of S. Our extensions are canonical and take values into finitely generated free abelian groups. The constructions are based on the 3-dimensional interpretation of the…

In 1964, John Stallings established an important relationship between the low-dimensional homology of a group and its lower central series. We establish a similar relationship between the low-dimensional homology of a group and its derived series. We also define a torsion-free-solvable completion of a group that is ana…

Study reveals vanishing Massey products on compact complex surfaces, impacting their fundamental group structure.

We study finite dimensional almost and quasi-effective prolongations of nilpotent Z-graded Lie algebras, especially focusing on those having a decomposable reductive structural subalgebra. Our assumptions generalize effectiveness and algebraicity and are appropriate to obtain Levi-Malčev and Levi-Chevalley decompositio…

In this note, we address the following question: Which 1-formal groups occur as fundamental groups of both quasi-Kähler manifolds and closed, connected, orientable 3-manifolds. We classify all such groups, at the level of Malcev completions, and compute their coranks. Dropping the assumption on realizability by 3-manif…

In this paper we prove that finite index subgroups of genus 3 mapping class and Torelli groups that contain the group generated by Dehn twists on bounding simple closed curves are not Kahler. These results are deduced from explicit presentations of the unipotent (aka, Malcev) completion of genus 3 Torelli groups and of…

The generalized Dehn twist along a closed curve in an oriented surface is an algebraic construction which involves intersections of loops in the surface. It is defined as an automorphism of the Malcev completion of the fundamental group of the surface. As the name suggests, for the case where the curve has no self-inte…

Let X and Y be finite-type CW-complexes (X connected, Y simply connected), such that the rational cohomology ring of Y is a k-rescaling of the rational cohomology ring of X. Assume H^*(X,Q) is a Koszul algebra. Then, the homotopy Lie algebra pi_*(Omega Y) tensor Q equals, up to k-rescaling, the graded rational Lie alge…

We explore the graded and filtered formality properties of finitely generated groups by studying the various Lie algebras over a field of characteristic 0 attached to such groups, including the Malcev Lie algebra, the associated graded Lie algebra, the holonomy Lie algebra, and the Chen Lie algebra. We explain how thes…

We analyze the degree-two part of the Torelli group's associated graded.

Let $Σ$ be a compact oriented surface. The Dehn twist along every simple closed curve $γ\subset Σ$ induces an automorphism of the fundamental group $π$ of $Σ$. There are two possible ways to generalize such automorphisms if the curve $γ$ is allowed to have self-intersections. One way is to consider the `generalized Deh…

Let S be a compact connected oriented surface with one boundary component, and let P be the fundamental group of S. The Johnson filtration is a decreasing sequence of subgroups of the Torelli group of S, whose k-th term consists of the self-homeomorphisms of S that act trivially at the level of the k-th nilpotent quoti…

This paper protects rankings from differential privacy breaches.

The paper addresses privacy in rank aggregation using randomized responses.

This paper addresses the problem of rank aggregation, which aims to find a consensus ranking among multiple ranking inputs. Traditional rank aggregation methods are deterministic, and can be categorized into explicit and implicit methods depending on whether rank information is explicitly or implicitly utilized. Surpri…

We study the problem of rank aggregation: given a set of ranked lists, we want to form a consensus ranking. Furthermore, we consider the case of extreme lists: i.e., only the rank of the best or worst elements are known. We impute missing ranks by the average value and generalise Spearman's ρto extreme ranks. Our main …

Develops a method to infer partial rankings from sparse comparisons.

Research characterizes learnability of multilabel ranking problems.

This paper compares rank aggregation methods for partial label ranking.

We study the problem of learning to rank from multiple information sources. Though multi-view learning and learning to rank have been studied extensively leading to a wide range of applications, multi-view learning to rank as a synergy of both topics has received little attention. The aim of the paper is to propose a c…

Paper tackles underranking in group-fair ranking systems, proving a trade-off and presenting an algorithm.

New ranking system balances fairness and user utility.

Introduces nondecreasing rank for matrices and tensors, developing methods and applications.

Analytic proof for minimal rank Sard conjecture.

Rank-one measurements limit feasible sets for low-rank PSD matrices.

We consider the problem of statistical inference for ranking data, specifically rank aggregation, under the assumption that samples are incomplete in the sense of not comprising all choice alternatives. In contrast to most existing methods, we explicitly model the process of turning a full ranking into an incomplete on…

The paper tackles learning true rankings from noisy, incomplete data.

Paper introduces GAMs for interpretable learning-to-rank models.

Low-rank framework for task-specific LLM ranking from sparse comparisons.

New method solves nonsmooth low-rank matrix optimization problems efficiently.

New methods rank players using covariates and comparisons, outperforming existing algorithms.

FedLoRU improves FL efficiency by using low-rank updates.

The paper addresses calibration in label ranking, a structured prediction task.

We propose Top-N-Rank, a novel family of list-wise Learning-to-Rank models for reliably recommending the N top-ranked items. The proposed models optimize a variant of the widely used discounted cumulative gain (DCG) objective function which differs from DCG in two important aspects: (i) It limits the evaluation of DCG …