96 citations · 190 across the 18 of their papers we have counts for
26 papers
Counting in Vieta graphs over
Bogdan Nica
We introduce and study a finite simple graph of algebraic origin: the Vieta graph on the solution set over to a symmetric, multivariate equation which is quadratic i…
On quadratic character sums over quartics
Bogdan Nica
We obtain transformation formulas for quadratic character sums with quartic and cubic polynomial arguments.
Variance of point-counts for families of cubic curves over and Jacobsthal sums
Bogdan Nica
We give explicit computations for the variance of the number of points along one-parameter families of cubic curves. We highlight evaluations of variances that involve Jacobsthal s…
Norms of spherical averaging operators for some geometric group actions
Bogdan Nica
We obtain asymptotic estimates for the -operator norm of spherical averaging operators associated to certain geometric group actions. The motivating example is the case of…
On an identity of Sylvester
Bogdan Nica
We discuss an algebraic identity, due to Sylvester, as well as related algebraic identities and applications.
Polynomials over structured grids
Bogdan Nica
We study multivariate polynomials over `structured' grids. We begin by proposing an interpretation as to what it means for a finite subset of a field to be structured; we do so by…
Kloosterman sums over finite Frobenius rings
Bogdan Nica
We study Kloosterman sums in a generalized ring-theoretic context, that of finite commutative Frobenius rings. We prove a number of identities for twisted Kloosterman sums, loosely…
On bounded elementary generation for over polynomial rings
Bogdan Nica
Let be the polynomial ring over a finite field . It is shown that, for , the special linear group is boundedly generated by the elementary matrices.
A relative bound for independence
Bogdan Nica
We prove an upper bound for the independence number of a graph in terms of the largest Laplacian eigenvalue, and of a certain induced subgraph. Our bound is a refinement of a well-…
Two applications of strong hyperbolicity
Bogdan Nica
We present two analytic applications of the fact that a hyperbolic group can be endowed with a strongly hyperbolic metric. The first application concerns the crossed-product C*-alg…
A brief introduction to Spectral Graph Theory
Bogdan Nica
Expanded lecture notes. Preliminary version, comments are welcome.
On operator norms for hyperbolic groups
Bogdan Nica
We estimate the operator norm of radial non-negative functions on hyperbolic groups. As a consequence, we show that several forms of Haagerup's inequality are optimal.
Unimodular graphs and Eisenstein sums
Bogdan Nica
Motivated in part by combinatorial applications to certain sum-product phenomena, we introduce unimodular graphs over finite fields and, more generally, over finite valuation rings…
A true relative of Suslin's normality theorem
Bogdan Nica
We prove a normality theorem for the "true" elementary subgroups of defined by the ideals of a commutative unital ring . Our result is an analogue of a normality theor…
Strong hyperbolicity
Bogdan Nica, Jan Spakula
We propose the metric notion of strong hyperbolicity as a way of obtaining hyperbolicity with sharp additional properties. Specifically, strongly hyperbolic spaces are Gromov hyper…
K-homological finiteness and hyperbolic groups
Heath Emerson, Bogdan Nica
Motivated by classical facts concerning closed manifolds, we introduce a strong finiteness property in K-homology. We say that a C*-algebra has uniformly summable K-homology if all…
Linear groups - Malcev's theorem and Selberg's lemma
Bogdan Nica
An account of two fundamental facts concerning finitely generated linear groups: Malcev's theorem on residual finiteness, and Selberg's lemma on virtual torsion-freeness.
The Mazur-Ulam theorem
Bogdan Nica
A short proof of the Mazur-Ulam theorem concerning isometries of real normed spaces.
Finitely summable Fredholm modules for boundary actions of hyperbolic groups
Heath Emerson, Bogdan Nica
We construct a family of odd, finitely summable Fredholm modules over the crossed product C*-algebra $C(\bd \G)\rtimes \G$ associated to the action of a non-elementary hyperbolic g…
Proper isometric actions of hyperbolic groups on -spaces
Bogdan Nica
We show that every non-elementary hyperbolic group $\G$ admits a proper affine isometric action on $L^p(\bd\G\times \bd\G)$, where $\bd\G$ denotes the boundary of $\G$ and is l…
Spectral morphisms, K-theory, and stable ranks
Bogdan Nica
We give a brief account of the interplay between spectral morphisms, K-theory, and stable ranks in the context of Banach algebras.
Homotopical stable ranks for Banach algebras
Bogdan Nica
The connected stable rank and the general stable rank are homotopy invariants for Banach algebras, whereas the Bass stable rank and the topological stable rank should be thought of…
On the degree of rapid decay
Bogdan Nica
A finitely generated group $\G$ equipped with a word-length is said to satisfy property RD if there are such that, for all non-negative integers , we have $\|a\|\le…
Group actions on median spaces
Bogdan Nica
We investigate the geometry of median metric spaces. The group-theoretic applications are towards Kazhdan's property (T) and Haagerup's property.