2 citations · 7 across the 16 of their papers we have counts for
18 papers
Structure of 2-step nilpotent ergodic averages for distinct-degree polynomials
Andreas Koutsogiannis, Borys Kuca, Wenbo Sun
We investigate manifestations of the Nilpotent Heuristic, which posits that recurrence and convergence phenomena known for measure-preserving -systems extend to nilpo…
Joint ergodicity - 40 years on
Borys Kuca
Recent years have seen dramatic progress in the study of joint ergodicity, i.e. a scenario in which a multiple ergodic average converges in norm to the product of integrals of indi…
Ergodic averages for sparse corners
Nikos Frantzikinakis, Borys Kuca
We develop a framework for the study of the limiting behavior of multiple ergodic averages with commuting transformations when all iterates are given by the same sparse sequence; t…
Resolving the joint ergodicity problem for Hardy sequences
Sebastián Donoso, Andreas Koutsogiannis, Borys Kuca +2
The joint ergodicity classification problem aims to characterize those sequences which are jointly ergodic along an arbitrary dynamical system if and only if they satisfy two natur…
Seminorm estimates and joint ergodicity for pairwise independent Hardy sequences
Sebastián Donoso, Andreas Koutsogiannis, Borys Kuca +2
We develop a robust structure theory for multiple ergodic averages of commuting transformations along Hardy sequences of polynomial growth. We then apply it to derive a number of n…
Corners with polynomial side length
Noah Kravitz, Borys Kuca, James Leng
A -polynomial corner, for a polynomial, is a triple of points for . In the case where has an…
Quantitative concatenation for polynomial box norms
Noah Kravitz, Borys Kuca, James Leng
Using PET and quantitative concatenation techniques, we establish box-norm control with the "expected" directions for counting operators for general multidimensional polynomial pro…
Multidimensional polynomial patterns over finite fields: bounds, counting estimates and Gowers norm control
Borys Kuca
We examine multidimensional polynomial progressions involving linearly independent polynomials in finite fields, proving power saving bounds for sets lacking such configurations. T…
Degree lowering for ergodic averages along arithmetic progressions
Nikos Frantzikinakis, Borys Kuca
We examine the limiting behavior of multiple ergodic averages associated with arithmetic progressions whose differences are elements of a fixed integer sequence. For each , w…
Seminorm control for ergodic averages with commuting transformations and pairwise dependent polynomial iterates
Nikos Frantzikinakis, Borys Kuca
We examine multiple ergodic averages of commuting transformations with polynomial iterates in which the polynomials may be pairwise dependent. In particular, we show that such aver…
Joint ergodicity for commuting transformations and applications to polynomial sequences
Nikos Frantzikinakis, Borys Kuca
We give necessary and sufficient conditions for joint ergodicity results of collections of sequences with respect to systems of commuting measure preserving transformations. Combin…
On a continuous Sárközy type problem
Borys Kuca, Tuomas Orponen, Tuomas Sahlsten
We prove that there exists a constant with the following property: if is a compact set which contains no pair of the form $\{x, x + (z,…
On several notions of complexity of polynomial progressions
Borys Kuca
For a polynomial progression we define four notions of complexity: Host-Kra complexity, Weyl complexity, true complexity and algebraic…
Multidimensional polynomial Szemerédi theorem in finite fields for polynomials of distinct degrees
Borys Kuca
We obtain a polynomial upper bound in the finite-field version of the multidimensional polynomial Szemerédi theorem for distinct-degree polynomials. That is, if are…
True complexity of polynomial progressions in finite fields
Borys Kuca
The true complexity of a polynomial progression in finite fields corresponds to the smallest-degree Gowers norm that controls the counting operator of the progression over finite f…
Further bounds in the polynomial Szemerédi theorem over finite fields
Borys Kuca
We provide upper bounds for the size of subsets of finite fields lacking the polynomial progression These are the first known u…
Structures in Additive Sequences
Borys Kuca
Consider the sequence constructed in a greedy fashion by setting , and defining as the smallest integer larger than that can b…
The Unreasonable Rigidity of Ulam Sets
Joshua Hinman, Borys Kuca, Alexander Schlesinger +1
We give a number of results about families of Ulam sets. Generalizing behavior of Ulam sets U(1,n), we prove using an novel model theoretic approach that there is a rigidity phenom…