19 citations · 57 across the 10 of their papers we have counts for
11 papers
On Sarnak's Density Conjecture and its Applications
Konstantin Golubev, Amitay Kamber
Sarnak's Density Conjecture is an explicit bound on the multiplicities of non-tempered representations in a sequence of cocompact congruence arithmetic lattices in a semisimple Lie…
High dimensional Hoffman bound and applications in extremal combinatorics
Yuval Filmus, Konstantin Golubev, Noam Lifshitz
One powerful method for upper-bounding the largest independent set in a graph is the Hoffman bound, which gives an upper bound on the largest independent set of a graph in terms of…
Graphical Designs and Extremal Combinatorics
Konstantin Golubev
A graphical design is a proper subset of vertices of a graph on which many eigenfunctions of the Laplacian operator have mean value zero. In this paper, we show that extremal indep…
On the support of a non-autocorrelated function on a hyperbolic surface
Konstantin Golubev
Let be a non-negative square-integrable function on a finite volume hyperbolic surface , and assume that is non-autocorrelated, that is, perpendicula…
Cutoff on Graphs and the Sarnak-Xue Density of Eigenvalues
Konstantin Golubev, Amitay Kamber
It was recently shown by Lubetzky and Peres (2016) and by Sardari (2018) that Ramanujan graphs, i.e., graphs with the optimal spectrum, exhibit cutoff of the simple random walk in…
Direct Sum Testing: The General Case
Irit Dinur, Konstantin Golubev
A function is a direct sum if it is of the form for some fu…
Cutoff on Hyperbolic Surfaces
Konstantin Golubev, Amitay Kamber
In this paper we study the common distance between points and the behavior of a constant length step discrete random walk on finite area hyperbolic surfaces. We show that if the se…
Lower bounds for the measurable chromatic number of the hyperbolic plane
Evan DeCorte, Konstantin Golubev
Consider the graph whose vertex set is the hyperbolic plane, where two points are connected with an edge when their distance is equal to some . Asking for the…
Mixing properties and the chromatic number of Ramanujan complexes
Shai Evra, Konstantin Golubev, Alexander Lubotzky
Ramanujan complexes are high dimensional simplical complexes generalizing Ramanujan graphs. A result of Oh on quantitative property (T) for Lie groups over local fields is used to…
Spectrum and combinatorics of two-dimensional Ramanujan complexes
Konstantin Golubev, Ori Parzanchevski
Ramanujan graphs have extremal spectral properties, which imply a remarkable combinatorial behavior. In this paper we compute the high dimensional Hodge-Laplace spectrum of Ramanuj…
On the chromatic number of a simplicial complex
Konstantin Golubev
In [Ho] A.J. Hoffman proved a lower bound on the chromatic number of a graph in the terms of the largest and the smallest eigenvalues of its adjacency matrix. In this paper, we pro…