3 citations · 12 across the 9 of their papers we have counts for
9 papers
Parsimonious cones
Aleksandr Berdnikov
We construct embeddings of simplicial complexes into a (surface of a) simplicial ball whose triangulation has bounded degrees and low volume. This construction can be used either t…
Degrees of maps and multiscale geometry
Aleksandr Berdnikov, Larry Guth, Fedor Manin
We study the degree of an -Lipschitz map between Riemannian manifolds, proving new upper bounds and constructing new examples. For instance, if is the connected sum of …
Waist of maps measured via Urysohn width
Alexey Balitskiy, Aleksandr Berdnikov
We discuss various questions of the following kind: for a continuous map from a compact metric space to a simplicial complex, can one guarantee the existence of a fiber l…
Local-to-global Urysohn width estimates
Alexey Balitskiy, Aleksandr Berdnikov
The notion of the Urysohn -width measures to what extent a metric space can be approximated by a -dimensional simplicial complex. We investigate how local Urysohn width bound…
Scalable spaces
Aleksandr Berdnikov, Fedor Manin
\emph{Scalable spaces} are simply connected compact manifolds or finite complexes whose real cohomology algebra embeds in their algebra of (flat) differential forms. This is a rati…
Lipschitz null-homotopy of mappings
Aleksandr Berdnikov
This work focuses on important step in quantitative topology: given homotopic mappings from to of Lipschitz constant , build the (asymptotically) simplest homotopy b…
Bounds on Multiplicities of Laplace-Beltrami Operator Eigenvalues on the Real Projective Plane
Aleksandr S. Berdnikov, Nikolai S. Nadirashvili, Alexei V. Penskoi
The known upper bounds for the multiplicities of the Laplace-Beltrami operator eigenvalues on the real projective plane are improved for the eigenvalues with even indexes. Upper bo…
Bounds on Multiplicities of Laplace Operator Eigenvalues on Surfaces
Aleksandr Berdnikov
In the present paper several bounds on multiplicities of eigenvalues of the Laplacian operator on surfaces are generalized from the case of either closed surface or simply-connecte…
Conical resolutions and cohomology of the moduli spaces of nodal hypersurfaces
A. S. Berdnikov, A. G. Gorinov, N. S. Konovalov
A projective hypersurface is nodal if it does not have singularities worse than simple nodes. We calculate the rational cohomology of the spaces of equations of nodal cubic and qua…