Dylan J. Altschuler

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20122026

most citedThe Zoo of Solitons for Curve Shortening in

R^{n}

19 citations · 36 across the 15 of their papers we have counts for

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Showing 2025 · math.MGShow all

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math.MG2025

Metric Poincaré inequalities for graphs

Dylan J. Altschuler, Pandelis Dodos, Konstantin Tikhomirov +1

This article obtains purely metric counterparts of cornerstone results in the theory of embedding graphs into normed spaces. Our first main result is a metric analogue of Matoušek'…

math.MG2025

Metric dimension reduction modulus for superlogarithmic distortion

Dylan J. Altschuler, Konstantin Tikhomirov

The metric dimension reduction modulus $k_{n}^{α} (ℓ_{\infty})$ is the smallest $k$ such that every $n$ --point metric space can be embedded into some $k$ -dimensional normed space, with…

math.MG2025

Discrete Poincaré inequalities and universal approximators for random graphs

Dylan J. Altschuler, Pandelis Dodos, Konstantin Tikhomirov +1

Nonlinear Poincaré inequalities are indispensable tools in the study of dimension reduction and low-distortion embeddings of graphs into metric spaces, and have found remarkable al…

math.MG2025

Universal geometric non-embedding of random regular graphs

Dylan J. Altschuler, Konstantin Tikhomirov

Let $Δ \geq 3$ be fixed, $n \geq n_{Δ}$ be a large integer. It is a classical result that $Δ$ --regular expanders on $n$ vertices are not embeddable as geometric (distance) graphs into E…