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Home » Thus, the simplified expansion is $ oxedx^2 - 4y^2 + 4yz - z^2 $. - AMAZONAWS

Thus, the simplified expansion is $ oxedx^2 - 4y^2 + 4yz - z^2 $. - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 In the 1940s Bardin began research on singularities using algebraic methods. He studied the equations that determine these singularities, proved individual finite classifications, and constructed families of singularities after systematic classification, mainly of isolated singularities. He established conjectures (later proved by Arnold) relating both classes of normal quasi-convex singularities to analytic classes. Bardin's own classifications were later found incomplete due to topological or differential subtleties, but stimulated developments in singularity theory. He was the first to use motivating examples of analytic classifications to develop formal algebraic categories, distinguishing equitional and analytic (geometric) notions. He also influenced the development of category theory, discussing Ricci equivalence (related to homological algebra) and homotopical aspects of classifications. Before and after his death Bardin continued to write about singularities, concluding a long series of papers with Coxeter and Arnold. Bardin supported rising mathematicians, including Arnold, Vladimir Arnold, Boris Gorshenin, and others.

📌 A ring of polynomials that defining a surface singularity is called a Bardin ring in his honor; Bardin–Whitney homology and cubical Bardin rings continue his work. The crater Baudardin on the Moon is named after him.

📌 Selected publications

📌 Elementarity of singularities of algebraic surfaces, Mathematische Zeitschrift 36 (1927), 193–225.

📌 Mémoire sur les singularités des fonctions algébriques, Dok l. Académie des sciences, mixed math. Ser., 37 (1928), 378–402.

📌 "On the rigidity of normal quasi-convex singularities of analytic type", Petitions of the USSR Academy of Sciences series physics and math (1978)

📌 Mathematicians from Moscow

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