Mark Agranovsky (Bar Ilan & HIT, Izrael): On integrable domains and surfaces

SZTE, TTIK, Bolyai Intézet, Kerékjártó szeminárium (online)

Absrract.  Integrability (algebraic, polynomial, rational, etc.) of domains or surfaces in $\mathbb{R}^n$ is defined in terms of sectional or solid volume functions, evaluating the volumes of the intersections, respectively, with affine planes or half-spaces.
The question: ``to what extent the shape of a domain is determined by the algebraic type of its volume function?'' is motivated by a problem of V.I. Arnold about describing algebraically integrable domains, which in turn goes back to the Newton’s Lemma about ovals.
The talk is devoted to recent results concerning the above question.

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