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Recent decades have witnessed a shift in interest from isolated objects to families of objects and their limit behavior, both in algebraic geometry and in commutative algebra. A series of various invariants have been introduced in order to measure and capture asymptotic properties of various algebraic objects motivated by geometrical ideas. The major goals of this workshop were to refine these asymptotic ideas, to articulate unifying themes, and to identify the most promising new directions for study in the near future. We expect the ideas discussed and originated during this workshop to be poised to have a broad impact beyond the areas of algebraic geometry and commutative algebra.
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Thomas Bauer, Susan Cooper, Brian Harbourne, Justyna Szpond, Mini-Workshop: Asymptotic Invariants of Homogeneous Ideals. Oberwolfach Rep. 15 (2018), no. 4, pp. 2739–2767