Foundations of Convex Algebraic Geometry

Definitions and mathematical statement

The supplied record, titled "Foundations of Convex Algebraic Geometry," contains the question

What is convex algebraic geometry?

It additionally states: "The report passage is retained verbatim as the relevant context for this extracted problem." However, no further report passage or mathematical definition is included in the supplied record.

The supplied statement-verification field reports that the official report immediately answers this expository heading by defining convex algebraic geometry, and that the heading is not posed as an open mathematical problem. It further states that no separate clean statement is promoted and that the original record remains publicly visible for provenance. The supplied statement status is therefore recorded as unrecoverable.

No precise mathematical assertion, conjecture, or requested construction can be recovered from this record. In particular, it supplies no mathematical objects, hypotheses, domains, quantifiers, boundary conditions, or criterion for a successful answer. A definition of the subject or a substitute conjecture would require additional source material and cannot be supplied as the intended problem on this evidence. The registry's open label is preserved as supplied metadata; it does not establish that this expository question is an open mathematical problem.

Short English statement

The record asks what convex algebraic geometry is. Its supplied verification identifies this as an expository heading answered in the report, rather than an open problem. The relevant definition and any distinct mathematical target are absent, so a precise problem statement cannot be recovered.

Sources

• Local UnsolvedMath registry, permanent ID $30004946$, source problem code catalogue entry, title "Foundations of Convex Algebraic Geometry." The record belongs to the Oberwolfach Reports Open Problems collection. No individual proposer is supplied; the proposed-year field is $2021$.
• Supplied report citation: Convex Geometry and its Applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/59, pp. 3187--3266. Supplied source URL and literature-source link, labeled "original OWR report": https://doi.org/10.4171/owr/2021/59.
• Supplied literature assessment dated 2026-08-22: the record is labeled open under the stated uncertainty rule because the extracted question is broad and has no precise claim or success criterion. This is supplied dated curation, not an independently verified literature assessment. The background requests independent verification of time-sensitive status and cited claims.
• Supplied statement verification: the official report is reported to answer the heading with a definition, rather than pose it as an open mathematical problem. This source characterization has not been independently verified here. No authoritative citation identifying a distinct open mathematical claim is supplied.