Real Algebraic Geometry Workshop Overview

Definitions and mathematical statement

Formulation status. The supplied record is a workshop overview, not a standalone mathematical problem. Its statement status is recorded as unrecoverable. No precise conjecture, decision problem, or theorem with specified hypotheses and quantifiers can be recovered from this excerpt. The supplied label open reflects the stated curation normalization; it does not establish that every topic or reported result below is an open problem.

Mathematical content retained from the excerpt. The overview reports the following subjects, without supplying the definitions and hypotheses needed to formulate individual mathematical claims:

1. Annie Raymond discussed the reported undecidability of the general problem of deciding algebraic inequalities between graph homomorphism densities. The input class, interpretation of the inequalities, and class of graphs over which they are to hold are unspecified.
2. Evelyne Hubert discussed an approach to optimizing symmetric trigonometric functions over ${\mathbb{R}}^n$, with applications to exploring a spectral bound on chromatic numbers of set avoiding graphs. The functions, graphs, and bound are unspecified.
3. Peter Bürgisser discussed real zeros of random structured polynomials and a reported proof of a probabilistic version of the real $\tau$ conjecture. Neither the probability model nor the conjecture's precise version is supplied.
4. Hamza Fawzi introduced $k$-local Hamiltonian systems and described computing their ground energy through a large convex optimization problem using entropy constraints. The systems, constraints, and intended meaning or accuracy of computation are unspecified.
5. An incomplete sentence fragment refers to nonreduced projective schemes naturally associated with certain faces of the cone of nonnegative polynomials. Its missing context and attribution cannot be recovered from the supplied text.
6. Lorenzo Baldi reported a characterization of extreme rays of the cone of nonnegative forms on elliptic normal curves using their group law and the real geometry of their $2$-torsion points. The relevant hypotheses and characterization are absent.
7. Matilde Manzaroli reported a bound for the real Betti numbers of a smooth fiber of a real semistable degeneration near a certain special fiber $X_0$, in terms of the complex geometry of $X_0$. The conditions on the degeneration and special fiber, and the bound itself, are absent.
8. Rainer Sinn discussed real cubic surfaces and the Schläfli double six in computer vision; no mathematical question is specified.
9. Chiara Meroni reported partial progress on two questions described as open in the overview: classification of zonoids, and description of directional convex hulls as semialgebraic sets. No ambient dimension, classification criterion, definition of directional convex hull, permitted directions, or hypotheses on the input sets are supplied. These descriptions cannot be promoted to universally quantified problems without adding assumptions.
10. Julian Vill discussed fiber bodies of projected convex sets, particularly Gram spectrahedra of binary sextics and ternary quartics, for which the overview reports that facial structure can be determined rather explicitly. No precise construction or facial description is given.

Statement-only conclusion. The intended mathematical target remains unresolved. Selecting one of these topics, defining its objects, or supplying missing hypotheses would create a formulation not determined by the record. The reported results above are preserved as source attributions, not independently verified assertions.

Short English statement

This record summarizes talks from a 2023 workshop on real algebraic geometry. It mentions reported results and two broadly described convexity questions, but supplies no standalone problem with sufficient definitions and hypotheses. A precise mathematical statement cannot be extracted without further source material. The supplied open label is a curation designation, and the record requires human mathematical review.

Sources

• Local UnsolvedMath registry, permanent ID $30005469$, exact source code catalogue entry, title Real Algebraic Geometry Workshop Overview, in the supplied Oberwolfach Reports Open Problems collection. The record gives 2023 as the proposed year and supplies no individual proposer.
• Supplied source citation: New Directions in Real Algebraic Geometry (2023), Oberwolfach Reports, pp. 813--881, DOI 10.4171/owr/2023/15. Source URL and supplied literature-source link, labeled "original OWR report": https://doi.org/10.4171/owr/2023/15.
• The overview attributes the discussions to Annie Raymond, Evelyne Hubert, Peter Bürgisser, Hamza Fawzi, Lorenzo Baldi, Matilde Manzaroli, Rainer Sinn, Chiara Meroni, and Julian Vill. These are talk attributions; the record does not identify an author of a standalone problem.
• Supplied literature assessment dated 2026-08-22: the excerpt is an introductory survey listing topics and results, with no uniquely triageable mathematical claim; its status remains open under the stated normalization. This is supplied dated curation, not an independently verified literature assessment. The supplied background requests independent verification of time-sensitive status and cited claims.
• The supplied statement-verification field says that the official report confirms the extraction is a workshop-summary paragraph containing no standalone open problem. This verification claim is part of the supplied record and has not been independently checked here.