Workshop Summary on Growth and Expansion in Groups

Definitions and mathematical statement

Formulation unavailable from the supplied record. The record for permanent UnsolvedMath ID $30005875$, source code catalogue entry, contains an incomplete workshop summary rather than a recoverable mathematical problem. Its supplied statement status is unrecoverable, and no clean statement is provided. Consequently, no precise conjecture, definitions, hypotheses, domains, boundary conditions, or quantifiers can be recovered without additional source material.

The passage reports seven individual lectures during the workshop and mentions the following topics: Vadim Alekseev (Dresden) discussed geometric property $(T)$ and its connection with property $(T)$ for sofic groups; Michal Doucha (Prague) discussed shadowing for actions on compact metric spaces, informally described as approximation of pseudo-orbits by actual orbits, and a reported shadowing result for hyperbolic groups acting on their "border"; Daniele Garzoni (Los Angeles) discussed the group large sieve method and random walks on groups with many quotients satisfying unspecified conditions. These are supplied descriptions of lecture topics and reported results, not a specified conjecture attributable to any of these speakers.

The initial word "conjecture" has no supplied antecedent. The random-walk sentence ends at "almost never" without identifying the event or conclusion. The precise relationship between the two properties $(T)$, the meaning and hypotheses of the reported boundary-action statement, and the quotient conditions and probabilistic quantifiers in the sieve discussion are absent. Thus there is no well-defined mathematical assertion here to state or resolve. The supplied label open records a curation decision concerning this incomplete extraction; it does not establish the existence or open status of a particular mathematical conjecture.

Short English statement

This record preserves an incomplete workshop summary about properties $(T)$, shadowing, and the group large sieve. It does not identify a precise mathematical problem. A statement requires recovery of the missing context and hypotheses; the supplied open label is a dated curation label.

Sources

• Local UnsolvedMath registry, permanent ID $30005875$, source code catalogue entry, title "Workshop Summary on Growth and Expansion in Groups," in the supplied Oberwolfach Reports Open Problems collection. The supplied record lists proposed year $2024$ and no proposer.
• Supplied report citation: Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, pp. 1005--1040, DOI 10.4171/owr/2024/17. Source URL and supplied literature-source link labelled "OWR report": https://doi.org/10.4171/owr/2024/17. The report citation is supplied provenance; it has not been independently consulted for this draft.
• Supplied lecture attribution: Vadim Alekseev (Dresden), Michal Doucha (Prague), and Daniele Garzoni (Los Angeles), for the respective topics described above. The record does not identify any of them as the proposer of a standalone problem.
• Supplied literature assessment, checked 2026-08-22: status open. The assessment says that the extracted passage is incomplete and consists of lecture-topic fragments, so no defensible resolution or counterexample can be assigned. This is supplied dated curation, not an independently verified literature assessment; time-sensitive status and cited claims require independent verification.
• Supplied statement-verification note: the official report is said to confirm that the extraction is workshop-summary prose and a list of lecture topics, rather than a standalone conjecture. No separate clean statement was promoted, and the original record was retained for provenance. This verification claim is supplied metadata, not a verification performed for this draft.