Open Problems in Thin Groups and Super-Approximation

Definitions and mathematical statement

Unrecoverable mathematical statement. The supplied record for permanent UnsolvedMath ID $30004870$, source code catalogue entry, contains a table-of-contents fragment rather than a mathematical assertion. Its supplied statement status is unrecoverable, and no clean statement is supplied. Consequently, no mathematical definitions, hypotheses, domains, boundary conditions, quantifiers, or conclusion can be recovered reliably from this record.

The fragment lists the following entries, with names and page numbers retained in their supplied sequence:

• "Conjecture", p. 2745; no associated name is recoverable from the fragment.
• Daniele Dona, "Approximate subgroups", p. 2747.
• Edna Jones, "Local-global I: Apollonian packings", p. 2750.
• Manuel Luethi, "Mixing and the decay of matrix coefficients", p. 2753.
• Antje Dabeler, "Exponential decay of matrix coefficients: the case of the critical exponent bigger than d2", p. 2756.
• Zhicheng Han, "Uniform exponential decay of matrix coefficients: the case of the critical exponent bigger than $d/2$", p. 2758.
• Wooyeon Kim, "Beyond Expansion Lecture I: Einsiedler-Lindenstrauss-Michel-Venkatesh Problem", p. 2761.
• Constantin Kogler, "On Spectral Gap of Compact Simple Lie Groups", p. 2763.
• Michael Chow, "Exponential mixing: the case of convex cocompact manifolds", p. 2768.
• Jeroen Winkel, "Expansion of SL2 (OK /I) with I square-free", p. 2770.

These are contents entries, not recovered problem statements or established problem attributions. The text d2 is retained without interpreting it as $d/2$, $d^2$, or another expression. Likewise, the symbols in "SL2 (OK /I)" have no supplied definitions. The record does not identify which entry, if any, is the intended mathematical target. Its supplied open label does not establish the existence or current status of a determinate conjecture.

Short English statement

The supplied passage is a table of contents covering several topics in thin groups and super-approximation. It does not identify a mathematical claim that can be stated precisely. UnsolvedMath ID $30004870$ therefore remains a statement-only provenance draft requiring recovery of the intended source passage and human mathematical review.

Sources

• Local UnsolvedMath registry: supplied complete record for permanent ID $30004870$, source code catalogue entry, titled "Open Problems in Thin Groups and Super-Approximation", in the "Oberwolfach Reports Open Problems" collection. The record supplies no proposer and records proposed year $2021$.
• Supplied report citation: Arbeitsgemeinschaft: Thin Groups and Super-approximation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/50, pp. 2721--2790. Supplied source URL and literature-source link labeled "OWR report": https://doi.org/10.4171/owr/2021/50. This reference is supplied provenance; the report has not been independently consulted for this draft.
• Supplied literature assessment, checked 2026-08-22: status "open"; the extracted text is a table-of-contents fragment rather than an identifiable mathematical claim, so no determinate resolution can be established. This is supplied dated curation derived from the OWR record, not an independently verified literature assessment. The supplied background requests independent verification of time-sensitive status and cited claims.
• Supplied statement-verification note: the official source passage is described as a table-of-contents fragment containing no mathematical claim; no separate clean statement is promoted, and the original record remains publicly visible for provenance. This description is retained as supplied, without asserting independent source verification.