3 problems

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Bodirsky–Schneider–Thom conjecture on singular mixed identities in oligomorphic groups
Bodirsky–Schneider–Thom conjecture. If $G\curvearrowright\Omega$ is oligomorphic, then all mixed identities of $G$ are singular.
Conjectureopengroup-theory mixed-identities oligomorphic-groupsarXiv posted 2 days ago
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Non-singular mixed identities conjecture for the orientation-preserving homeomorphism group of the interval
Non-singular mixed identities conjecture. There do not exist non-singular mixed identities for
Conjectureopengroup-theory homeomorphism-groups mixed-identitiesarXiv posted 2 days ago
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Singularity conjecture for mixed identities of oligomorphic automorphism groups
Singularity conjecture. Every mixed identity for the group $\operatorname{Aut}(X,R)$ is singular.
Conjectureopenautomorphism-groups mixed-identities oligomorphic-groupsarXiv posted 2 days ago

Bodirsky–Schneider–Thom conjecture on singular mixed identities in oligomorphic groups