Generalization/Refinement of the t-birational Section Conjecture

The t-birational Section Conjecture (t-BSC) is one of the several
conjectures resulting from Grothendieck's Section Conjecture (SC).
The t-BSC was formulated by Bresciani (it seems, inspired by work
of Esnault-Wittenberg) and proved (Inventiones 2024) in the context
of SC. In this talk I plan to give a quick introduction to the several
variants of SC, and further present both: First, a wide generalization
of the context in which t-BSC holds, and second, a 'minimalistic'
refinement of t-BSC, in which one uses only minimal geometrical
Galois information. The presentation is accessible to anyone who
is familiar with basics of algebraic geometry and basics of (etale)
fundamental groups / Galois Theory.