This is the book of abstracts from the workshop. It includes research topics in differential geometry, Riemannian geometry, and geometric analysis. Below is a summary of the abstracts:
1. Shuli Chen discusses the long-standing conjecture that closed aspherical manifolds do not admit positive scalar curvature (PSC) metrics. The study extends previous results to show that certain connected sums and modified manifolds also lack complete PSC metrics.
2. Azahara de la Torre Pedraza explores the problem of prescribing non-constant Q and T curvatures on the four-dimensional upper hemisphere. This is an extension of classical curvature prescription problems, and the results rely on a non-standard variational approach.
3. Anna Maria Fino presents an overview of strong geometries with torsion, focusing on metric connections with skew-symmetric torsion, particularly in Hermitian and \( G_2 \)-structured 7-manifolds.
4. Alba Dolores García Ruíz investigates high-energy Laplace eigenfunctions in integrable billiards, analyzing their behavior in relation to Berry’s random wave conjecture.
5. Lilia Mehidi studies fundamental groups of compact manifolds in relation to Auslander’s conjecture. The work examines affine and plane wave structures, connecting them to the Lorentzian conformal Lichnerowicz conjecture.
6. Artemis Aikaterini Vogiatz introduces a new quartic curvature pinching condition for submanifolds under mean curvature flow. The research provides codimension estimates and describes the long-term behavior of such submanifolds.
This compilation highlights contemporary advances in geometry, particularly in curvature analysis, geometric flows, and topology.