Greg Galloway
Existence of CMC hypersurfaces in cosmological spacetimes
Constant mean curvature (CMC) spacelike hypersurfaces have played an important role in mathematical relativity, in particular in the study of the Einstein equations, both in terms of solving the initial data constraints, and in evolving CMC initial data. In this talk we review some older, and present some newer, existence results for CMC spacelike hypersurfaces in the class of cosmological (spatially closed) spacetimes. These results were motivated in part by the Bartnik splitting conjecture, as well as more recent conjectures of Dilts and Holst (arXiv:1710.03209). Some connections to the causal boundary of spacetime are also discussed. This is joint work with Eric Ling.
José M M Senovilla
Miguel's conjecture and some joint ventures
I will discuss some work by Miguel and in particular his conjecture concerning the existence of tensor fields with vanishing higher-order covariant derivative on Riemannian manifolds.
Olaf Müller
Browsing the universe
The talk explores Miguel Sanchez's contributions to the long-standing open question of the existence of Cauchy temporal functions and metric splittings on globally hyperbolic spacetimes, beginning with the ground-breaking joint result with Antonio Bernal answering this question, which allows for slicing the book of the universe into pages of equal time. The talk gives an overview of the history of this question and the answer as well as later refinements, ramifications and consequences, e.g. for symmetric-hyperbolic equations, steep temporal functions, closed isometric embeddings, conformal embeddings, and functors joining Lorentzian and Riemannian categories.
Alfonso Romero
This talk offers a warm and academic tribute to Professor Miguel Sánchez in celebration of his 60th birthday at the XII International Meeting on Lorentzian Geometry. Moving from early personal anecdotes starting in 1989 to his groundbreaking 1994 doctoral thesis, the address explores the core of his research philosophy: the balance between pioneering theory and constructive examples that opened new avenues in global Lorentzian geometry. In addition to reviewing his versatile scientific trajectory, special emphasis is placed on his outstanding human qualities, his dedication as a mentor to generations of younger mathematicians, and his pivotal role as a co-founder of this conference series in 2001.
Anna María Candela
Miguel and Bari: 30 years of friendship and research
The talk points out the bond of friendship and the scientific shared interests which link Miguel to Bari.