Department of Mathematics
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Institute of Algebra and Geometry
Research Group Algebraic and Geometric Topology
AG Algebraic und Geometric Topology

João Lobo Fernandes

Title:Stable moduli spaces of high dimensional manifolds
Speaker:João Lobo Fernandes
Time:Thursday, 08.05.2025, 14:30
Place:SR 3.69

Abstract:
Moduli spaces are geometric objects that classify families of mathematical structures: their points correspond to individual objects, while paths between points describe ways of deforming these objects. The study of moduli spaces sits at the crossroads of algebraic geometry, group theory, topology, and dynamics. In this talk, I will present a topologist’s perspective on moduli spaces, with a particular focus on moduli spaces of smooth manifolds and their homology. I will highlight three key phenomena that arise in this context: homological stability, the structure of stable homology, and stability of stable homology.