String topology of the space of paths with endpoints in a submanifold
Montag, 13.11.23, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
String topology is the study of algebraic structures on the homology of the free loop space of a closed manifold.\nThe most famous operation is the Chas-Sullivan product which is a graded commutative and unital product on the homology of the free loop space.\nIn this talk we study the space of paths in a manifold whose endpoints lie in a chosen submanifold.\nIt turns out that the homology of this space also admits a product which is defined similarly to the one of Chas and Sullivan.\nMoreover, the homology of this path space is a module over the Chas-Sullivan ring. \nWe will see that in some situations both structures together form an algebra - i.e. the product on homology of the path space with endpoints in a submanifold is an algebra over the Chas-Sullivan ring - but that this property does not hold in general.
Positive intermediate Ricci curvature, surgery and Gromov's Betti number bound
Montag, 20.11.23, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
Positive intermediate Ricci curvature is a family of interpolating curvature conditions between positive sectional and positive Ricci curvature. While many results that hold for positive sectional or positive Ricci curvature have been extended to these intermediate conditions, only relatively few examples are known so far. In this talk I will present several extensions of construction techniques from positive Ricci curvature to these curvature conditions, such as surgery, gluing and bundle techniques. As an application we obtain a large class of new examples of manifolds with a metric of positive intermediate Ricci curvature, including all homotopy spheres that bound a parallelisable manifold, and show that Gromov's Betti number bound for manifolds of non-negative sectional curvature does not hold from positive Ricci curvature up to roughly halfway towards positive sectional curvature. This is joint work with David Wraith.\n
Poisson structures from corners of field theories
Mittwoch, 29.11.23, 16:15-17:15, Hörsaal II, Albertstr. 23b
The BV formalism and its shifted versions in field theory have a nice compatibility with boundary structures. Namely, one such structure in the bulk induces a shifted (possibly degenerated) version on its boundary, which can be interpreted as a Poisson structure (up to homotopy). I will present the results for some field theories, in particular, 4D BF theory and 4D gravity.\n\n