Deformations of Lagrangian Q-submanifolds
Monday, 5.6.23, 16:00-17:00, Raum 125, Ernst-Zermelo-Str. 1
Positively graded symplectic Q-manifolds encompass a lot of well-known mathematical structures, such as Poisson manifolds, Courant algebroids, etc. Lagrangian submanifolds of them are of special interest, since they simultaniously generalize coisotropic submanifolds, Dirac-structures and many more. In this talk we set up their deformation theory inside a symplectic Q-manifold via strong homotopy Lie algebras.
Gluing spaces with Bakry-Emery Ricci curvature bounded from below
Monday, 12.6.23, 16:15-17:15, Raum 125, Ernst-Zermelo-Str. 1
In this talk I will explain the Bakry-Emery Ricci tensor and the metric gluing construction between two (weighted) Riemannian manifolds along isometric parts of their boundary. When the (weighted) Riemannian manifolds admit a lower bound for the (Bakry-Emery) Ricci curvature, I will present a necessary and sufficient condition such that the metric glued space has synthetic Ricci curvature bounded from below.
On Line Bundle Twists for Unitary Bordisms
Monday, 26.6.23, 16:15-17:15, Raum 125, Ernst-Zermelo-Str. 1
Classical theorems of Conner-Floyd and Hopkins-Hovey say that complex \(K\)-theory is completely determined by unitary bordism and \(\bmathrm{Spin}^c\) bordism respectively. The isomorphisms appearing in these theorems are induced by the maps that send a bordism class to its orientation-class in complex \(K\)-theory. Despite this geometric description, the proofs that they are indeed isomorphism are rather abstract and homotpy-theoretical.\n\nMotivated by theoretical physics, Baum, Joachim, Khorami and Schick extend Hopkins and Hovey’s result in a forthcoming paper to twisted \(\bmathrm{Spin}^c\) bordism and twisted \(K\)-theory. Here, the twists are given by (representatives of) elements in third integral cohomology.\n\nSince every almost complex structure induces a \(\bmathrm{Spin}^c\) structure and since the classical Conner-Floyd orientation factors through the Hopkins-Hovey orientation, one may wonder whether there is a twisted unitary bordism theory and a twisted Conner-Floyd orientation that extends the result of Baum, Joachim, Khorami and Schick ‘to the left’.\nIn this talk, I answer this question in the negative.