Profinite Sets and Extremally Disconnected Sets
Friday, 10.3.23, 10:00-11:00, Hörsaal II, Albertstr. 23b
This lecture is providing back ground knowledge for the Crash Course in the following week.
Ext-Groups
Friday, 10.3.23, 14:00-15:00, Hörsaal II, Albertstr. 23b
Lecture 1
Monday, 13.3.23, 10:00-11:00, Hörsaal II, Albertstr. 23b
Hopf-Galois extension in noncommutative differential geometry
Monday, 13.3.23, 15:00-16:00, Raum 404, Ernst-Zermelo-Str. 1
In this seminar I give a gentle introduction to the theory of Hopf-Galois extensions and their role in noncommutative differential geometry. From a geometric point of view they correspond to principal bundles on noncommutative algebras with a Hopf algebra replacing the structure group. Principality of such a bundle can equivalently be phrased in terms of a noncommutative Atiyah sequence. We continue by discussing differential calculi on Hopf-Galois extensions, proving that in the faithfully flat case such a calculus amplifies to a graded Hopf-Galois extensions if and only if the corresponding Atiyah sequence is exact, as well. As an example we discuss the q-monopole fibration. The presentation is partially based on a collaboration with Aschieri, Fioresi and Latini.
Lecture 2
Tuesday, 14.3.23, 10:00-11:00, Hörsaal II, Albertstr. 23b
Discrete hyperbolic curvature flow in the plane
Tuesday, 14.3.23, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
\n\nAbstract: Hyperbolic curvature flow is a geometric evolution equation that in the plane\ncan be viewed as the natural hyperbolic analogue of curve shortening flow.\nIt was proposed by Gurtin and Podio-Guidugli to model certain wave\nphenomena in solid-liquid interfaces. We propose a semidiscrete finite difference method\nfor the approximation of hyperbolic curvature flow and prove error bounds in natural norms.\nWe also present numerical simulations, including the onset of singularities starting\nfrom smooth strictly convex initial data. This is joint work with Robert N\b"urnberg (Trento).
Lecture 3
Wednesday, 15.3.23, 10:00-11:00, Hörsaal II, Albertstr. 23b
Lecture 4
Thursday, 16.3.23, 10:00-11:00, Hörsaal II, Albertstr. 23b
Lecture 5
Friday, 17.3.23, 10:00-11:00, Hörsaal II, Albertstr. 23b
Lecture 6
Friday, 17.3.23, 14:00-15:00, Hörsaal II, Albertstr. 23b
Rhine Seminar on Transcendence
Thursday, 23.3.23, 10:30-11:30, IRMA Strasbourg