A bounded numerical solution with a small mesh size implies existence of a smooth solution to the Navier-Stokes equations
Tuesday, 1.12.20, 14:15-15:15, Hörsaal II, Virtual Raum Lasker
Abstract: We prove that for a given smooth initial value, if the finite element solution of the three-dimensional Navier-Stokes equations is bounded in a certain norm with a relatively small mesh size, then the solution of the Navier-Stokes equations with this given initial value must be smooth and unique, and is successfully approximated by the numerical solution.
Enriques surface fibrations of even index
Friday, 4.12.20, 10:30-11:30, SR 404
Equivariant Cerf theory and perturbative SU(n) Casson invariants
Monday, 7.12.20, 16:00-17:00, vSR 404 (Lasker)
In 1985, Casson introduced an invariant for integer homology 3-spheres by counting SU(2) representations of the fundamental groups. Boden-Herald generalized the Casson invariant to SU(3) by considering the critical orbits of perturbed Chern-Simons functionals. In this talk, we will present a construction of perturbative SU(n) Casson invariant for all n. The construction is based on an equivariant transversality argument of Wendl. This is joint work with Shaoyun Bai.
On variational models for martensitic inclusions
Tuesday, 8.12.20, 13:30-14:30, Hörsaal II (virtuell:Lasker)
Shape-memory alloys are special materials that are able to "remember" their original shapes after deformation. Microstructures in these materials are often modeled in the context of the calculus of variations by singularly perturbed multiwell elastic energy functionals. \nIn this talk, I shall discuss recent analytical results on variational models for martensitic nuclei based on linearized elasticity, and solutions to related partial differential inclusion problems.
... und wie erklärst du?
Tuesday, 8.12.20, 19:30-20:30, Hörsaal Rundbau, Albertstr. 21a
Fragt man Schülerinnen und Schüler, was eine gute Lehrkraft auszeichnet, nennen diese zumeist die Fähigkeit, gut erklären zu können. Doch was zeichnet verständliche und lernförderliche Erklärungen aus? Worauf sollten Lehrkräfte achten, wenn Sie Erklärungen für Schülerinnen und Schüler formulieren? Woran liegt es, dass viele Lehrkräfte durchaus in der Lage sind, gut zu erklären, dies jedoch im Schulkontext oftmals trotzdem nicht tun? Diesen und weiteren Fragen geht Frau Dr. Weinhuber in Ihrem interaktiven Vortrag am 8.Dez.2020 nach.
..sth around Riemann-Zariski space of valuations
Friday, 11.12.20, 10:30-11:30, SR 404
Thousand and one genes: Next Generation Sequencing for neurodevelopmental disorders
Friday, 11.12.20, 15:00-16:00, online: Zoom
Homogenität und Anisotropie in der ART
Monday, 14.12.20, 16:15-17:15, Kasparov
In diesem Vortrag werden wir sehen wie stark uns die\nForderung nach Homogenität und Isotropie bei der Suche nach Lösungen\nder Einsteinschen Feldgleichungen begrenzt. Besonders die Forderung\nnach Isotropie schränkt uns dabei ein und wir werden sehen was für\nModelle des Universums wir erhalten wenn wir diese fallen lassen.\n\n
Linear and nonlinear methods for model reduction
Tuesday, 15.12.20, 14:15-15:15, Hörsaal II (virtuell:Lasker)
We consider reduced order methods for the approximation of classes of high-dimensional functions, such as solutions of parametric PDEs. The usual approach to model reduction for parametric PDEs is to construct a low dimensional linear space Vn which accurately approximates the solution manifold and use it to built an effcient forward solver. In some cases, the construction of one suitable linear space Vn is not feasible numerically, for instance if the target accuracy is too small. It is well-known that nonlinear methods may provide improved effciency. In a so-called library approximation, the idea is to replace Vn by a collection of linear (or affine) spaces V1, . . . , VN of dimension m < n.\n\nIn this talk, we first introduce various analytic anisotropic model classes based on Taylor expansions and study their approximation by finite dimensional polynomial spaces PΛ described by lower sets Λ of cardinality n. Then, in the framework of parametric PDEs, we present a possible strategy that can be used to built a library and provide an\nanalysis of its performance.\n\nThis is a joint work with: A. Bonito, A. Cohen, R. DeVore, P.\nJantsch, and G. Petrova.
o-minimal homotopy theory
Friday, 18.12.20, 10:30-11:30, SR 404