tba
Montag, 1.2.21, 16:15-17:15, vSR318 (Kasparov)
Spectral theory of infinite-volume hyperbolic manifolds
Montag, 1.2.21, 16:15-17:15, vSR318 (Kasparov)
In this talk, we define a twisted Laplacian on an orbibundle over a hyperbolic surface (that might be of infinite volume). We prove the meromorphic continuation of the resolvent to the entire complex plane and prove an upper bound on the number of resonances. Additionally, we introduce the corresponding scattering matrix and prove an explicit formula for its determinant in terms of the Weierstrass product over the resonances.\n\nThis is a joint work with M. Doll and A. Pohl.\n\nP.S. The announcement is duplicated, because I have forgotten the password for the previous announcement.
Singular Solutions and Adaptive Approximations of Total Variation Problems
Dienstag, 2.2.21, 14:15-15:15, Hörsaal II (virtuell:Lasker)
Total variation problems are often encountered in image denoising, for example in the well-known Rudin-Osher-Fatemi model. Since the model admits all functions of bounded variation, the P1 finite element method converges suboptimal in this case. In recent works from Chambolle & Pock and Bartels, the approximation via Crouzeix-Raviart finite elements was analyzed and error estimates were established if the dual solution of the problem is Lipschitz continuous.\n\nWe will show an example with a non-Lipschitz continuous dual solution of the Rudin-Osher-Fatemi model on which the optimal convergence rate is still achieved. With a graded grid approach, we are able to improve the converge rates from uniform grids on examples where the primal solution is piecewise constant. With a reconstruction formula for the Crouzeix-Raviart finite elements to obtain a feasible dual solution, we are able to use the dual-gap error estimator presented in a recent work from Bartels & Milicevic to adaptively refine the mesh grid. This more general approach results in improved experimental convergence rates, which are slightly slower than the obtained convergence rates on graded grids. This is the presentation of the results of my master thesis.\n
tba
Freitag, 5.2.21, 10:30-11:30, SR 404
Multi-state models for inferring patient pathways from clinical routine data
Freitag, 5.2.21, 15:00-16:00, online: Zoom
The Laplace on unbounded domains with mixed boundary conditions
Montag, 8.2.21, 16:15-17:15, vSR318 (Kasparov)
In the first part we are going to talk about basic preliminaries to show existence of solutions of the Possion problem.\nIn the second part we will see the invertibility of the Laplace with mixed boundary conditions on manifolds with finite width and bounded geometry. I will also adress the problems in generalising the former proof to the problem with pure Neumann conditions.
Dienstag, 9.2.21, 14:15-15:15, Hörsaal II (virtuell:Lasker)
Variational convergences for functionals and differential operators depending on vector fields
Dienstag, 9.2.21, 14:15-15:15, Hörsaal II (virtuell: Lasker)
In this seminar, I present an extract of my PhD thesis, which concerns variational convergences for functionals and differential operators depending on a family of locally Lipschitz continuous vector fields X. This setting was introduced by Folland and Stein and has recently found numerous applications in the literature. The convergences taken into account date back to the 70’s and are Γ-convergence, introduced by Ennio De Giorgi and Tullio Franzoni, dealing with functions and functionals, and H-convergence, whose theory was initiated by François Murat and Luc Tartar and which deals with differential operators.\nThe main result presented today, under a linear independence condition on the family of vector fields X, is a Γ-compactness theorem and ensures that sequences of integral functionals depending on vector fields, with standard regularity and growth conditions, Γ-converge in the strong topology of Lp, up to subsequences, to a functional belonging to the same class.\nAs an interesting application of the Γ-compactness theorem, I finally show that the class of linear differential operators in X-divergence form is closed in the topology of the H-convergence. The variational technique adopted to this aim relies on a new approach recently introduced by Nadia Ansini, Gianni Dal Maso and Caterina Ida Zeppieri.
Use the Market’s Heartbeat to Predict Extreme Financial Risks
Freitag, 12.2.21, 12:00-13:00, online: Zoom
Deep Learning for Tabular Datasets
Freitag, 12.2.21, 15:00-16:00, online: Zoom
Complex rank 3 vector bundles on CP^5
Freitag, 12.2.21, 15:00-16:00, zoom
Given the ubiquity of vector bundles, it is perhaps\nsurprising that there are so many open questions about them -- even on\nprojective spaces. In this talk, I will outline some results about\nvector bundles on projective spaces, including my ongoing work on\ncomplex rank 3 topological vector bundles on CP^5. In particular, I\nwill describe a classification of topological bundles which involves a\nsurprising connection to topological modular forms; a concrete,\nrank-preserving additive structure which allows for the construction of\nnew rank 3 bundles on CP^5 from "simple" ones; and future directions\nrelated to this project, including questions I have about how to make\nthis picture more "algebraic".\n
Gelfand-Tripel
Montag, 15.2.21, 16:15-17:15, vKasparov
On the space of metrics with invertible Dirac operator
Donnerstag, 25.2.21, 15:00-16:00, Sonderkolloquium – Angewandte Mathematik virtueller Konferenzraum 3 (Konferenz3210)
Ammann, Dahl and Humbert showed that the property that a manifold admits a metric with invertible Dirac operator persists under the right surgeries. That is the Dirac-counterpart of the Gromov-Lawson construction on the question of existence of postive scalar curvature metrics and has also implications on this question. \nWe consider now the question whether we can also obtain a homotopy equivalence statement for spaces of metrics with invertible Dirac operator under surgery in the spirit of the positive scalar curvature result by Chernysh/Walsh. This is joint work with N. Pederzani.\n
Deep Learning for Brain Signals
Freitag, 26.2.21, 12:00-13:00, online: Zoom