Fractional total variation denoising model with L^1 fidelity
Donnerstag, 2.6.22, 11:15-12:15, Raum 226, Hermann-Herder-Str. 10
We study a nonlocal version of the total variation-based model with \(L^1\) fidelity for image denoising,\nwhere the regularizing term is replaced with the fractional s-total variation.\nWe discuss regularity of the level sets and uniqueness of solutions, both for high and low values of the fidelity parameter.\nWe analyse in detail the case of binary data given by the characteristic functions of convex sets.\n
On the existence of isoperimetric sets on nonnegatively curved spaces
Donnerstag, 2.6.22, 12:15-13:15, Raum 226, Hermann-Herder-Str. 10
We consider the isoperimetric problem on Riemannian manifolds with nonnegative\nRicci curvature and Euclidean volume growth, i.e., such that the volume of balls grows\nlike the one of Euclidean ones as the radius diverges. The problem aims at minimizing the\nperimeter among sets having a fixed volume. Under an additional natural assumption on\nasymptotic cones to the manifold, we prove existence of minimizers, called isoperimetric\nsets, for any sufficiently large volume. The existence result holds without additional\nassumptions on manifolds with nonnegative sectional curvature.\nThe proof builds on an asymptotic mass decomposition result for minimizing sequences, on a sharp isoperimetric inequality, and on concavity properties of the isoperimetric profile.\nMore generally, the results hold on N-dimensional RCD(0, N) metric measure spaces,\nwhich are spaces having Ricci curvature bounded from below by zero in a generalized\nsense.\nThe results mentioned are contained in works in collaboration with G. Antonelli, E.\nBru`e, M. Fogagnolo, S. Nardulli, E. Pasqualetto, and D. Semola.
Donnerstag, 2.6.22, 15:15-16:15, Hörsaal II, Albertstr. 23b
Global properties of period maps at infinity
Freitag, 3.6.22, 10:30-11:30, Hörsaal II, Albertstr. 23b
Orbit Method: From Matrices to Unitary Representations
Dienstag, 14.6.22, 10:30-11:30, Raum 218, Ernst-Zermelo-Str. 1
The talk is intended as a leisurely introduction to one of the fundamental tasks of representation theory: the construction of irreducible unitary representations. I will first discuss two major sources of unitary representations of Lie groups, one from Symplectic Geometry (Kirillov theory) and another from Number Theory (Arthur’s conjecture). I will then introduce a constructive method called theta lifting which has been fruitful for representations of classical groups and discuss some recent applications of this method to unitary representation theory.\n
Theory and Implementation of Bowed Strings using Cosserat Rod theory and the Null Space method
Dienstag, 21.6.22, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
\n\nStarting point is the so called Helmholtz Motion discovered by Helmholtz in 1877 for bowed string instruments. We aimed to simulate the same motion.\nFirst we adapt the existence theory for struts designed as Cosserat Rod (Paper of S. Antman and T. Seidman [2005]) to a clamped violin string. The existence theory is still in progress.\nFocus is set on the implementation of a bowed string including bowing and torsional constraints that also can appear in bowed strings. We are able to show the same energy behavior as in the theoretical part.\nMoreover we present the Null Space method for Cosserat rods (Paper by P. Betsch [2005]) and how to apply it in this setting.\nThe second main aspect is the inclusion of a two-step algorithm to realize mechanical damping in order to get the desired energy decay and get more realistic simulations.\nFinally, numerous simulations are shown produced with C++ and MatLab.
Blockfilters as Parameter Sets of Tree-Forcings
Dienstag, 21.6.22, 14:30-15:30, Raum 404, Ernst-Zermelo-Str. 1
The space of blocks consists of all non-empty finite sets of natural numbers. Given any filter on the natural numbers, the sets of blocks of filter elements generate a filter on the blockspace and, vice versa, each filter on the blockspace yields a filter on the natural numbers by taking unions of filter elements.\nIn this talk, we will make some observations about this relation and the question of whether the maximality of filters is or can possibly be preserved by it. As an application we will show how filters and coideals on the blockspace can be used as parameter sets of tree-forcings with the aim of diagonalizing a given filter on the natural numbers.\n \n
Binomialkoeffizienten - verstehen oder rechnen?
Dienstag, 21.6.22, 19:30-20:30, Hörsaal II, Albertstr. 23b
\nIn diesem Vortrag geht es um Altbekanntes, aber offenbar in Vergessenheit Geratenes, nämlich Konzepte und nachhaltige Erkenntnis im Zusammenhang mit Binomialkoeffizienten. Dabei spielen binäre Tupel eine Schlüsselrolle. Diese Tupel sind auch grundlegend für ein wirkliches Verständnis der Binomialverteilung, die momentan als Schlüsselkonzept fungiert.
The derived category of permutation modules
Freitag, 24.6.22, 10:30-11:30, Hörsaal II, Albertstr. 23b
To a field k and a finite group G one associates the derived\ncategory of kG-modules, an important invariant that is difficult to\nunderstand in general. At least, its tensor-triangulated structure\nadmits a familiar description in terms of the support variety.\n\nWe propose to study a refinement, the derived category of G-permutation\nmodules over k. It has interesting interpretations in algebraic\ngeometry, representation theory and equivariant homotopy theory. We\nwill say a few things we know about its tensor-triangulated structure. \nThis is based on joint work, mostly in progress, with Paul Balmer.
Generalised Tree Properties
Dienstag, 28.6.22, 14:30-15:30, Raum 404, Ernst-Zermelo-Str. 1
The talk will be a survey of my master's thesis. The topic of the thesis are two cardinal properties which are similar to the tree property and arise naturally from the consideration of a generalised tree.\nWe will first introduce both properties and then outline their similarities and differences, both in the way they can be proven consistent at small cardinals and what they imply.\nWe will show that, despite being equivalent for inaccessible cardinals, one property is strictly stronger than the other at small cardinals.