Related papers: Oberwolfach report : Discretization of Hilbert com…
This short note gives an overview of how a few conjectures and theorems of the author and collaborators fit together. It was prepared for Oberwolfach's workshop Differentialgeometrie im Gro{\ss}en, 28 June - 4 July 2015, and contains no new…
These are the notes from an Oberwolfach Seminar which we ran from 23--29 May 2010.
This is an extended abstract of my talk at the Oberwolfach Workshop "Algebraic Groups" (April 22 - 28, 2007). It is based on a joint work with H.Derksen and J.Weyman (arXiv:0704.0649v2 [math.RA]).
This is an extended abstract of my talk at the Oberwolfach-Workshop "Representation Theory of Finite-Dimensional Algebras" (February 6 - 12, 2005). It gives self-contained and simplified definitions of quantum cluster algebras introduced…
This is an overview of recent developments regarding the complexity of matrix multiplication, with an emphasis on the uses of algebraic geometry and representation theory in complexity theory.
This is an extended abstract of my talk at the Oberwolfach Workshop "Representation Theory of Quivers and Finite-Dimensional Algebras" (February 12 - February 18, 2023 ). It is based on a joint work with R. Bennett-Tennenhaus…
This is an extended abstract for the Oberwolfach Workshop 2101b \emph{Geometry, Dynamics and Spectrum of Operators on Discrete Spaces} organized by David Damanik, Matthias Keller, Tatiana Smirnova-Nagnibeda, and Felix Pogorzelski. It took…
In this work, we introduce a novel abstract framework for the stability and convergence analysis of fully coupled discretisations of the poroelasticity problem and apply it to the analysis of Hybrid High-Order (HHO) schemes. A relevant…
A low-order nonconforming finite element discretization of a smooth de Rham complex starting from the $H^2$ space in three dimensions is proposed, involving an $H^2$-nonconforming finite element space, a new tangentially continuous…
This article reports on the confluence of two streams of research, one emanating from the fields of numerical analysis and scientific computation, the other from topology and geometry. In it we consider the numerical discretization of…
These are the notes from lectures I gave at the Oberwolfach Seminar "Tensor Triangular Geometry and Interactions" which was held in October 2025. The aim of these notes is twofold: We develop notions of support for triangulated categories,…
We want to propose a new discretization ansatz for the second order Hessian complex exploiting benefits of isogeometric analysis, namely the possibility of high-order convergence and smoothness of test functions. Although our approach is…
This is an extended abstract of my talk at the Oberwolfach-Workshop "Representation Theory of Finite-Dimensional Algebras" (19-24 January 2020). It introduces a geometric orbifold model for the bounded derived category of a skew-gentle…
We investigate the Hilbert complex of elasticity involving spaces of symmetric tensor fields. For the involved tensor fields and operators we show closed ranges, Friedrichs/Poincare type estimates, Helmholtz type decompositions, regular…
This is an extended abstract of my talk at the Oberwolfach Workshop ''Cluster Algebras and Related Topics'' (December 8 - 14, 2013). It is based on a joint work with A. Zelevinsky (arXiv:1306.3495).
A scheme to form a basis and a frame for a Hilbert space of quaternion valued square integrable function from a basis and a frame, respectively, of a Hilbert space of complex valued square integrable functions is introduced. Using the…
In this work we develop a novel fully discrete version of the plates complex, an exact Hilbert complex relevant for the mixed formulation of fourth-order problems. The derivation of the discrete complex follows the discrete de Rham…
In this work we investigate from a broad perspective the reduction of degrees of freedom through serendipity techniques for polytopal methods compatible with Hilbert complexes. We first establish an abstract framework that, given two…
This is an extended abstract for a survey talk given in Oberwolfach on 1st December 2022, slightly updated in June 2023. I survey some work around the notion of quasiminimality and some of the progress towards Zilber's conjecture from the…
A survey of general results on the singularities of inverses to meromorphic functions is given, with applications to holomorphic dynamics. This is a lecture delivered at the workshop "The role of complex analysis in complex dynamics" in…