Quantitative unique continuation or “If we don’t know everything, how much do we actually know”?

Matthias Täufer, Analysis group, FernUniversität in Hagen, Germany Date: 1th March 2024, Friday Time: 13:00 Place: DEU, Faculty of Science, Department of Mathematics, Room B255

Abstract: Unique continuation is a basic property of many partial differential equations stating that solutions vanishing on subsets must be identically zero. In many cases one would like to have a quantitative version of that, meaning that one can bound the norm of solutions by their norm on subsets. In this talk, we review some history of quantitative unique continuation and present several results on quantitative unique continuation in unbounded domains. Based on joint works with Ivica Nakic (Zagreb), Martin Tautenhahn (Leipzig), Sedef Özcan (Dokuz Eylül), Paul Pfeiffer (Hagen), Albrecht Seelmann (Dortmund) and Ivan Veselic (Dortmund).

How I Succeeded? From Student to Academician

This month’s theme of our career event, which we organized in cooperation with DEU Career Planning Center and DEU Faculty of Science Department of Mathematics, is “How I Succeeded”. The talk titled “From Student to Academician”, which we will hold under the moderation of our Mathematics Department KPMI Student Representative Ayşenur YAZICI and with the participation of Mathematics Department faculty member Asst.Prof. Dr. Murat ALTUNBULAK, is open to everyone and everyone who is interested is welcome.

Speaker: Asst.Prof.Dr. Murat ALTUNBULAK
Moderator: Ayşenur YAZICI
Date and Time: 23.02.2023, 12:00
Location: Classroom B256 (Faculty of Science, Department of Mathematics)

Computing eigenvalues of the discrete p-Laplacian via graph surgery

Matthias Hofmann, Texas A&M University Date: 16th February 2024, Friday Time: 13:00 Place: DEU, Faculty of Science, Department of Mathematics, Room B255

Abstract: We discuss the dependence of the eigenvalues and eigenfunctions for the discrete signed p-Laplacian under perturbation by a cut parameter. In particular, we prove a formula for the derivative of the eigenvalues and show that the eigenvalues of the discrete signed p-Laplacian on the original graph can be characterized via extremal points of the perturbed system. In this context, we elaborate on how graph surgery can be used in order to compute eigenvalues of the discrete (signed) p-Laplacian by looking at some examples. The derivation formula is reminiscent of the formula for linear eigenvalue problems given by the Hellmann-Feynman theorem and our results extend previous results for the linear case p=2 attained by [Berkolaiko, Anal. PDE 6 (2013), no. 5, 12131233].