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).

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].


Prof. Dr. Güçkan YAPAR, Department of Statistics, Faculty of Science, DEU, İzmir Date: December 13, 2023, Wednesday Time: 15:00 Place: Classroom B256, Department of Mathematics, Faculty of Science, DEU, İzmir.

Abstract: ATA forecasting method is a new method which is proposed as an alternative to basic forecasting method exponential smoothing (ES) and ARIMA. Although Ata method is structurally similar to the ES method but it is completely different in content. Ata method is simple, fast and more accurate than its alternatives. Ata method has taken its place in the literature by proving its success with its forecasting performance in M-competition data sets.

On rings whose cyclic modules have cyclic injective hulls

Prof. Dr. Christian Lomp, Department of Mathematics, University of Porto in Porto, Portugal. Date: 19th of April 2023, Wednesday. Time: 11:00. Place: Online/Microsoft Teams- Meeting ID: 351 128 968 15 Passcode: Gy4n4B

Abstract: In 1964, Barbara Osofsky proved in her PhD thesis that a ring whose cyclic modules are injective is semisimple Artinian. William Cadwell in his PhD thesis from 1966 studied when injective hulls of cyclic modules are cyclic and termed them hypercyclic rings. He characterised left perfect left hypercyclic rings as well as commutative local hypercyclic rings. In this talk we will revise the literature on rings whose cyclic modules have cyclic injective hulls and present some more recent results, obtained jointly with Mohamed Yousif and Yiqiang Zhou.