last seminars

Applications of Symplectic Supergeometries in Particle, String and Membrane Models

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Cem Yetişmişoğlu, İstanbul Technical University Postdoctoral Researcher.

Date: 30th of  April, 2024, Tuesday.

Time: 11.30 – 12.30.

Place: Zoom (https://itu-edu-tr.zoom.us/j/94090890378?pwd=RHpFc1l6MFBjcWU3ZGdidW9qcWRGUT09

Meeting ID: 940 9089 0378

Passcode: 035170.)

Abstract: In this talk we will talk about symplectic supergeometries and their applications coming from different areas of mathematical physics. In the first part, we will look at an application regarding statistical mechanical applications to systems with discrete degrees of freedom (math-ph:2311.05711). In the second part, we will talk about algebraic structure of symmetries associated with string/membrane models which are called algebroids. Moreover for string dualities one is interested in bialgebroids and their Drinfel’d doubles. These notions can naturally be studied using symplectic supergeometries (Voronov, Roytenberg). In this talk we will talk about reformulations of these structures in terms of vector bundles and calculi that we defined on them (hep-th:2312.06584).

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

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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

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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].