SEMINARS

Project meetings: the PAT Seminars

The PAT Seminars are jointly organized by the four Research Units of the project, and are held both in person and online. If you wish to be included in our mailing list, and to receive the Zoom link for online attendance, please contact Davide Buoso or Luigi Provenzano.

• Bounds for Steklov eigenvalues of warped products, by Bruno Colbois (Université de Neuchâtel), February 7, 2024, Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Sapienza Università di Roma, room 1B1, 16:30 (GMT+1)
  Abstract. I will give sharp upper bounds for the Steklov eigenvalues of warped product between an interval [0,L] and a compact Riemannian manifold of dimension 2. I will also consider the case of revolution metrics on the ball of dimension n. In this situation, I will give sharp upper bound for the ratio of two consecutive eigenvalues, in the sense of a Payne-Polya-Weinberger inequality, and, in dimension 3, for the gap between two consecutive eigenvalues. These results are obtained in collaboration with Jade Brisson and Katie Gittins.

• Factorization of matrix-functions: Recent results and some applications, by Sergei Rogosin and Maryna Dubatovskaya (Belarusian State University), November 8, 2023, Dipartimento di Matematica "Tullio Levi-Civita", room 1BC45, 12.30 (GMT+1).
  Abstract. The content of the report is related to the project “Perturbation problems and asymptotics for elliptic differential equations: variational and potential theoretic methods” developed at the Department of Mathematics, Padova university. The report is addressed to the recent results in the factorization of matrix-function as well as in the development of the Wiener-Hopf technique. Partly it is related to the results presented during a one-month research programme “Bringing pure and applied analysis together via the Wiener–Hopf technique, its generalisations and applications” organized by the Isaac Newton Institute for Mathematical Sciences, Cambridge, UK. Among the theoretical results we mention perturbation analysis applied to the study of stability of partial indices and further development of the factorization of the triangular matrix-functions. A few applications are outlined in the report. First, we discuss the usage of the factorization technique to solve the R-linear conjugation problem, which is important for the study of different problems of elasticity and composite materials. Second, application to electromagnetic problems is briefly outlined. At last, we present some procedures which show how the Wiener-Hopf technique is working in analysis of static and dynamic problems of fracture mechanics.

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