The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on October 30, 2018 at 14:00 in Room 478 of IMI. A talk on: Nash problem in arc spaces will be delivered by Peter Petrov, IMI-BAS. Everybody is invited. Abstract. After introducing briefly the arc and jet spaces of an algebraic variety with examples I will state the Nash theorem and I will formulate the Nash problem. The main results obtained will be mentioned, together with the counterexamples in dimension 4 (Kollar and Ishii) and 3 (de Fernex). Then will be stated the Nash problem for pairs and will be shown its solution in the case of pairs of toric varieties, obtaining from it  positive answer of Nash [...]

The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on September 18, 2018 at 14:00 in Room 478 of IMI. A talk on: Existence and Multiplicity of Solutions for Higher-order p-Laplacian Differential and Fractional Equations will be delivered by Stepan Tersian. Everybody is invited. Abstract. The multiplicity of periodic solutions for 2n-th order p-Laplacian differential equations is studied. Variational method and generalized Clark’s theorem are applied. Dirichlet’s problem for fractional differential equations is also considered. The results are published in the papers [1], [2] and [3]. [1] P. Drábek, M. Langerová, S. Tersian, Existence and multiplicity of periodic solutions to one-dimensional p-Laplacian, Electronic Journal of Qualitative Theory of Differential Equations 2016, No. 30, 1–9. [2] L. Saavedra, [...]

The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on June 05, 2018 at 14:00 in Room 478 of IMI. A talk on: Geodesic flow, Laplace spectra, and quantization on Riemannian symmetric spaces of rank one will be delivered by Gueo Grantcharov, Florida International University, USA. Everybody is invited. Abstract. In a project, joint with D. Grantcharov, we extend the observation by I. Mladennov and V. Tsanov that the eigenvalues and eigenspaces of the Laplace operator on the sphere correspond via specific quantization scheme to the energy level of the geodesic flow, to Riemannian symmetric spaces of rank one. In the talk I'll discuss also the relations with other constructions like twistor theory and possible extension to [...]