The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on July 4, 2023 at 2:00 pm (UTC+3)  in Room 478 of IMI. A talk on: Independence Structures in Random Matrix Theory and Random Partitions  will be delivered by Yacine Barhoumi-Andréani, University of Bochum, Germany. Everybody is invited. Abstract.We consider two models of random objects: eigenvalues of random matrices and random integer partitions for two classical measures: the GUE and the Schur measure. We express the largest element of these sets as maxima of independent random variables. The method uses orthogonal polynomials on the real line in the random matrix case and on the unit circle in the second case. The distribution involved in the random matrix case uses the [...]

The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on June 13, 2023 at 1:00 pm (UTC+3)  in Room 478 of IMI. A talk on: Functions holomorphic over finite-dimensional complex commutative algebras  will be delivered by Marin Genov, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences. Everybody is invited. Abstract. Every morphism 𝜑:𝐴 →𝐵 in the category of finite-dimensional complex commutative associative unital (Banach) algebras gives rise to a structure sheaf of functions of a single 𝐴-variable and taking values in 𝐵 and whose differential respects the 𝐴-module structure of 𝐵. Even though these are holomorphic mappings of several complex variables, it turns out they also share many features of the theory of holomorphic functions of a single [...]

The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on May 9, 2023 at 2:00 pm (UTC+3)  in Room 478 of IMI. A talk on: Riemannian four-manifolds and twistor spaces: some rigidity results  will be delivered by Davide Dameno, Department of Mathematics "Federigo Enriques", University of Milan. Everybody is invited. Abstract. It is well-known that four-dimensional Riemannian manifolds carry many peculiar properties, which give rise to the existence of unique canonical metrics. In order to find conditions for the existence of such metrics, in 1978 Atiyah, Hitchin and Singer adapted Penrose’s construction of twistor spaces to the Riemannian context, paving the way for the study of many other characterizations of curvature properties for Riemannian four-manifolds. After giving an overview [...]

The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on May 2, 2023 at 2:00 pm (UTC+3)  in Room 478 of IMI. A talk on: Introduction to spectral graph theory 3  will be delivered by Peter Petrov, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences. Everybody is invited.

The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on April 18, 2023 at 2:00 pm (UTC+3)  in Room 478 of IMI. A talk on: Introduction to spectral graph theory 2  will be delivered by Peter Petrov, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences. Everybody is invited. Abstract. In the second lecture we will ntroduce the incidence matrix and the line graph of given graph with their properties. Spectral graph drawing and partition into clusters will be discussed also. Unlike the first talk when the stress was on the motivation, in this talk it will be on results accompanied by typical examples.

The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on April 4, 2023 at 2:00 pm (UTC+3)  in Room 478 of IMI. A talk on: Introduction to spectral graph theory  will be delivered by Peter Petrov, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences. Everybody is invited. Abstract. This is the first lecture of a series of 2-3 lectures on algebraic graph theory. A very basic knowledge in linear algebra should be enough as a prerequisite, so that the talk could be understood by people from informatics or biology, also by students. Simple examples will accompany any notion. All knowledge needed from graph theory will be given. The Laplacian of a simple graph will be defined, showing [...]

The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on November 15, 2022 at 11:00 am (UTC+3)  in Room 478 of IMI. A talk on: Zener model with General fractional calculus: Thermodynamical Restrictions  will be delivered by Teodor M. Atanackovic and Stevan Pilipovic, Serbian Academy of Sciences and Arts and University of Novi Sad, Serbia. Everybody is invited. Abstract. We study a Zener type model of viscoelastic body within the context of general fractional calculus and derive restrictions on coefficients that follow from the dissipation inequality that is, the entropy inequality under isothermal conditions. We show, for a stress relaxation and a wave propagation, that the restrictions that follow from the entropy inequality are sufficient to guarantee the existence [...]

The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on November 8, 2022 at 1:30 pm (UTC+3)  in Room 478 of IMI. A talk on: Surfaces Associated with Pascal and Catalan Triangles  will be delivered by Leonard DAUS1, Marilena JIANU1 and Adela MIHAI1,2 1 Technical University of Civil Engineering Bucharest, Romania 2 Transilvania University of Brasov, Romania. Everybody is invited. Abstract. An open problem in reliability theory is that of finding all the coefficients of the reliability polynomial associated with particular networks. Because reliability polynomials can be expressed in Bernstein form (hence linked to binomial coefficients), it is clear that an extension of the classical discrete Pascal’s triangle (comprising all the binomial coefficients) to a continuous version [...]

The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on April 28, 2022 at 1:00 pm (UTC+3)  in Room 478 of IMI. A talk on: Isotropic Killing vector fields and structures on complex surfaces  will be delivered by Gueo Grantcharov, Florida International University, USA. Everybody is invited. Abstract. In a 4-dimensional vector space with scalar product of signature (2,2), two independent vectors spanning a maximal isotropic (null) plane determine a canonical action of the para-quaternioins. We noticed that on an oriented 4-manifold with such pseudo-Riemannian metric, existence of two isotropic (null) Killing vector fields leads to integrability of the induced structure - called para-hypercomplex, and the metric is anti-selfdual. Using the Kodaira classification one can describe the [...]