The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on October 22, 2024 at 2:00 pm (UTC+2)  in Room 478 of IMI. A talk on: Higher order estimates for Monge-Ampere type equations motivated by quaternionic geometry  will be delivered by Marcin Sroka, Jagiellonian University, Kraków, Poland. Everybody is invited. Abstract. In the talk I will discuss obstacles for obtaining higher order a priori estimates for equation introduced by Alesker and Verbitsky in 2010 on HKT manifolds in relation to Calabi type conjecture on those manifolds (and similar type PDEs studied since on hypercomplex manifolds). After presenting the state of art, I will focus on the key second order estimate. For the real Monge-Ampere equation on Riemannian manifolds it [...]

The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on October 15, 2024 at 2:00 pm (UTC+2)  in Room 478 of IMI. A talk on: Unimodality Preservation by Ratios of Functional Series and Integral Transforms  will be delivered by Dmitrii Karp, Holon Institute of Technology, Holon, Israel. Everybody is invited. Abstract. Elementary, but very useful lemma due to Biernacki and Krzyz (1955) asserts that the ratio of two power series inherits monotonicity from that of the sequence of ratios of their corresponding coefficients. Over the last two decades it has been realized that, under some additional assumptions, similar claims hold for more general series ratios and integral transforms as well as for unimodality in place of monotonicity. In [...]

The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on January 23, 2024 at 2:00 pm (UTC+2)  in Room 478 of IMI. A talk on: Complex Dirac structures on flag manifolds  will be delivered by Carlos Augusto Bassani Varea, Universidade Tecnológica Federal do Paraná, Brazil. Everybody is invited. Abstract.In this talk we present a description of the invariant complex Dirac structures with constant real index on a maximal flag manifold in terms of the roots of the Lie algebra which defines the flag manifold. As a particular case, when the real index is zero, we have the description of all invariant generalized complex structures on a maximal flag manifold. We also present a classification of the complex Dirac [...]

The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on November 7, 2023 at 2:00 pm (UTC+2)  in Room 478 of IMI. A talk on: New and little known properties of the Fox and Fox-Wright functions  will be delivered by Dmitrii Karp, Holon Institute of Technology, Holon, Israel. Everybody is invited. Abstract.In the talk, I will introduce the functions H of Fox and W of Wright (its general case known as Fox-Wright function) and some motivation behind them. Then, I will discuss the extension of Gauss' expansion and summation formulas for the hypergeometric function to the case of general Fox-Wright function and Norlund's expansion for the Meijer's G function to the case of Fox's H function. I will [...]

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.