Seminar "Analysis, geometry and topology" Tuesday, July 29-th, 1:00 pm, room 403 of IMI-BAS. Speaker: Asia Mainenti, IMI and ICMS, Sofia Hodge-Riemann balanced structures on non-Kähler manifolds Abstract: A Hodge-Riemann balanced structure on a complex manifold is the datum of a balanced metric whose (n-1)-th power can be decomposed into the wedge product of two differential forms, satisfying the classical Hodge-Riemann bilinear relations. Such structures were introduced by X. Chen and R. Wentworth, to generalize the nonabelian Hodge correspondence to non-Kähler Hermitian metrics. However, there are no known examples of Hodge-Riemann balanced structures on non-Kähler manifolds. The aim of this talk is to address this lack of examples, highlighting the relation with p-Kähler structures and discuss some obstruction results in the class of solvmanifolds. Lastly, [...]

Seminar "Analysis, geometry and topology" Tuesday, July 22-nd, 13:00 o'clock, room 403 of IMI-BAS. Elia Fusi, University of Torino. Special metrics in hypercomplex geometry Abstract: The existence of special hyperHermitian metrics plays an important role in the study of hypercomplex manifolds. In this talk, after a brief overview of the basic definitions in hypercomplex Geometry, we will discuss two of the main types of special metrics in the hypercomplex setting: quaternionic Gauduchon and strong HKT metrics. First of all, we will discuss sufficient and equivalent conditions for a quaternionic Gauduchon metric to exist.  Afterwards, we will show that strong HKT and balanced hyperHermitian metrics cannot coexist on a compact non-hyperKähler manifold, proving a particular instance of the Fino-Vezzoni conjecture. Finally, we will introduce an Einstein [...]

On July 15, 2025, at 1:00 pm in Room 403 there will be a joint seminar of the Analysis, Geometry and Topology Department and the International Center for Mathematical Sciences – Sofia (ICMS-Sofia). A talk on: Weak Metric Structures on Generalized Riemannian Manifolds will be delivered by Milan Zlatanovic, University of Niš, Serbia. Abstract. Linear connections with torsion are important in the study of generalized Riemannian manifolds (M , G=g+F ), where the symmetric part g of G is a non-degenerate (0,2)-tensor and F is the skew-symmetric part. Some space-time models in theoretical physics are based on (M, G=g+F) , where F is defined using a complex structure. In the lecture, we will show more general models, where F [...]

The inaugural lecture by Assoc. Prof. Mikhail Shkolnikov at the Analysis, Geometry and Topology Department will be held on May 13, 2025, at 3:15 pm in Room 403 of IMI - BAS. Speaker: Mikhail Shkolnikov (IMI – BAS) Title: Introduction to amoebas and tropicalization Abstract: We will start by reviewing the most classical aspects of the theory of amoebas deeply rooted in complex analysis and geometry. Next, we will pass to the notion of a tropical limit of amoebas, and will see how restoring the phase allows to recover topology and deduce intersection-theoretic results. After that, we will discuss some results (and their limitations) obtained with Grigory Mikhalkin in the context of non-commutative versions of amoebas of surfaces and tropical limits of curves inside [...]

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 [...]