Анализ, геометрия и топология

Общ семинар на секцията

Следваща сбирка:

30 септември 2025 г., 11:00 часа, зала 403

Concircularly Semi-Symmetric Metric Connection

Miroslav Maksimović, University of Priština in Kosovska Mitrovica, Kosovska Mitrovica, Serbia, and Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria

30 септември 2025 г., 11:00 часа, зала 403

Резюме: A concircularly semi-symmetric metric connection is a special class of semi-symmetric metric connection when its generator is a concircular vector. In this talk, we will present results on this connection on pseudo-Riemannian manifolds, and in particular, we will observe the application to Lorentzian manifolds and the theory of relativity. We demonstrate that a Lorentzian manifold reduces to a GRW space-time when the generator of the observed connection is a unit timelike vector. At the same time, the mentioned connection becomes a semi-symmetric metric P-connection. At the end, we determine the equation of state on a perfect fluid space-time. These are the results of a joint work with prof. Milan Zlatanović published in J. Geom. Phys. 217 (2025).

The lecturer is supported by the Scientific Programme “Enhancing the Research Capacity in Mathematical Sciences (PIKOM)”, No. DO1-67/05.05.2022.

Предишни сбирки:

Higher order estimates for Monge-Ampere type equations motivated by quaternionic geometry

Marcin Sroka, Jagiellonian University, Kraków, Poland

22 октомври 2024 г., 14:00 часа, зала 478

Резюме: 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 follows essentially by Pogorelov calculation, for the complex Monge-Ampere equation, in relation to Calabi conjecture, it was proven by Aubin and Yau. I will use those two as comparison to underline new difficulties related to concavity properties of quaternionic Monge-Ampere operator.

Unimodality Preservation by Ratios of Functional Series and Integral Transforms

Dmitrii Karp, Holon Institute of Technology, Holon, Israel

15 октомври 2024 г., 14:00 часа

Резюме: 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 talk, we discuss conditions on the functional sequence and the kernel of an integral transform ensuring such property. Numerous series and integral transforms appearing in applications satisfy our sufficient conditions, including Dirichlet, factorial and inverse factorial series, Laplace, Mellin and generalized Stieltjes transforms, among many others. The key role in our considerations is played by the notion of sign regularity.

Презентация

Complex Dirac structures on flag manifolds

Carlos Augusto Bassani Varea, Universidade Tecnológica Federal do Paraná, Brazil

23 януари 2024 г., 14:00 часа

Резюме:

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 structures under the action of B-transformation. This is a joint work with Cristian Ortiz (IME-USP).

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