February 19, 2024
Ishrak Hajj Hassan (University of Ostrava)
Stochastic differential equations for studying species competition
Abstract:
The talk investigates stochastic processes in ecological modeling, emphasizing the multi-species competition of the Lotka-Volterra model. Through three stochastic approaches, including numerical simulations, one model is validated, while the other two present intriguing possibilities. The study explores the impact of noise on extinction and persistence, with implications for diverse fields like population dynamics and epidemiology.
Slides
April 9, 2024
Alexander Zuevsky (Institute of Mathematics, Czech Academy of Sciences, Prague)
Continual Lie algebras determined by chain complexes
Abstract:
Continual Lie algebras are infinite-dimensional generalizations of Lie algebras with discrete root system by considering continual root systems. We establish a general relation between chain complexes and continual Lie algebras. The natural orthogonality condition with respect to a product among elements of a chain complex \(\mathcal C\) spaces brings about to \(\mathcal C\) the structure of a graded algebra with differential relations. We prove that a chain complex endowed with an appropriate Leibniz-property product of elements of its spaces brings about the structure of a continual Lie algebra with the root space determined by parameters for the complex. That provides a new source of examples of continual Lie algebras. Finally, as an example, we consider the case of Čech-de Rham complex associated to a foliation of a smooth manifold. In a particular case of this chain complex, we derive explicitly the commutation relations for the corresponding continual Lie algebra.
Slides
