Research leader name
Tibor Krisztin
The research group aims to do fundamental research in the areas of functional analysis, functional differential equations, and stochastics.
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Investigating transformations that preserve mathematical objects’ structure is an important problem in many areas of mathematics. In the functional analytic part of the project, we plan to determine the symmetries of the positive cone of operator algebras that correspond to different operator means and to understand their associated algebraic structures better. We will examine operations, relations, and numerical quantities related to operator means. In addition to these, we plan to achieve novel and stronger results than the existing ones concerning the rigidity properties of the automorphism groups of operator and matrix structures.
The functional differential equations form a special class of infinite dimensional dynamical systems. Primarily the wide range of real-world applications motivates the study of these types of equations. We work on the two main problems of the field: the description of the complex dynamics of Mackey–Glass type equations, the understanding of the smoothness issues, and qualitative theory for the class of differential equations with state-dependent delays.
Studying asymptotic and statistical properties of stochastic processes are important theoretical areas, which have many known applications as well. We deal with such questions in the case of branching and autoregressive processes. We also plan to derive limit theorems for several kinds of means of independent and identically distributed random variables and to study risk measures that play important roles in financial mathematics.
Members of the research group: Tibor Krisztin, István Balázs, Mátyás Barczy, Ferenc Bartha, Ábel Garab, Lajos Molnár
