Research leader name
Dr. Hajdu Lajos
We carry out research in several areas of mathematics and applied mathematics, which are related to each other in different depths, sometimes overlapping. We place particular emphasis on applications of our theoretical results, including in the field of digital image processing. The main topics under investigation are.
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Exponential Diophantine equations. Many fundamental number-theoretic problems can be
reduced to exponential diophantine equations. We focus our research on various key issues in
this area.
Polynomial Diophantine equations. An extremely important area of Diophantine number
theory. In our research, we focus on the Diophantine analysis of products of consecutive
integers and related problems.
Integer bases and monogeneity of algebraic number fields. This area is an important
application of the previous topic. There has been a recent breakthrough in this area, partly due
to the results obtained by colleagues in Debrecen – we focus our research in this direction.
Local properties of functions on operator algebras. We investigate several important issues,
including commutativity properties on structures of Hilbert space operators, and relations
between certain local properties of continuous scalar functions.
The theory of generalized Berwald spaces. Our primary goal is to study the compatibility
equation for connectives with minimal torsion.
Asymptotic characterization of random graph evolution models. We investigate the degree
number distribution in discrete and continuous-time random graph models and general
continuous-time random graph evolution mechanisms.
Stochastic optimization. Our main objective is to develop a stochastic optimization method
that determines the minimum required size of the batch used in a given iteration instead of
varying the learning rate.
