Solar activity regularly affects the Sun's plasma and energetic particle populations which are in interaction with the Earth's magnetic field. These effects and changes on the terrestrial system causes what we call Space Weather. which influences Earth's long-term climate trends and advanced technologies we became so dependent on in our lives. It would be of great importance to understand the working of the solar dynamo, namely how the solar dynamo actually operates to generate the extensive and complex solar magnetic fields that we observe and predict future solar cycles with great precision.

The Babcock-Leighton dynamos are unquestionably the best examples of flux transport dynamos. The widely used Babcock-Leighton flux-transport solar dynamo models have been successful in reproducing many solar cycle features including equatorward migration of sunspot belts, poleward drift of poloidal fields and correct phase relationship between them. The models are relatively well-supported by observations. The Babcock-Leigton flux-transport dynamo models are able to simulate long-term prediction of extensive solar activity, and also to determine the possible solar influences on terrestrial climate and in the dynamical regime, this class of models can explain the solar-like torsional oscillation pattern.

2D Babcock-Leighton models cannot explain the longitude-dependent solar cycle features. There exist plenty of observations of how longitude-dependent solar cycle features vary with solar cycle. For longer than half a century, it has been observed that solar active regions tend to emerge near the location of previous or currently existent magnetic flux. These preferential longitudes of solar activity, which are commonly referred to as active longitudes, have also been observed in some cool stars, active stars and young solar analogs. We build a 3D Babcock-Leighton solar dynamo model to reproduce the longitude-dependent solar cycle features principally.

One of the main research interests in the general field of solar and space plasma physics is the plasma heating. The physical processes that generate and sustain the observed high temperature of the solar and stellar atmospheres have so far defied a quantitative understanding despite the multitude of efforts spanning over half a century. The key point here is that the temperature of the solar surface, called the photosphere, is about 2-3 orders of magnitude less than the temperature of the magnetised plasma above it (called the chromosphere, transition region and solar corona). The higher one rises in the solar atmosphere, the hotter it becomes. On the other hand, at the same time, the solar plasma becomes more and more magnetically dominated as one travels away from the surface of the Sun into the upper layer of the solar atmosphere. This continuously and often burstly expanding hot and magnetised solar atmosphere has a fundamental effect determining space weather conditions and life on Earth.

In order to understand the plasma heating processes, theoretical (both numerical and exact analytical methods) and observational studies (joint ground-based and satellite missions) are carried out where the interaction of magnetic field and the plasma is investigated. In recent years, more and more particular attention is paid to unveiling the subtle details of magnetic coupling mechanisms in the solar atmosphere, as it was realised by solar physicists that the entire Sun-Earth system should be seen as a unique physical system where magnetism plays a role of glueing together the dynamic plasma. Another aspect that has recently been realised is the importance to the mechanism(s) of solar influence on Space Weather, i.e. the plasma conditions around the Earth.

Further, understanding the subtleties of plasma confinement and plasma dynamics at high temperatures is also strongly linked to modern fusion physics with great potentials to industrial applications. A multi-disciplinary research approach (including the methods and tools of e.g. magneto-hydrodynamics (MHD), computational fluid dynamics (CFD), applied mathematics and statistical methods) has direct relevance to the emergence of the new discipline of solar magnetoseismology (SMS). With the tools of SMS we are now able not only to look into the deep subsurface interior regions of the Sun, but we can also diagnose its atmosphere and the very high-speed streams of plasma that continuously fill the interplanetary space in our Solar System.

The spatial distribution of sunspot groups is not homogenous. There is an enhanced longitudinal belt on the Sun, called active longitude. Connecting the phenomena of active longitudinal zones and the longitudes of dominant flare- and CME- productivity may potentially forecast a flare and/or CME source several Carrington rotations in advance. The temporal behaviour of active regions and solar eruptive events may also indicate unpleasant space weather conditions.

Studying solar flare oscillation patterns is also one of our aims. The temporal recurrence of micro-flare occurrences is studied in a time interval preceding and following major, energetic solar flares by several hours. The observed periods are interpreted as signatures of global oscillations of the entire solar atmosphere encompassing everything from photosphere to corona.

We develop a new automatic, real time solar feature database. The aim of the project is the recognition and identification of sunspots and other small and large scale characteristics. The public catalog will provide crucial information about active regions such as morphological and spatial behaviours.

Several different phenomena with a wide range of sizes and dynamics are visible in the chromosphere. One of the most widely known objects are spicules with 7000-8000 km length and 10-12 minutes lifetime. They can be observed both on-disc and at the limb. Our research is about to carry out a detailed statistical investigation of the "bigger brothers" of spicules, the so called macrospicules. According to their length (60'000 - 70'000 km) and lifetime (around 30 minutes), macrospicules have a potential to carry energy and momentum into the upper region of the solar atmosphere, the solar corona. Our aim is to obtain more information about the generation and evolution of macrospicules. To find their possible connection to the solar cycles (the roughly 11-year long variation of solar activity), we have built up a multiple-year long database of macrospciules based on observations of the Solar Dynamics Observatory.

Studying of solar tachocline has a key role for a variety of reasons to understand the global dynamics of the Sun. The solar tachocline, being the seat of the solar dynamo, is located at the interface between the differentially rotating outer convection zone and the rigid radiative interior at a radius of at most 0.70 times the Solar radius, as indicated by helioseismology. The thickness of the tachocline is between 2% and 5% of the solar radius. This layer is located where the radial temperature gradient changes from subadiabatic gradient characteristic of the radiative zone to adiabatic.

Models of solar dynamos have particular interest in reconstructing the inner latitudinal differential rotation profile with great precision. Latitudinal and temporal variations of the tachocline parameters are also of particular interest in order to constrain models. The solar tachocline is also probably the location of strong toroidal fields that are likely to be the source of the strong photospheric fields seen in sunspots, as well as many other manifestations of magnetic activity observed at the solar surface and above. We study the global HD/MHD instabilities in the solar tachocline to understand the global magnetohydrodynamic (MHD) processes in shear layer and contribution to some properties of solar activity and the solar cycle.

The solar atmosphere is a dynamic and inhomogeneous medium, in which wave phenomena are created on a variety of length scales by the ubiquitous magnetic fields and their interactions with the plasma. The behaviour and mutual interactions of the plasma and the magnetic field lines may be examined and described mathematically by the approach of magnetohydrodynamics (MHD).

As early as the second half of the twentieth century, this approach established the theoretical expectation that the solar atmosphere, especially the corona, is able to support magnetohydrodynamic waves. As the past few decades have brought a spectacular improvement in the spatial and temporal resolution of both imaging and spectroscopic instruments, observational results corroborated the pre-existing analytical conclusions. Several types of MHD waves (slow, fast, Alfvén) were detected in different layers and structures of the atmosphere (such as in coronal loops and prominences).

Theoretical and practical interest in MHD waves on the Sun is generated by the fundamental questions of solar physics. Namely, the propagation and dissipation of such waves provides an explanation as to where the energy sufficient for maintaining the multimillion degree temperature of the hot corona comes from, and how it reaches such heights above the cooler atmospheric layers.

A further motivation for the study of MHD waves is the science of solar magneto-seismology. Generally speaking, physical and geometric characteristics of a medium are the factors that determine the properties of waves propagating in said medium. Consequently, the waves themselves then carry information about the medium through which they have travelled. By making comparisons between measurements of wave phenomena and the results gained from theoretical investigations, it becomes possible to deduce physical parameters which are difficult or outright impossible to measure directly (such as magnetic field strengths) in a given medium (in this case, a certain layer or feature within the solar atmosphere).