We have developed an algorithm, AutoTAB, for automatically detecting and tracking the bipolar magnetic regions from magnetograms. Here are the research papers on the development of the algorithm and the initial results. Details can be found here:

A. Sreedevi, B. Jha, B.B. Karak, & D. Banerjee, AutoTAB: Automatic Tracking Algorithm for Bipolar Magnetic Regions, APJS 268, 2, 58 (2023). 

A. Sreedevi, B. K. Jha, B. B. Karak & D. Banerjee: Analysis of BMR tilt from AutoTAB catalog: Hinting towards the thin flux tube model? , ApJ, 966, 112 (2024)  

For the first time, we show that the nonlinear loss of toroidal flux through magnetic buoyancy can explain why solar cycles decay at the same rate. The paper was published in the prestigious journal PRL.Details can be found here:

A. Biswas, A., B. B. Karak R., & Cameron: Toroidal flux loss due to flux emergence explains why solar cycles rise differently but decay in a similar way, Physical Review Letters (PRL), 129, 241102 (2022) 

Using the rise rate of the polar field, we have predicted the amplitude of the solar cycle 25.  In this method, we have shown that we can predict the solar cycle 2-3 years before the usual landmark of the prediction, which is around the solar minimum. Details can be found here:
P. Kumar, A. Biswas, A. & B. B. Karak:  Physical link of the polar field build-up with the Waldmeier effect broadens the scope of early solar cycle prediction: Cycle 25 is likely to be stronger than Cycle 24, MNRAS Letters 513, L 112-116 (2022)
Biswas, B.B. Karak, & P. Kumar, Exploring the reliability of polar field rise rate as a precursor for an early prediction of solar cycle, MNRAS, 526, 3, 3994–4003 (2023). 

P. Kumar, Nagy, M., L. Alexandre, B. B. Karak & K. Petrovay:  The polar precursor method for solar cycle prediction: comparison of predictors and their temporal range, The Astrophysical Journal 909, 87; arXiv:2101.05013 (2021)

A group from various institutes including IIT-BHU has recently measured the global magnetic field in the solar corona for the first time. The team used observations from the Coronal Multi-channel Polarimeter (COMP), an instrument operated by High Altitude Observatory, USA. See the published paper for more details:

Z. Yang, C. Bethge, H. Tian, S. Tomczyk, R. Morton, G. Zanna, SW. McIntosh, B. B. Karak, S. Gibson, T. Samanta, J. He, Y. Chen, L. Wang:       Global maps of the magnetic field in the solar corona​, Science 369, 6504 (2020). 

With a Russian group lead by Dr. A. Mordvinov (institute of Solar-Terrestrial Physics, Irkutsk) and Prof. Dipankar Banerjee (IIST, Trivandrum), we for the first time produced the magnetic map corresponding to the Cycles 15-19 (1915-1965) using its proxies. We use the Ca II K line intensity and H alpha map from Kodaikanal Solar Observatory (KoSO) of Indian Institute of Astrophysics. See the publication:
A. V. Mordvinov, B. B. Karak, D. Banerjee, S. Chatterjee, E. M. Golubeva, A. L. Khlystova: Long-term evolution of the sun's magnetic field during cycles 15-19 based on the proxies from Kodaikanal Solar Observatory, Astrophysical Journal Letters, 902, L15 (2020)

In this figure nth cycle peak polar field strongly corelates only (n + 1)th solar cycle toroidal field amplitude.

In this figure nth cycle peak polar field strongly corelates with multiple cycle toroidal field amplitude.

In our study, we explore the possibility of the opration of the dynamo in the subcritical region using the Babcock-Leighton type kinametic dynamo model. In some parameter regimes, we find that the dynamo shows hysteresis behaviour, i.e., two dynamo solutions are possible depending on the initial parameters--decaying solution if started with weak field and strong oscillatory solution ( subcritical dynamo) when started with a strong field. Click on the link to know more.