Harish-Chandra Research Institute (HRI) Archives

Dr. Saikatul Haque is a Postdoctoral Fellow at Harish-Chandra Research Institute, Allahabad since 2021. He obtained his Ph.D. in 2021, under the supervision of Prof. Sandeep Kunnath, at Tata Institute of Fundamental Research – Centre for Applicable Mathematics (TIFR-CAM), Bengaluru. He earned his master’s in 2016 from TIFR-CAM after completing his bachelor’s in 2014 at R K Mission Vidyamandira, University of Calcutta, Kolkata.

Dr. Haque’s research work focuses on the study of well-posedness and regularity for elliptic and time dependent partial differential equations. He has published several research articles in reputed international journals. He also qualified IIT JAM in 2014 and CSIR UGC NET held in December 2015. He has been selected for the INSPIRE faculty fellowships in 2023 by Department of Science & Technology, Government of India.

As a Fulbright-Nehru Postdoctoral Research fellow, Dr. Haque is studying mainly three partial differential equations: the nonlinear Schrödinger equation (NLS), a modified Korteweg-de Vries (mKdV) equation, and a related heat equation. The main focus of this project is to understand the global time behavior of the energy-critical focusing inhomogeneous fractional NLS. This includes research into local and global well-posedness, variational estimates for elliptic problems, linear profile decomposition, and rigidity. For the cubic NLS, mKdV and nonlinear heat equation, Dr. Haqueis investigating well-posedness and ill-posedness in modulation spaces.

Dr. Manpreet Singh is a postdoctoral F ellow at Harish-Chandra Research Institute (HRI), Prayagraj (Allahabad). His research interest is in low dimensional topology. Before joining HRI, he was an Integrated PhD student in the Department of Mathematical Sciences at the Indian Institute of Science Education and Research (IISER) Mohali. He received his master’s degree and PhD under the supervision of Dr. Mahender Singh, in 2021. During his PhD, he worked on algebraic and combinatorial aspects in knot theory. He has published several research articles in reputed international journals.

During the Fulbright-Nehru Postdoctoral Research Fellowship, he will work on exploring connections among algebraic and geometric invariants of knots. He aims at understanding certain colorings of alternating diagrams of prime links using the elements of the first homology groups of cyclic branched coverings of links. In the last two decades, many algebraic structures have been introduced as invariants of (ramified) knots. Dr. Singh is planning to delve into the intricacies of such invariants from a geometric facet.