We are delighted to congratulate Dr. Vishvesh Kumar on his new position at Department of Mathematical Sciences at IIT BHU Varanasi as an Assistant Professor. This is a wonderful milestone in his academic career, and a moment of pride for all of us at the Ghent Analysis & PDE Center.

Since joining our group as a postdoctoral researcher at Ghent University, Dr. Kumar has been an active and inspiring member of our community. Working within the Department of Mathematics: Analysis, Logic and Discrete Mathematics and the Ghent Analysis & PDE Center headed by Prof. Michael Ruzhansky, he has contributed significantly to our core areas of research.  

Research contributions in our group

Dr. Kumar’s research lies at the intersection of abstract harmonic analysis, pseudo-differential operators, geometric analysis, and partial differential equations on Lie groups.  

During his time in Ghent, he has:

• Co-authored numerous papers on nonlocal and subelliptic problems on stratified Lie groups, including work on Brezis–Nirenberg type problems, critical equations, and fractional Sobolev-type inequalities.  
• Made substantial contributions to the theory of damped and fractional wave equations on graded and stratified Lie groups, including results for higher order hypoelliptic equations with data in negative order Sobolev spaces.  
• Advanced functional inequalities and harmonic analysis on symmetric spaces and hypergroups, with applications to Fourier multipliers, Strichartz estimates, and related analytic inequalities.  

His work has appeared, or is forthcoming, in several respected international journals such as Journal of Evolution Equations, Mathematische Annalen, Journal of Geometric Analysis, Israel Journal of Mathematics, and others, reflecting both the depth and breadth of his contribution to our field.  

A valued colleague

On a personal level, Vishvesh has been a generous collaborator and a supportive colleague. His willingness to discuss ideas, share expertise, and encourage younger researchers and visitors has left a strong and positive impression in our group. Many of us have benefited from his clarity of thought, his calm problem-solving approach, and his enthusiasm for mathematics.

---

Looking ahead

While we will miss having him at the Ghent Analysis & PDE Center, we are equally excited to see him take this next step as an Assistant Professor at IIT BHU Varanasi. We are confident that he will continue to build a vibrant research program, inspire students, and develop new collaborations that will further strengthen the links between our institutions.