Manas Bhatnagar

Manas Bhatnagar is a Visiting Assistant Professor in the Department of Mathematics and Statistics at the University of Massachusetts Amherst. His research focuses on the analysis of partial differential equations, particularly hyperbolic balance laws and critical threshold phenomena. He earned his Ph.D. in Mathematics from Iowa State University in Summer 2022, under the supervision of Dr. Hailiang Liu. Currently, he works under the mentorship of Dr. Robin Young in his postdoctoral position.

Education:

• Ph.D. in Mathematics, Iowa State University, 2022

Research Interests:

Bhatnagar specializes in hyperbolic systems, critical thresholds for PDE stability, and nonlocal dynamics. His work examines conditions under which solutions to hyperbolic balance laws remain smooth or develop singularities, with applications to fluid dynamics and collective behavior models. Key areas include Euler-Poisson systems, alignment dynamics, and relaxation effects in nonlocal equations.

Publications:

His recent work explores critical thresholds in hyperbolic systems across dimensions, with contributions to both theoretical analysis and numerical methods. Key themes include global dynamics of alignment systems, sharp threshold characterizations, and front tracking schemes for weak* solutions.

Awards & Honors:

No specific awards mentioned, though his work has been published in reputable journals like Journal of Differential Equations and Discrete and Continuous Dynamical Systems.

Advising & Grants:

No advising roles or grants explicitly listed. His current focus is on postdoctoral research in critical threshold phenomena.

Labs/Teams:

Not specified in available information.