Dr. Muhammad Usman has joined us as Assistant Professor-Tenure Track in the Department of Mathematics - (SBASSE).

Dr. Usman obtained his PhD in Mathematics from Imperial College London in 2012 prior to joining University of Stockholm, Sweden as Postdoctoral Fellow. Dr Usman completed his MSc and BSc in Mathematics from King’s College London and COMSATS Institute of Information Technology in 2008 and 2006, respectively. His research interests are in spectral theory of differential operators and spectral theory of quantum graphs. In particular, he is interested in the spectral bounds of quantum graphs which is essential for establishing estimates on bound state energies of quantum systems. Dr. Usman has taught undergraduate level courses at Stockholm and COMSATS and has also co-supervised and examined Master level students’ theses at the Stockholm University. Prior to joining LUMS, he was associated with COMSATS Institute of Information Technology as Assistant Professor.

His research interests include:

·       Spectral Theory

·       Scattering Theory

·       Quantum Graphs

Title Publication Author Year
Sharp Spectral Inequalities for Fourth Order Differential Operators on Semi-Axis Mathematical Physics Analysis and Geometry 2019
Trace formulas for Schr??dinger operators on star graphs with general matching conditions Journal of Physics A: Mathematical and Theoretical 2018
Sobolev type inequalities for compact metric graphs Journal of Inequalities and Applications 2018
On vertex conditions for elastic systems Physics Letters, Section A: General, Atomic and Solid State Physics 2015
RT-Symmetric Laplace Operators on Star Graphs: Real Spectrum and Self-Adjointness Advances in Mathematical Physics 2015
On Some Sharp Spectral Inequalities for Schr??dinger Operators on Semiaxis Communications in Mathematical Physics 2014
Trace formulas for Schr??dinger operators on the half-line Bulletin of Mathematical Sciences 2011