About me

I am a Professor and Head of Department at Mathematics Department, Swansea University.

My research focuses on the Analysis of Nonlinear Partial Differential Equations (PDE). Specifically, I use methods from the Calculus of Variations and Potential Theory to explore fundamental properties of nonlinear elliptic equations, such as existence, qualitative properties, asymptotic decay of solutions, concentration, blow-up, and singular phenomena.

My recent work is centered around Choquard and Schrödinger-Poisson type equations and other classes of nonlinear equations with nonlocal interactions. These equations describe the collective behavior of self-interacting many-body systems at different scales, from atoms and molecules to flock patterns in animal swarms and up to the formation of stars and galaxies. What sets these models apart from classical local PDEs is the presence of nonlocal terms in the equations via Coulombian type interactions or via a fractional Laplacian term, or both.

My earlier research interests focused on the area of topological and variational methods of Nonlinear Analysis, specifically in Critical Points Theory, infinite-dimensional Morse Theory, and their applications to nonlinear elliptic equations and nonlinear problems associated with non-local integral operators.

I am always interested in hearing from prospective PhD or postdoctoral candidates interested in working in the area of Nonlinear PDEs.

My undergraduate teaching portfolio consists of a broad variety of courses in Analysis and Differential Equations.

In recent years, I have held several key administrative roles within the department and have been involved in several external editorial and research advisory roles.

Department of Mathematics
Swansea University
Swansea SA1 8EN
Wales, UK

+44 (0)1792 602763
Office: 322 CoFo

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