Welcome to the Melgaard Group
We are a dynamic research group in the Department of Mathematics. Our aim is to develop mathematical
methods for application to problems in physics, in particular quantum mechanics and quantum chemistry and to prove mathematical
theorems expressing the properties of the quantum system. To this end, we use a wide variety of mathematical theories and methods to tackle these
problems: linear and nonlinear analysis, functional analysis, ordinary and partial differential equations, calculus of variations, operator theory,
spectral and scattering theory etc.
Currently, we are mainly focusing on two different research topics: (1) Electronic structure models (Nonlinear PDEs); (2) Resonances (Spectral and scattering properties of differential operators). Please see Research for more information.
We are located at University of Sussex, the birthplace of the study of Applied Partial Differential Equations in the United Kingdom.
We exchange ideas and work with our neighbors from Chemistry, in particular, Theoretical and Computational Chemistry, as well as with the colleagues in the Atomic, Molecular and Optical Physics group in the Department of Physics.
We are looking for passionate new PhD students, Postdocs, and Master students to join the team (more info) !
Over the years, we have gratefully been funded by the University of Sussex, The British Academy, Engineering and Physical Sciences Research Council, Leverhulme Trust, Royal Academy of Engineering, The Royal Society, European Research Council, Science Foundation Ireland, Royal Swedish Academy of Sciences, Swedish Institute, and Swedish Research Council, among others.
News
3. June 2024Prof. Melgaard gives the talk Density functional theory with magnetic fields at MCC-35, the 35th International Conference on the Interfaces among Mathematics, Chemistry and Computer Sciences, June 3-7, 2004, Dubrovnik, Croatia.
20. May 2024The paper entitled Bound-state stability of Coulomb three-body systems using numerical tensor methods has been accepted for publication in Physical Review A.
8. January 2024The paper Spectral approximation scheme for a hybrid, spin-density Kohn–Sham density-functional theory in an external (nonuniform) magnetic field and a collinear exchange-correlation energy, joint with V. Syrjanen, has been published in Journal of Mathematical Chemistry.
29. December 2023Prof Melgaard gives the Chemistry Colloquium talk Quantum Chemistry. A Mathematical Discipline, Department of Applied Chemistry, National Yang Ming Chiao Tung University, Taiwan.
26. December 2023Prof Melgaard gives the talk Tour of spectral and scattering theory: eigenvalues, resonances, and numerics, Department of Applied Mathematics, National Yang Ming Chiao Tung University, Taiwan.
22. December 2023Prof Melgaard gives the talk Quantum Chemistry. A Mathematical Discipline, School of Mathematics, East Chinese University of Science and Technology, Shanghai, China.
18. December 2023Prof Melgaard gives the Physics Colloquium talk Quantum Chemistry. A Mathematical Discipline, School of Physics and Electrical Engineering, Jiangsu University, Nanjing, China.
14. December 2023Prof Melgaard gives the Colloquium talk Tour of spectral and scattering theory: eigenvalues, resonances, and numerics, School of Mathematical Sciences, Nanjing Normal University, Nanjing, China.
13. October 2023Prof. Melgaard is an invited speaker at the forthcoming 26th International Workshop on Quantum Systems in Chemistry, Physics, and Biology (QSCP-XXVI) held in Jaipur, Rajasthan, India on October 14-20, 2023. Title of talk Tensor-structured numerical approach to the stability of Coulomb three-body systems, October 19, 2023.