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.

Prof Melgaard gives the Chemistry Colloquium talk *Quantum Chemistry. A Mathematical Discipline*, Department of Applied Chemistry, National Yang Ming Chiao Tung University, Taiwan.

Prof 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.

Prof Melgaard gives the talk *Quantum Chemistry. A Mathematical Discipline*, School of Mathematics, East Chinese University of Science and Technology, Shanghai, China.

Prof Melgaard gives the Physics Colloquium talk *Quantum Chemistry. A Mathematical Discipline*, School of Physics and Electrical Engineering, Jiangsu University, Nanjing, China.

Prof Melgaard gives the Colloquium talk *Tour of spectral and scattering theory: eigenvalues, resonances, and numerics*, School of Mathematical Sciences, Nanjing Normal University, Nanjing, China.

Prof. 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.

Prof. Melgaard gives the talk *Poisson wave trace formula for Dirac resonances at thresholds and its applications* at the 20th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics, 31 July - 04 August, 2023, Koc University, Istanbul.

Team members attend the conference Numerical Methods in Quantum Chemistry 2023, June 5-8, Tromso, Norway.

26. April 2023Laura Monk (Bristol) gives a talk entitled *Spectral properties of random hyperbolic surfaces*. This is in the context of the seminar series on Mathematical Physics.