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, EPSRC, The Royal Society, ERC, SFI, KVA, SI, and SRC, among others.

News

10. June 2021

Upcoming event. Fields medalist, Prof. Alessio Figalli (ETH, Zurich), will give a public (virtual) lecture when the Dr Perry James Browne Research Centre on Mathematics and its Applications is officially launched on June 10, 2021. Further details will be announced. For more information, read about the donation to the Department of Mathematics in the form of a Legacy gift.

27. May 2021

Our paper entitled Solitary waves and excited states for Boson stars has been accepted for publication in Analysis and Applications.

19. May 2021

Wonderful news from the Royal Society. We've been granted the APEX Award 2021 (two-year grant).

5. February 2021

Our new paper on the maximum ionization in restricted and unrestricted Hartree-Fock theory has been published in Atoms.

28. September 2020

The module Functional Analysis (G1029/851G1) begins.

18. August 2020

Due to the global pandemic the Nordic Congress of Mathematicians, August 18-21, 2020, Aalto, Finland, has been postponed until 2022.

31. July 2020

Our paper on the Poisson wave trace formula for Dirac resonances at spectrum edges and applications is accepted for publication in Asian Journal of Mathematics.

8. April 2020

Our paper, jointly with our colleagues in Chemistry, has been accepted for publication in Advances of Quantum Chemistry vol. 81.

18. November 2019

Please join us in congratulating Bobby Cheng on successfully defending his Ph.D. dissertation this afternoon. We wish him success in all his future endeavours.

... see all News