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

15. June 2022

Together with colleagues in Chemistry and Engineering, we are organizing a Royal Society APEX Masterclass entitled Big Data Calculations in STEM. More information under Outreach.

6. June 2022

Prof. Melgaard gives talk Shining Light in the Darkness: the Mathematics of Boson stars at Cardiff University. Also available on Youtube.

9. May 2022

Upcoming event on May 9. Prof. H. Cox (Chemistry, Sussex), will give a talk on Bound State Stability in Three-Body Coulomb Systems in the Mathematical Physics seminar series. Link to the MP seminar series schedule.

18. March 2022

Our paper entitled Regularity, symmetry and asymptotic behaviour of solutions for some Stein-Weiss type integral systems has been accepted for publication in Pacific Journal of Mathematics.

24. January 2022

Prof. M. Yang (Zhejiang Normal University, China) gives a virtual talk entitled On critical Hartree equations, qualitative analysis and its applications. This is in the context of the seminar series on Analysis and PDEs.

2. december 2021

Seminar talk entitled `Shining Light in the Darkness: the Mathematics of Boson stars' by Prof. Melgaard at York University (time 4:15pm).

17. September 2021

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

10. June 2021

Upcoming event on June 10. 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. For more about the donation to the Department of Mathematics in the form of a Legacy gift. Link to the lecture.

27. May 2021

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

... see all News