Michael Melgaard

Professor of Mathematics (since February 1, 2013)
email: m.melgaard@sussex.ac.uk

Subject Chair in Analysis and Partial Differential Equations

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M. D. Chan

Member of the group from 2019 to 2023. Ph.D. awarded January 26, 2024.
Role: Ph.D. student funded by University of Sussex (Chancellor’s International Research Scholarship), Great Britain.

M. Chan has left Academia.

• Title of Ph.D. thesis (2023) "Quasiresonances for 2 x 2 Schrödinger operators", University of Sussex, Great Britain.
• MSc in Mathematics, University of Sussex, 2018
• BSc in Mathematics, Universidad Autonoma de Yucatan, Mexico, 2017

V. J. J. Syrjanen

Member of the group from 2016 to 2021. Ph.D. awarded July 6, 2022.
Role: Ph.D. student funded by University of Sussex, Great Britain.

Ville has co-authored 3 papers with Prof. Melgaard.

• Title of Ph.D. thesis (2021) "Rigorous mathematical results for electronic structure models", University of Sussex, Great Britain.
• MSc Mathematics, University of Warwick, 2016
• BA Honours Mathematics, University of Cambridge, 2015.

M. Almusawa

Member of the group from 2017 to 2021. Ph.D. awarded June 30, 2022.
Role: Ph.D. student funded by government of Saudi Arabia.

• Title of Ph.D. thesis (2021) "Some results on singular scattering theory", University of Sussex, Great Britain.
• MSc in Applied and Computational Mathematics, University of Massachusetts Lowell, U.S.A., 2015
• BSc in Mathematics, Jazan University, Saudi Arabia, 2012.

W. Hamali

Member of the group from 2017 to 2020. Ph.D. awarded October 15, 2021.
Role: Ph.D. student funded by government of Saudi Arabia.

• Title of Ph.D. thesis (2021) "Asymptotic observables for quantum Hamiltonians with external fields", University of Sussex, Great Britain.
• MSc in Mathematics, Murray State University, U.S.A., 2015
• BSc in Mathematics, King Abdul-Aziz University, Jeddah, Saudi Arabia, 2008.

Bobby Cheng

Member of the group from 2015 to 2019, now an assistant manager at Deloitte (City of London)
Role: Ph.D. student funded by EPSRC, University of Sussex, Great Britain.

Bobby co-authored 1 paper with Prof. Melgaard.

• Title of Ph.D. thesis (2020) "Trace formulas for Dirac operators with applications to resonances", University of Sussex, Great Britain.
• MSc in Applied Mathematics, Imperial College London, 2012.
• BSc in Physics with Theoretical Physics, University of Manchester, 2011.

Jimmy Kungsman

Member of the group from 2008 to 2014. He works as a system developer at Saab, Stockholm, Sweden.
Role: Ph.D. student, Uppsala University, Sweden.

Jimmy co-authored 4 papers with Prof. Melgaard.

• Title of Ph.D. thesis (2014) "Resonances for the Dirac operator"
• MSc in Mathematics, Uppsala University, 2008.

Frederic Zongo

Member of the group from 2008 to 2013. Frederic is a lecturer in Mathematics at the Institut Des Sciences, Ouagadougou, Burkina Faso.
Role: Ph.D. student, jointly Uppsala University, Sweden and Universite de Ouagadougou, Burkina Faso.

• Title of Ph.D. thesis (2013) "Etudes de problemes anisotropiques nonlineaires et d'equations quasirelativisties de type Choquard"

Carlos Argáez

Member of the group from 2009 to 2013, now a post-doctoral fellow at the Science Institute, University of Iceland.
Role: Ph.D. student funded by SFI Research Frontier programme, Science Foundation Ireland, Dublin Institute of Technology, Repulic of Ireland.

Carlos has co-authored 4 papers with Prof. Melgaard. He has held several post-doctoral positions since he earned his Ph.D. and his expertise includes analysis and PDEs, quantum chemistry, dynamical systems, numerical analysis, and scientific computing.

• Title of Ph.D. thesis (2013) "Rigorous results on nonlinear equations arising in Quantum Chemistry"
• B.Sc. in Physics (2007), National Autonomous University of Mexico, Mexico City, Mexico.

Mattias Enstedt

Member of the group from 2005 to 2011.
Role: Ph.D. student, Uppsala University, Sweden.

Mattias has co-authored 4 papers with Prof. Melgaard. After he earned his Ph.D., he has worked in the private sector.

• Title of Ph.D. thesis (2011) "Selected Topics in Partial Differential Equations"
• M.Sc. in Applied Physics and Electrical Engineering (2005), Linköping University, Linköping, Sweden.

Saul Douglas

MMath student (Mathematics), University of Sussex, 2025.

• Title of MMath dissertation "Finite element methods applied to an ocean model".

Yusuf Kerim Ciger

MSc student (Data Science), University of Sussex, 2025.

• Title of MSc dissertation "Automating stock trading using deep learning. A predictive modeling approach on public SP 500 and NASDAQ data".

Simay Kaynar

MSc student (Data Science), University of Sussex, 2025.

• Title of MSc dissertation "Bayesian multimodal tensor framework for personalized Alzheimer risk estimation".

Joseph Maina

MSc student (Mathematical Sciences), AIMS, Rwanda, 2025.

• Title of MSc dissertation "Conditional Wasserstein GAN for probabilistic regression in Renewable energy consumption prediction".

Evariste Migabo

MSc student (Mathematical Sciences), AIMS, Rwanda, 2025.

• Title of MSc dissertation "Solving Partial Differential Equations using Physics-informed Neural Networks".

Olivier Deyo Moucheu

MSc student (Mathematical Sciences), AIMS, Cameroon, 2025.

• Title of MSc dissertation "Graph-based neural weather prediction for limited area modelling (Cameroon area)".

Erine Cabrelle Toukap Wankap

MSc student (Mathematical Sciences), AIMS, Rwanda, 2025.

• Title of MSc dissertation "Optimizing compartmental model in epidemiology using physics-informed neural networks".

James Watson

MSc student (Data Science), University of Sussex, 2025.

• Title of MSc dissertation "Physics-informed neural networks for parametric and non-parametic option pricing. From Black-Scholes to stochastic volatility".

Precious Awoleye

MSc student (Mathematical Sciences), AIMS, Cameroon, 2025.

• Title of MSc dissertation "Solving the Schrödinger equation using Physics-informed Neural Networks".

Yogeswara Reddy Badepalle

MSc student (Data Science), University of Sussex, 2024.

• Title of MSc dissertation "Approximations of high-dimensional eigenvalue problems using tensor neural networks".

Srija Karmakar

MSc student (Data Science), University of Sussex, 2024

• Title of MSc dissertation "Image classification and detection of brain tumors types using deep learning and tensor methods".

Asika Khatun

MSc student (Data Science), University of Sussex, 2024.

• Title of MSc dissertation "Finite element method in quantum mechanics".

Sai Myana

MSc student (Data Science), University of Sussex, 2024.

• Title of MSc dissertation "Stock trend prediction using news sentiment analysis".

Ramesha

MSc student (Data Science), University of Sussex, 2024.

• Title of MSc dissertation "Numerical solutions to Schrödinger equation using FEM, NTM, and TT methods".

Abhishek Srivastav

MSc student (Data Science), University of Sussex, 2024.

• Title of MSc dissertation "Time series modelling of the number of deaths in East and West Sussex".

Kiran Karthikeyan

Master student (Data Science), University of Sussex, 2023.

• Title of MSc dissertation "Deep learning in quantum physics".

Nishith Gupta

Master student (Data Science), University of Sussex, 2023.

• Title of MSc dissertation "Face recognition using tensor decomposition".

Peter Russell

MChem student (co-supervised with Prof H. Cox, Chemistry), University of Sussex, 2023.

• Title of MChem dissertation "Development of tensor-structured calculations on few particle systems".

Benedict Chukwudebe

Master student (Data Science), University of Sussex, 2022.

• Title of MSc dissertation "Higher order tensor methods applied to streaming video completion".

Taiki Yotsumoto

MMath student, University of Sussex, 2022.

• Title of MSc dissertation "Semiclassical approximation of matrix valued Hamiltonians".

Hana Osman

Master student (Data Science), University of Sussex, 2022.

• Title of MSc dissertation "Using Chebyshev interpolation and tensor techniques in treating high dimensional financial data".

Apurva Joshi

Master student, University of Sussex, 2022.

• Title of MSc dissertation "Tensor decomposition with application in numerical integration".

Ashraf Khan

Master student, University of Sussex, 2022.

• Title of MSc dissertation "Deep learning in Material Science".

Gayathri Sooraj

Master student, University of Sussex, 2022.

• Title of MSc dissertation "Low rank tensor decompositions for face recognition".

Yash Singh

Master student, University of Sussex, 2022.

• Title of MSc dissertation "Deep learning applied in option pricing".

Mariana D. Chan

Master student, University of Sussex, 2018.

Mariana was awarded the Chancellor’s International Research Scholarship and she is currently pursuing her Ph.D. under Prof. Melgaard’s supervision.

• Title of MSc dissertation "Low-energy scattering for Schrödinger operators".

Chukwudi Ogadinma

Master student, University of Sussex, 2016.

• Title of MSc dissertation "Existence of resonance for three-dimensional Schrödinger operator"

Nigel Orr

Master student, Dublin Institute of Technology, Ireland, 2013.

Nigel did his MSc while he was in full-time employment. He is currently pursuing a PhD at Dublin Institute of Technology (once again part-time since he is working full-time). His research interests are Camassa-Holm equations.

• Title of MSc dissertation "Perturbations of embedded eigenvalues for Schrödinger operators with matrix potentials".

Ben Li

Master student, Uppsala University, Sweden, 2012.

Ben Li went on to earn a PhD in Mathematics from Case Western Reserve University in 2018. He then joined Tel Aviv University as a postdoctral researcher. Ben works on convex geometry, Banach space theory, and their application to Quantum information theory.

• Title of MSc dissertation "Solutions to the Muller model in Quantum Chemistry".

Stefan Hellander

Master student, Uppsala University, Sweden, 2008.

Stefan went on to achieve a Ph.D. in Scientific Computing from Uppsala University in 2013, with the thesis “Stochastic Simulation of Reaction-Diffusion Processes”, advised by Prof. Em. Per Lötstedt. He then went on to work as a postdoc in the lab of Prof. Linda Petzold at UCSB, until returning to Uppsala in August of 2017. His research interests include microscopic and mesoscopic modeling and simulation of reaction-diffusion systems, as well as multiscale modeling with the aim of accurately integrating the different scales. Today he is working as a Machine Learning Engineer at Scaleout (Uppsala, Sweden).

• Title of MSc dissertation "A geometric approach to stability of Matter".

Jimmy Kungsman

Master student, Uppsala University, Sweden, 2008.

Jimmy earned a Ph.D. in Mathematics from Uppsala University in 2014, with the thesis “Resonances for the Dirac operator”, advised by Prof. M. Melgaard. He works as a system developer at Saab, Stockholm, Sweden.

• Title of MSc dissertation "Approximating resonances with the Complex Absorbing Potential method".

Tomas Johnson

Master student, Uppsala University, Sweden, 2005.

As a spin-off of this MSc thesis, Tomas published a paper with Prof M. Melgaard entitled “On the maximal ionization for the atomic Pauli operator” (Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 2005). Subsequently, Tomas earned a Ph.D. in Mathematics from Uppsala University in 2009, with the thesis “Computer-aided Computation of Abelian Integrals and Robust Normal Forms”. He held several post-doctoral postions from 2010 to 2013 (e.g., spending 1 year at Cornell University) before he took up a position as Applied Researcher at the Fraunhofer-Chalmers Centre for Industrial Mathematics, Gothenburg, Sweden. To date, he has published more than 20 papers, primarily on dynamical systems and ergodic theory, fluid mechanics and numerical analysis.

• Title of MSc dissertation "Maximal ionization of atoms and molecules in external magnetic fields"

Christophe Lacave

Master student, Uppsala University, Sweden, 2004.

Christophe earned a Ph.D. in Mathematics from Université Claude Bernard (Lyon) in 2009, with the thesis “Fluides autour d’obstacles minces”, advised by Dragos Iftimie. He is currently a Senior Lecturer at Institut Fourier, Université Grenoble Alpes. He has published more than 25 papers on mathematical fluid mechanics.

• Title of MSc dissertation "Geometrical approach to inverse quantum scattering".

Camille Illand

Master student, Uppsala University, Sweden, 2004.

Camille later earned a Ph.D. in Mathematics (Probability and Finance) from Université Pierre et Marie Curie. He works as a quantitative analyst at AXA Investment Managers, Paris, France.

• Title of MSc dissertation "Functional calculus"

Aurélien Monteillet

Master student, Uppsala University, Sweden, 2004.

Aurélien went on to earn a Ph.D. in Mathematics from Université de Brest, France, in 2008, with the thesis “Contribution à l’étude d’équations de propagations de fronts locales et non-locales”, advised by Pierre Cardaliaguet. In his doctoral thesis he proves integral formulations of the eikonal equation, equivalent to the notion of viscosity solution in the framework of the set-theoretic approach to front propagation problems. He applies these integral formulations to investigate the regularity of the front.

• Title of MSc dissertation "Atomic Schrödinger operator"