# Maths Research Associates 2021 Nottingham

Lead Research Organisation:
University of Nottingham

Department Name: Sch of Mathematical Sciences

### Abstract

Abstracts are not currently available in GtR for all funded research. This is normally because the abstract was not required at the time of proposal submission, but may be because it included sensitive information such as personal details.

## People |
## ORCID iD |

Thomas Sotiriou (Principal Investigator) |

### Publications

Chattopadhyay Pratik

*Dark Matter from Evaporating PBH dominated in the Early Universe*
Dorigoni D
(2022)

*Modular graph forms from equivariant iterated Eisenstein integrals*in Journal of High Energy Physics
Drewitt J
(2022)

*Laplace-eigenvalue equations for length three modular iterated integrals*in Journal of Number Theory
Kalise D
(2023)

*Consensus-based optimization via jump-diffusion stochastic differential equations*in Mathematical Models and Methods in Applied Sciences
Radley T
(2024)

*Quadrature-free polytopic discontinuous Galerkin methods for transport problems*in Mathematics in Engineering
Thaalba F
(2023)

*Black hole minimum size and scalar charge in shift-symmetric theories*in Classical and Quantum Gravity
Ventagli G
(2024)

*Incompatibility of gravity theories with auxiliary fields with the standard model*in Physical Review DDescription | This grant supported 6 Research Associates for periods from 6 to 12 months. Their research spanned several areas of Mathematical Sciences (Applied Mathematics, Pure Mathematics, Mathemetical Physics) and their work made important contribution in the following topics: Optimization, Stochastic Differential Equations, Computational Mathematics, Modular Forms, Number Theory, String Theory, and Gravitation. |

Exploitation Route | The research outcomes of this award will lead to further advances to several areas of Computational Mathematics, Number theory, and Mathematical Physics and might have more long-term impact on sectors such as Engineering and Finance. |

Sectors | Other |

Description | Computational methods for colliding particles under constant temperature |

Amount | £3,000 (GBP) |

Organisation | International Centre for Mathematical Sciences (ICMS) |

Sector | Academic/University |

Country | United Kingdom |

Start | 08/2022 |

End | 09/2022 |

Description | Stochastic Numerics for Sampling on Manifolds |

Amount | £80,189 (GBP) |

Funding ID | EP/X022617/1 |

Organisation | Engineering and Physical Sciences Research Council (EPSRC) |

Sector | Public |

Country | United Kingdom |

Start | 03/2023 |

End | 03/2024 |

Description | Collaborations with Matthes, Dorigoni, Doroudiani, Hidding, Kleinschmidt, Schlotterer and Verbeek |

Organisation | Durham University |

Country | United Kingdom |

Sector | Academic/University |

PI Contribution | This colloboration is on 'Modular graph forms from equivariant iterated Eisenstein integrals': Joshua Drewitt worked with Nils Matthes to help provide a Number theory perspective to the problem in String theory of understanding modular graph forms, and how they connect to Francis Brown's real analytic modular forms. He used his previous reserach on real analytic modular forms including his work on 'Laplace-eigenvalue equations for length three modular iterated integrals' to help find this connection. |

Collaborator Contribution | Using the above Daniele Dorigoni, Axel Kleinschmidt and Oliver Schlotterer built upon their previous theory from 'Poincaré series for modular graph forms at depth two' Parts I and II to provide the first validations that modular graph forms are contained in the space of real analytic modular forms. Mehregan Doroudiani, Martijn Hidding, and Bram Verbeek were also crucial in providing this validation and were a key part of producing a large dataset of explicit examples in mathematica. |

Impact | Modular graph forms from equivariant iterated Eisenstein integrals https://link.springer.com/article/10.1007/JHEP12(2022)162 |

Start Year | 2021 |

Description | Collaborations with Matthes, Dorigoni, Doroudiani, Hidding, Kleinschmidt, Schlotterer and Verbeek |

Organisation | Max Planck Society |

Department | Max Planck Institute for Gravitational Physics |

Country | Germany |

Sector | Academic/University |

PI Contribution | This colloboration is on 'Modular graph forms from equivariant iterated Eisenstein integrals': Joshua Drewitt worked with Nils Matthes to help provide a Number theory perspective to the problem in String theory of understanding modular graph forms, and how they connect to Francis Brown's real analytic modular forms. He used his previous reserach on real analytic modular forms including his work on 'Laplace-eigenvalue equations for length three modular iterated integrals' to help find this connection. |

Collaborator Contribution | Using the above Daniele Dorigoni, Axel Kleinschmidt and Oliver Schlotterer built upon their previous theory from 'Poincaré series for modular graph forms at depth two' Parts I and II to provide the first validations that modular graph forms are contained in the space of real analytic modular forms. Mehregan Doroudiani, Martijn Hidding, and Bram Verbeek were also crucial in providing this validation and were a key part of producing a large dataset of explicit examples in mathematica. |

Impact | Modular graph forms from equivariant iterated Eisenstein integrals https://link.springer.com/article/10.1007/JHEP12(2022)162 |

Start Year | 2021 |

Description | Collaborations with Matthes, Dorigoni, Doroudiani, Hidding, Kleinschmidt, Schlotterer and Verbeek |

Organisation | Solvay |

Country | Global |

Sector | Private |

PI Contribution | This colloboration is on 'Modular graph forms from equivariant iterated Eisenstein integrals': Joshua Drewitt worked with Nils Matthes to help provide a Number theory perspective to the problem in String theory of understanding modular graph forms, and how they connect to Francis Brown's real analytic modular forms. He used his previous reserach on real analytic modular forms including his work on 'Laplace-eigenvalue equations for length three modular iterated integrals' to help find this connection. |

Collaborator Contribution | Using the above Daniele Dorigoni, Axel Kleinschmidt and Oliver Schlotterer built upon their previous theory from 'Poincaré series for modular graph forms at depth two' Parts I and II to provide the first validations that modular graph forms are contained in the space of real analytic modular forms. Mehregan Doroudiani, Martijn Hidding, and Bram Verbeek were also crucial in providing this validation and were a key part of producing a large dataset of explicit examples in mathematica. |

Impact | Modular graph forms from equivariant iterated Eisenstein integrals https://link.springer.com/article/10.1007/JHEP12(2022)162 |

Start Year | 2021 |

Description | Collaborations with Matthes, Dorigoni, Doroudiani, Hidding, Kleinschmidt, Schlotterer and Verbeek |

Organisation | University of Copenhagen |

Country | Denmark |

Sector | Academic/University |

PI Contribution | |

Collaborator Contribution | |

Impact | |

Start Year | 2021 |

Description | Collaborations with Matthes, Dorigoni, Doroudiani, Hidding, Kleinschmidt, Schlotterer and Verbeek |

Organisation | Uppsala University |

Country | Sweden |

Sector | Academic/University |

PI Contribution | |

Collaborator Contribution | |

Impact | |

Start Year | 2021 |