Research
Contact
- Name: Domenico Mergoni
- Email: d.mergoni -at- lse.ac.uk
- Work: London School of Economics
Future Projects
I welcome collaboration with anyone who would like to work with me on one (or more) of the following. These are only the projects for which I HAVE a clear research path in mind, with specific implementations, experiments, and analysis to do, I just didn’t have the time to implement them yet. Please get in touch with me even just to chat about them, or if you’re interested in collaborating.
- Can RL learn Combinatorial Games? Reinforcement Learning (RL) is really good at games, but is possibly really bad at Graph Theory (although initial results were quite optimistic [1, 2]). Would RL be good at Combinatorial Games? I am particularly interested to explore this about games on graphs. In particular the Balance Game or some Maker Breaker games.
- What can RL do in Graph Theory? There are some results that seem to indicate that RL is not good at Graph Theoretical problems [3, 4]. However, RL is clearly good at solving certain Graph-theoretical problems, and initial results were quite optimistic [1, 2]. What is the reason behind this variying behaviour?
- Sparsity? Quantization? What about both? Two well-known memory-reduction methods in Neural Networks are Sparsity and Quantization. These two methods are not orthogonal. However I do believe that there is a way of improving the current SotA to produce a lighter version of NN using the interplay between the two. The literature in the area seems to go towards a natural direction that hasn’t been developed, in my opinion, to the fullest.
- Let’s make EU healthier This is a project that has a wider breath and is not only linked to research. If you’re passionate about nutrition, hardcore computer science, and want to make a tangible impact, do get in touch.
Past and Present Projects
Work in progress
- Methodology for carbon credit assessment
with A. Perrella, G. Marastoni (2025++) - Partition universality for hypergraphs
with P. Allen, J. Böttcher (2025++) - An extension of the transference principle
with P. Allen, J. Böttcher, J. Lada (2025+) - Best Response Dynamics for Random Games
with G. Ashkenazi-Golan, E. Plumb, J. Skokan (2025++)
Submitted
- Simultaneous Best-Response Dynamics in Random Potential Games
with G. Ashkenazi-Golan, E. Plumb
Submit. to double-blind conference
Paper with code - Reinforcement Learning, Collusion, and the Folk Theorem.
with G. Ashkenazi-Golan, E. Plumb
Submit. Econometrica (2025) - Dirac’s theorem for graphs of bounded bandwidth.
with A.E. Díaz, P. Gupta, O. Parczyk, A. Sgueglia
Submit. Electron. J. Comb. (2024)
Accepted
- Graphs with large minimum degree and no short odd cycles are 3-colourable.
with J. Böttcher, N. Frankl, O. Parczyk, J. Skokan
Accept. Comb. Theory
Published
On product Schur triples in the integers.
with L. Mattos, O. Parczyk
SIAM Journal on Discrete Mathematics. Vol 39, Iss. 2 (2025)The Ramsey numbers of squares of paths and cycles
with P. Allen, B. Roberts, J. Skokan
The Electronic Journal of Combinatorics. Vol 31, Iss. 2 (2024), P2.11
Notes/Not for publication
Re-ILS: a metaheuristic approach for cardinality-constrained optimization
with Jian Shen (internal Amazon publication)Density of small diameter subgraphs in \(K_r\)-free graphs.
with E.K. Hng
| Title | Date | Occasion | Place |
|---|---|---|---|
| Product-free subsets of \([n]\) | Oct ’23 | LSE Seminar | London |
| Partition Universality | Aug ’23 | Eurocomb | Prague |
| The Ramsey numbers of \(P_{3n}^2\) and \(C_{3n}^2\) | Sep ’23 | DMV (Invited speaker) | Ilmenau |
| Apr ’23 | Invited seminar | Prague | |
| Jul ’22 | ICGT | Montpellier | |
| Jul ’22 | Invited seminar | TU Hamburg | |
| Chromatic profile of \(\{C_3,\dots{},C_{2k-1}\}\) | Mar ’23 | PCC | Birmingham |
| Jul ’22 | RSA | Poznan | |
| Jul ’22 | ICGT | Montpellier | |
| Jul ’22 | Invited seminar | TU Hamburg | |
| About the Pentagon Conjecture | Nov ’20 | LSE Seminar | London |
| Minimal Ramsey Graphs for Ciclicity | May ’19 | ETHZ Mittagsseminar | Zurich |
| Dimensione di Hausdorff del Moto Browniano | May ’19 | BSc Defense | Pisa |
| What | When | Where | Why |
|---|---|---|---|
| Graph-theoretical Tools in Statistics | 2022 | LSE | Mini-internship |
| A discussion about the Pentagon Problem | 2020 | ETHZ | MSc Thesis |
| Separator Theorems | 2019 | ETHZ | Semester Paper |
| A Glimpse of Young’s Tableaux | 2019 | ETHZ | Reading Course |
| On the Hausdorff Dimension of Brownian Motion | 2018 | Pisa Univ. | BSc Thesis |
| What | When | Where | Instit. | Type | Funded |
|---|---|---|---|---|---|
| DMV | Oct ’23 | Ilmenau | Conference (invited) | LSE | |
| CPMC | Sept ’23 | Zagreb | Workshop | LSE | |
| Eurocomb | Aug ’23 | Prague | Conference | LSE | |
| EEML | Jul ’23 | Košice | Summer School | LSE | |
| ALGA | Jun ’23 | Ragusa | Conference | CIVICA Grant | |
| UCLW | May ’23 | London | UCL | Workshop | |
| PSSC | Apr ’23 | Prague | Charles Uni. | Summer School | Charles Uni. |
| PCC | Mar ’23 | Birmingham | Conference | LSE | |
| Research Visit | Aug ’22 | Berlin | FU Berlin | Visit | LMS Grant |
| RSA | Aug ’22 | Gniezno | Conference | LSE | |
| Research visit | Jul ’22 | Prague | Czech Academy of Science | Visit | Czech Academy of Science |
| PSSDM | Jul ’22 | Prague | Charles Uni. | Summer School | Summer School |
| ICGT | Jul ’22 | Montpellier | Conference | LSE | |
| Research visit | May ’22 | Hamburg | TU Hamburg | Visit | TU Hamburg |
- Organiser
- PCC (Main organiser), Apr 2023, University of London and BCC. (National conference for postgraduate students).
- LSE PhD CGO Seminar (Main Organiser), 2022/23.
- Grants and invitations
- DMV Invited Speaker. Ilmenau. 2023.
- LMS Computer Science Small Grant (700£). London Mathematical Society. Funded visit to Berlin. 2022.
- LSE Contribution Award. Dept of Mathematics. LSE. 2021.