**Marcelo Campos**

e-mail: mc2482@cam.ac.uk

arxiv

**About me:**

I am a Junior Research Fellow at Trinity College in Cambridge and Pesquisador Adjunto (Assistant Professor) at IMPA. Before that I did a postdoc with Peter Keevash at the University of Oxford. I completed my
PhD

with Rob Morris at IMPA in March 2023.

My interests have been focused mainly on ramsey theory, random matrix theory, convex geometry, probabilistic and additive combinatorics, but I am open to learning about and working on any nice problems :).

**Research:**

**Upper bounds for multicolour Ramsey numbers,**

with Paul Balister, Béla Bollobás, Simon Griffiths, Eoin Hurley, Robert Morris, Julian Sahasrabudhe and Marius Tiba,

submitted

**A new lower bound for sphere packing,**

with Matthew Jenssen, Marcus Michelen and Julian Sahasrabudhe,

submitted

**An exponential improvement for diagonal Ramsey,**

with Simon Griffiths, Robert Morris and Julian Sahasrabudhe,

submitted

**Towards an optimal hypergraph container lemma,**

with Wojciech Samotij,

submitted

**On the independence number of sparser random Cayley graphs,**

with Gabriel Dahia and João Pedro Marciano,

accepted to *Journal of the London Mathematical Society*

**The singularity probability of a random symmetric matrix is exponentially small,**

with Matthew Jenssen, Marcus Michelen and Julian Sahasrabudhe,

accepted to *Journal of the American Mathematical Society *

**The least singular value of a random symmetric matrix,**

with Matthew Jenssen, Marcus Michelen and Julian Sahasrabudhe,

*Forum of Mathematics, Pi *, volume 12, e3 (2024)

**Counting orientations of random graphs with no directed k-cycles**

with Maurício Collares and Guilherme Oliveira Mota,

*Random Structures and Algorithms*, volume 64, pages 676 — 691 (2024)

**Towards Hadwiger's conjecture via Bourgain Slicing,**

with Peter van Hintum, Robert Morris and Marius Tiba,

*International Mathematics Research Notices *, rnad198 (2023)

**The typical approximate structure of sets with bounded sumset,**

with Matthew Coulson, Oriol Serra and Maximilian Wötzel,

*SIAM Journal on Discrete Mathematics*, volume 37, issue 3, pages 1386 — 1418 (2023)

**Singularity of random symmetric matrices revisited,**

with Matthew Jenssen, Marcus Michelen and Julian Sahasrabudhe,

*Proceedings of the American Mathematical Society*, volume 150, no. 7, pages 3147 — 3159 (2022)

**The typical structure of sets with small sumset,**

with Maurício Collares, Robert Morris, Natasha Morrison and Victor Souza,

*International Mathematics Research Notices *, volume 2022, issue 14, pages 11011 — 1055 (2022)

**On the singularity of random symmetric matrices**,

with Letícia Mattos, Robert Morris and Natasha Morrison,

*Duke Mathematical Journal *, volume 170, no. 5, pages 881 — 907 (2021)

**On the number of sets with a given doubling constant**,

*Israel Journal of Mathematics*, volume 236, pages 711 — 726 (2020)