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:

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

On the independence number of sparser random Cayley graphs,
with Gabriel Dahia and João Pedro Marciano,
submitted

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)