Research

My research topics are intrinsically connected to the investigation of determinantal point processes arising from random matrix models and their underlying integrable systems. Some other key concepts in my research include partition functions, deformations of reproducing kernels, integrable hierarchies, asymptotic analysis and Riemann-Hilbert problems.
In earlier career I also worked with tight binding for graphene, inclusive physics education and gamification.

Cafasso, M., da Silva Pinheiro, C. M., "Unitary ensembles with a critical edge point, their multiplicative statistics and the Korteweg-de-Vries hierarchy". 2026.
Journal of the London Mathematical Society 113 (3), e70496 

da Silva Pinheiro, C. M., Neves, L., Perini, A. P., Silva, M. F., "Modelos didáticos para ensino inclusivo de física nuclear" (Didactic models for inclusive nuclear physics education).
Revista em Extensão, v. 20, p. 213-227, 2022. DOI: 10.14393/REE-v20n22021-60479.

Neri, H.; Silva, J.; da Silva Pinheiro, C. M.; Dantas, C.; Takahashi, E., "Jogo Digital para Aprendizagem de Ondulatória" (Digital game for learning of wave theory)
Workshops of CBIE 2016, p.886-890. DOI:10.5753/cbie.wcbie.2016.886

Cafasso, M., da Silva Pinheiro, C. M., "Asymptotics for solutions of the Korteweg-de-Vries hierarchy associated to a deformation of the higher order Painleve I kernel".
2025. Preliminary version: here.

da Silva Pinheiro, C. M.,  "Asymptotic expansion for multiplicative statistics in a Hermitian matrix model connected to the lower tail of the KPZ equation".
2025. Arxiv:2511.01120

PhD dissertation: Asymptotic behaviour of Painlevé transcendents and random matrix models. (In English)

Master Thesis: Integrable Systems and Partition Functions of Random Matrix Models. (In English)

Undergraduate Thesis: Problema do grafeno com modificações: uma solução a partir de Tight Binding. (In Portuguese)