Research

Current interests

I am part of Professor Susanna Zimmermann's research group funded by the State Secretariat for Education, Research and Innovation (SERI). Previously, the team worked on the ERC-funded Saphidir project, which sought to describe all Sarkisov links in any dimension and in non-classic settings. 

Furthermore, I am interested in the birational geometry of Calabi-Yau pairs and a refined version of the Sarkisov Program, which is called volume preserving. Some of my goals are to produce new examples of special subgroups of higher-dimensional Cremona groups via log Calabi-Yau geometry and to give a nice description of them. Additionally, I am interested in describing which birational maps between certain Calabi-Yau pairs are volume preserving, aiming at classification purposes. Recently, I have also been thinking about correspondences between abelian and K3 surface fibrations of Calabi-Yau threefolds. 

My research can be found on arXiv, Google Scholar, ResearchGate and Academia.

Preprints

• E. Alves da Silva, F. Figueroa, J. Moraga. Algebraic tori in the complement of quartic surfaces, 2024. [arXiv:2411.03506] (Submitted).

• E. Alves da Silva. Birational geometry of log Calabi-Yau pairs (P^3, D) of coregularity 2, 2024. [arXiv:2402.13970] (Submitted).

• E. Alves da Silva. On the decomposition group of a nonsingular plane cubic by a log Calabi-Yau geometrical perspective, 2024. [arXiv:2402.13968] (Submitted).

Theses

• PhD thesis: Log Calabi-Yau geometry and Cremona maps. IMPA. 2023. Slides & Video.

• Master dissertation (in Portuguese): Weighted forms of Euler's Theorem and rooted partitions: establishing a combinatorial treatment for certain Ramanujan identities. UFRGS. 2018. Slides.

• Undergraduate completion work (in Portuguese): A parallel between Felix Klein's ideas and the effects of OBMEP. UFRGS. 2017. Slides.

Posters presented

• Algebraic tori in the complement of quartic surfaces, École d'été en Mathématiques : Le groupe de Cremona, Institut Fourier - Université Grenoble Alpes, 26 June 2025. Poster.

• Log Calabi-Yau geometry and Cremona maps, VI BrAG meeting, University of Sheffield, 10 April 2024. Poster.

• Log Calabi-Yau geometry and Cremona maps, 34th Brazilian Mathematics Colloquium, IMPA, 24 July 2023. Poster.

• A parallel between Felix Klein's ideas and the effects of OBMEP, III Simpósio Nacional da Formação do Professor de Matemática, Colégio Militar do Rio de Janeiro, 17 - 18 November 2017. Poster.

• Weighted forms of Euler's Theorem and some results on rooted partitions, Workshop de Verão e PICME em Matemática do ICMC, ICMC - USP, 27 January 2017. Poster.

Previous interests

During my Master I studied Combinatorics and integer partitions. My advisor was Professor Eduardo Brietzke.

The goal of my Master dissertation was to understand weighted forms of Euler's Theorem to give a combinatorial treatment for certain Ramanujan's formulas.