Students

I endorse Federico Ardila's axioms:

Axiom 1. Mathematical talent is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries. 

Axiom 2. Everyone can have joyful, meaningful, and empowering mathematical experiences. 

Axiom 3. Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs. 

Axiom 4. Every student deserves to be treated with dignity and respect.

What follows is a biographical listing of students with whom I have worked on research projects.

• Rodolfo Reis Soldati: Rodolfo completed an undergraduate Iniciação Cientifica project at the Federal University of Minas Gerais (UFMG) on ribbon graphs in 2013–2014. He has recently completed a Ph.D in theoretical physics split between the University of São Paulo (USP) and the University of Stuttgart.

• Rafael Barbosa da Silva: Rafael completed a Ph.D thesis at UFF (2016-2020) on the combinatorics of numerical semigroups motivated by the algebraic geometry of curves. He is currently an assistant professor at the Federal Rural University of Pernambuco. Our co-authored paper is here: Weight bounds for (3,gamma)-hyperelliptic curves

• Vinícius Lara Lima: Vinícius recently completed a Ph.D at UFMG (2016-2020) on the geometry and combinatorics of cuspidal rational curves in projective space. I was a co-advisor, along with Renato Vidal Martins (UFMG). Our three-person paper is here: Severi dimensions for unicuspidal curves 

• Alexandre Silva dos Reis : Alexandre recently completed a Ph.D at UFMG (2018-2022) on the geometry and combinatorics of cuspidal rational curves in projective space, and in the process verified (natural extensions) of conjectures postulated in Vinícius' thesis. I was a co-advisor, along with Renato Vidal Martins and Vinícius Lima of UFMG. Our four-person paper is here: Certified Severi dimensions for hyperelliptic and supersymmetric cusps 

• Renata Vieira Costa: Renata started a Ph.D at UFF in fall 2020. She is studying value semigroups of generic cusps associated with fixed ramification types, and the function that to a given ramification type assigns the corresponding genus (i.e., delta-invariant) of the generic cusp of that type. I am a co-advisor, along with Juliana Coelho (UFF). Our three-person paper with Nathan Kaplan is here: Cusps in C^3 with prescribed ramification 

• Lucas Henrique Martins da Silva: Lucas started a master's at Unicamp in spring 2023. He is studying the geometry and combinatorics of cuspidal rational curves, with a view to verifying new instances of conjectures developed in collaboration with Renato Vidal Martins and Vinícius Lara Lima.

• Juliana Calderón Moreno: Juliana started a Ph.D at Unicamp in fall 2023. She is studying Brill--Noether theory on cuspidal rational curves.

• Leonardo Garcia de Castro: Leonardo started a Ph.D at Unicamp in fall 2023. He is studying generalized Severi varieties of cuspidal rational curves.