Complex Analysis
Riemann zeta function, transcendental equations, and holomorphic dynamics.
Research
Focus and interests
My main research area is Analytic Number Theory. I am especially interested in the asymptotic behavior of arithmetic functions, counting problems, and the use of complex-analytic and probabilistic tools in number theory.
Number Theory
Sieve methods, the distribution of primes, and additive problems.
Combinatorics
Enumerative, analytic, and symbolic combinatorics, especially through generating functions.
Probability
Probabilistic methods in analytic number theory, random matrices, and unexpected probabilistic structures in arithmetic.
Questions
Problems that guide my interests
- How can the Circle Method be generalized?
- What is the intrinsic relationship between probability and number theory?
- How can the Siewert–Burniston method be used in different analytic settings?
Current project
Master's thesis
In progress
A Probabilistic Approach to the Bateman–Horn Conjecture
I am studying how ideas related to the Zeta distribution can be brought into the study of the Bateman–Horn conjecture, with the aim of understanding how far a probabilistic formulation can be developed and what analytic information it can recover.
Thesis
Undergraduate work
El Método del Círculo de Hardy–Littlewood
A historical and mathematical study of the Hardy–Littlewood Circle Method, from additive equations and generating functions to the modern formulation of the technique.
Publications
Papers and preprints
Papers in preparation.