I am a mathematician and computer scientist. I began my career working (mostly) on the problem of solving (polynomial) equations in different types of algebraic structures (rings, algebras, groups, monoids). These topics live at the intersection of abstract algebra, group theory, computer science, and discrete optimization. Later I focused my work on cryptography and blockchain technology, specializing on zero-knowledge proofs.

## APPOINTMENTS/EDUCATION

Currently: Lead Cryptography Researcher, Nethermind.

Currently: Postdoctoral fellow, Basque Center of Applied Mathematics (BCAM) (Bilbao, Spain).

2022-2023: Blockchain and Cryptography Researcher, Nethermind.

2017-2021: Postdoctoral fellow, University of the Basque Country (Bilbao, Spain),

2012-2017: PhD in mathematics, Stevens Institute of Technology (New Jersey, USA).

2007-2012: Licenciature in mathematics, Polytechnic University of Catalonia (Barcelona, Spain).

Contact: garreta.a@gmail.com

## LINKS

Google Scholar, Machine learning competitions, Github profile. Twitter

# Selected Work

These are what I think are the most relevant projects I have worked on, listed in no particular order. A full list of publications is available here.

## Solving equations

Diophantine problems in solvable groups, Bulletin of Mathematical Sciences, Vol. 10, No. 01, 2050005 (2020), 21 pages, with Alexei Miasnikov and Denis Ovchinnikov.

Diophantine problems in rings and algebras: undecidability and reductions to rings of algebraic integers, preprint, with Alexei Miasnikov and Denis Ovchinnikov.

In these papers we study the problem of solving equations in different types of rings, algebras, and solvable groups. A connection is established between this problem and the problem of solving polynomial equations in rings of algebraic integers O. The latter, a generalization of Hilbert's 10th Problem (undecidability of integer polynomial equations), is a major open problem in number theory. Informally speaking, we prove that, for large classes of rings, algebras, and solvable groups A, solving equations in O can be reduced to solving equations in A. In some cases, we are able to prove that solving equations in A is an undecidable problem.

Here is a talk I gave on this topic.

## StarkNet hackathon

2nd place project at the first StarkNet Hackathon (Amsterdam, 2022). StarkNet is a Layer 2 network that uses zero-knowledge proofs to scale Ethereum. Here is the Repository

## Classifying stars

Results of the Photometric LSST Astronomical Time-series Classification Challenge (PLAsTiCC), with Renee Hlozek et al. The Astrophysical Journal Supplement Series, Volume 267, Number 2, 2023, doi

This paper describes the 10 best solutions to the Kaggle competition Photometric LSST Astronomical Time-series Classification Challenge (PLAsTiCC). In this challenge, participants had to infer the type of a star given time-series data of its light emissions.

Our solution was ranked 9th out of 1089

# Miscellaneous

## Cinema

I love cinema. These are some of my favorites movies since 2013 (in chronological order) :) and this is my letterboxd

## Painting

I have been painting occasionally over many years. Some of the results can be found here.