# Albert Garreta

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 discrete optimization, computer science, number theory, and group theory. Later I became interested in different more applied areas such as machine learning (particularly reinforcement learning), and in cryptography and blockchain technology.

## APPOINTMENTS/EDUCATION

• Currently: Blockchain and Cryptography Researcher, Nethermind

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

• 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

## INTERESTS

Algorithmic problems in rings, monoids, groups.

Cryptography

Blockchain technology and development

Machine learning

CV (last updated May 2022)

Machine learning competitions

Github profile.

# 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, and all my work can be found in my CV , in my github profile, and in my kaggle profile.

## Solving equations

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.

Note: The journal Bulletin of Mathematical Sciences is ranked 17 out of 312 in the category of Mathematics (JCR ranking)

## StarkNet hackathon and Cairo Underhanded Contest

• 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

• Honorable mention at the Cairo Underhanded contest (this contest had a total of 1 winner and 2 honorable mentions). Cairo is a programming language for writing provable programs (via zero-knowledge proofs). The goal of the contest was to produce a seemingly innocent piece of Cairo code with a hidden bug/exploit within it.

Here is the Repository.

## Private computation in the blockchain

• SMPC & BLOCKCHAIN: Creating Private Data Marketplace (link, submitted to a journal), with Julen BernabĂ© and Oscar Lage,

• Blockchain Homomorphic Encryption (link), with Leire Etxebarria and Oscar Lage.

These are two theses I co-directed within the master's degree Blockchain Technology and Crypto-Economy (link in Spanish). They center around implementing privacy-enabling computation techniques (Multi Party Computation and Homomorphic Encryption) within a blockchain framework. The first is currently being reviewed for publication.

## Classifying stars

• Results of the Photometric LSST Astronomical Time-series Classification Challenge (PLAsTiCC), with Renee Hlozek et al. to appear.

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.

Note: Our solution was ranked 9th out of 1089

# Teaching

I am currently teaching two cryptography courses as part of the master's degree in Blockchain Technology and Crypto-Economy at the University of the Basque Country UPV (Spain).

In 2020 I taught a PhD introductory course to Deep Learning at UPV. The course videos can be found here.

Prior to that I taught basic data science and python programming in ESADE (Barcelona, Spain), and, during my PhD years, I taught Differential Equations at Stevens Institute of Technology (New Jersey, USA).

More details on my teaching activity can be found in my CV.

# Programming

I enjoy programming and learning about different languages. I am very comfortable with Python, I have an intermediate level of Solidity and Cairo, and recently I started programming in Rust. I also have basic notions of C++ from my university years.

Github profile

# Miscellaneous

## Painting

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

## Cinema

I love cinema. If you are curious you can see the movies I have watched and how I have rated them here