# 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**

**APPOINTMENTS/EDUCATION**

Currently:

**Blockchain and Cryptography Researcher,**NethermindCurrently:

**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**

**INTERESTS**

Algorithmic problems in rings, monoids, groups.

Cryptography

Blockchain technology and development

Machine learning

# 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**

**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.

**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**

**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**

**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),

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**

**Classifying stars**

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

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.