Algebra - Combinatorics - Distributed storage - Corrector codes - Information theory

Umberto Martínez Peñas

Algebra and Code Theory SINGACOM Research Group IMUVA
My research career

I obtained my bachelor's degree in Mathematics and my master's degree in Mathematics research from the University of Valladolid in 2013 and 2014, respectively. From 2014 to 2017, I did my PhD in Mathematics at Aalborg University (Denmark), which focused on the algebraic theory of error-correcting codes. In 2018 and 2019, I was a postdoctoral researcher in the department of Electrical and Computer Engineering at the University of Toronto (Canada). In 2020 and 2021, I was maître assistant in the departments of Mathematics and Computer Science at the University of Neuchâtel (Switzerland). Since the beginning of 2022, I am a Maria Zambrano researcher in the Department of Algebra, Mathematical Analysis, Geometry and Topology at the University of Valladolid. In 2016, I obtained an EliteForsk Rejsestipendium grant (elite research travel grant, in Spanish) from the Danish Ministry of Education. In 2018, I obtained a PhD thesis award from the Danish Academy of Natural Sciences (Danmarks Naturvidenskabelige Akademi in Danish), and in 2019, I obtained the Vicent Caselles Mathematical Research Award from the Spanish Royal Mathematical Society (RSME) and the BBVA Foundation.

My research

My main object of study is error correcting codes, and their applications in Distributed Storage, data security and privacy, Secret Sharing, and Network Coding. For this, I mainly use tools from Algebra, Combinatorics and Algebraic Geometry.

One of the main codes I have designed are linearized Reed-Solomon codes. These codes are the first known optimal codes for the sum-rank metric, which generalizes the Hamming and rank metrics at the same time, and is of interest in distributed storage (for the construction of PMDS codes), in Space-Time Coding and in multishot Network Coding, among others.