Joint Statistics and Applied Mathematics Colloquium: Giacomo Micheli (USF)
applied number theory and computer science
Location
Sondheim Hall : 409
Date & Time
February 19, 2025, 12:00 pm – 1:00 pm
Description
Title: Data Storage using Galois Theory over global function fields
Abstract: Distributed storage systems have scaled significantly in recent years, with data typically stored across multiple servers, each containing several terabyte-sized hard drives. A critical challenge in these systems is recovery from node failures, which can be caused by permanent unavailability (e.g., hard drive crashes) or temporary unavailability (e.g., updates or reboots). This talk will explore how Galois theory can be used to construct optimal locally recoverable codes (LRCs) over finite fields—algebraic structures that facilitate efficient data recovery. The construction relies on the Chebotarev Density theorem and the Tamo-Barg method for optimal LRCs. Specifically, we demonstrate that building optimal LRCs of large dimension and length is equivalent to finding extensions of global function fields with small Galois closures and specific structural properties.
References:
[1] Constructions of Locally Recoverable Codes which are Optimal, IEEE Transactions on Information Theory
[2](with A. Ferraguti) An equivariant isomorphism theorem for mod p reductions of arboreal Galois representations, Transactions of the American Mathematical Society
[3](with A. Ferraguti) Exceptional scatterdness in prime degree, Journal of Algebra
[4](with D. Bartoli) Algebraic constructions of complete m-arcs, Combinatorica