Carleton Finite Fields eSeminar - Summer 2021 Abstracts
Summer 2021 Abstracts
Date/Time: August 4, 2021
Speaker: Emina Soljanin (Rutgers University)
Title:
Codes, Graphs, and Hyperplanes in Data Access Service
Abstract:
Distributed computing systems strive to maximize the number of
concurrent data access requests they can support with fixed
resources. Replicating data objects according to their relative
popularity and access volume helps achieve this goal. However,
these quantities are often unpredictable. Erasure-coding has
emerged as an efficient and robust form of redundant storage.
In erasure-coded models, data objects are elements of a finite
field, and each node in the system stores one or more linear
combinations of data objects. This talk asks 1) which data
access rates an erasure-coded system can support and 2) which
codes can support a specified region of access rates. We will
address these questions by casting them into some known and
some new combinatorial optimization problems on graphs. We
will explain connections with batch codes. This talk will also
describe how, instead of a combinatorial, one can adopt a
geometric approach to the problem.
slides, video
Date/Time: July 7, 2021
Speaker: Alexander Pott (Otto von Guericke University Magdeburg)
Title: Relaxations of almost perfect nonlinearity
Abstract: abstract,
video,
slides.
Date/Time: June 2, 2021
Speaker: Gary McGuire (University College Dublin)
Title: Linear Fractional Transformations and Irreducible
Polynomials over Finite Fields
Abstract:
We will discuss polynomials over a finite field where linear fractional
transformations permute the roots. For subgroups G of PGL(2,q) we
will demonstrate some connections between factorizations of certain
polynomials into irreducible polynomials over Fq, and the field of
G-invariant rational functions. Some unusual patterns in the
factorizations are explained by this connection.