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CRM > English > Activities > Workshop on Polynomials over Finite Fields: Functional and Algebraic Properties
Workshop on Polynomials over Finite Fields: Functional and Algebraic Properties
Basic and last minute information

Dates: May 19 to 24, 2014
Objectives

The theory of polynomials over finite fields is fundamental for the study of finite fields, which in turn plays a central role in many areas of pure and applied mathematics. This is a classical area of mathematics with a rich history, going back to Gauss and Galois. The exciting and challenging problems concerning univariate and multivariate polynomials over finite fields are of intricate algebraic and number theoretic flavour and their study requires deep mathematical and computational tools. The determination and construction of special types of (irreducible, primitive, permutation) univariate and multivariate polynomials, for example, as well as understanding many of their functional and algebraic properties (composition, decomposition, iteration, factorization, size of value sets) are long standing problems in the theory of finite fields. These areas have attracted further attention in recent years due to their applications in cryptography, coding theory, combinatorics, design theory, quasi-Monte Carlo methods, communications.

Although the last decades have witnessed a vast amount of work and meetings on polynomials over finite fields, leading to solutions of some of the fundamental problems, inevitably many new questions and conjectures have emerged, with relevance to new areas of pure and applied mathematics. This workshop aims to provide means to meet these new challenges. To exemplify some of the newly emerged open research directions that will be addressed at this workshop, we can mention functional graphs of polynomials, iterations of polynomials over finite fields and orbit structures. Indeed, novel constructions of non-classical dynamical systems over finite fields and the classification of their anomalous behaviour, which is not present in standard constructions of complex dynamical systems, have led to innovative solutions to problems in cryptography, Monte Carlo methods, biological and physical systems. The combination of problems to be discussed in the proposed workshop are particularly selected not only because they are of great interest in theory and applications, but also because they are closely related and advancement in one may lead to solutions of others.

The research directions proposed for this workshop are closely related to finite fields, number theory, commutative algebra, cryptography, dynamical systems, combinatorics, to mention just a few. Thus, researchers of different backgrounds and in possession of different technical toolboxes sometimes work on similar questions without knowing each other's ideas and results. The goal of the workshop is to establish new collaborations, discuss potential solutions to open problems, formulate new ones, and try to advance the theory with innovative results. We believe that it is time to assess the progress, while proposing future directions of research.

Invited speakers
Pär Kurlberg, KTH Royal Institute of Technology
Wen-Ching Li, The Pennsylvania State University
Gary McGuire, University College, Dublin
Brigitte Vallée, Université de Caen
Organising Committee

Joachim von zur Gathen, Universität Bonn
Jaime Gutiérrez, Universidad de Cantabria
Alina Ostafe, University of New South Wales
Daniel Panario, Carleton University
Alev Topuzoglu, Sabanci University

Registration

Regular, junior and senior registration includes: documentation package, lunch tickets, reception, and coffees.

  • Regular registration fee: 230 €

  • Registration fee (junior and senior)*: 160 € 

  • Registration fee for participants affiliated to a Catalan University or members of the "Societat Catalana de Matemàtiques": 60 € (lunch tickets are not included)

(*) Retired or PhD students or postdocs whose thesis is not more than two years old.
 
Deadline for registration and payment: April 27, 2014

IMPORTANT: Due to the nature of the workshop as a research-oriented meting, the capacity is limited, attendance is by invitation, and not every participant will be able to give a talk. Much of the work will take place in small groups. If you are interested in attending the meeting, you must pre-register by sending an expression of interest before March 1, 2014 to Ms. Consol Roca (croca@crm.cat). The organising committee will reply by April 1, 2014.

Extended abstracts of the workshop (up to 4 pages) will be published in the new subseries “Research Perspectives CRM Barcelona” of the Birkhäuser's series “Trends in Mathematics”, the deadline being approximately one month after the event.

See here for more information.
Lodging

For lodging in the area please click here

For off-campus accommodation click here
Contact information

If you have any questions please contact Consol Roca (croca@crm.cat)