CLASSICAL AND CONSTRUCTIVE NONASSOCIATIVE ALGEBRAIC STRUCTURES:
FOUNDATIONS AND APPLICATIONS – CaCNAS:FA 2021

June 30 – July 02, 2201

Introduction to nonassociative algebra
OR
Playing havoc with the product rule?
(Bernard Russo, 2012)


The history of nonassociative algebraic structures can be traced at least to the middle of the 19th century. Today, the theory of nonassociative algebraic structures is an enormously broad and greatly advanced area. Interesting new algebraic ideas arise, with challenging opportunities to discover connections to other areas of mathematics, natural sciences and engineering. On the other hand, computer-assisted methods proved useful in the development of the theory of nonassociative algebraic structures, in particulary in finding proofs and constructing examples. We will try to present a brief overview of the origins of nonassociative algebraic structures, selection of current research topics and future directions, generalizations within the framework of classical, fuzzy and intuitionistic logic, and further applications. Topics include, but are not limited, to:

 

 

  • Groupoids (binary systems) and their generalizations (AG-groupoids, quasigroups, loops);
  • Nonassociative algebras and their generalizations (left almost algebras);
  • Ordered nonassociative algebraic structures (logical algebras);
  • Applications within natural sciences and engineering;
  • Computer-aided development and transformation of the theory of nonassociative algebraic structures;
  • Algebraic geometry and its relations with quiver algebras;
  • Enumerative combinatorics;
  • Representation theory;
  • Fuzzy Logic and Foundation Theory;
  • Fuzzy Algebraic Structures;
  • Group amalgams;
  • Actions of groups on various geometric objects, such as diagram geometric and buildings;
  • Constructive nonassociative algebraic structure

Speakers:

Victor Abramov, University of Tartu, Estonia
Chengming Bai, Chern Institute of Mathematics, China
M. Norbert Hounkonnou, University of Abomey-Calavy, Benin
Madad Khan, COMSATS University, Islamabad, Pakistan
Sergei Sivestrov, Mälardalen University, Sweden
Balazs Szendrol, University of Oxford, UK
Alice-Barbara Tumpach, Universite Lille 1, France
Melanija Mitrovic, University of NIS, Serbia
Sergey Shpectorov, University of Birmingham, UK

Organizers:

Mujahid Abbas
Melanija Mitrović
Mahouton Norbert Hounkonnou
Madad Khan

Local Organizing Committee:
Dr. Hassan Azad
Muhammad Imran Khan
Rizwan Anjum
Muhammad Bin Nasir
Raheel Farooki
Shakeela Riasat