Faculty of Mathematics and Computer Science, "Ovidius" University of Constanta, Romania, in partnership with

Institute of Mathematics of the National Academy of Sciences of Ukraine

Centre for Systems and Information Technologies, University of Nova Gorica, Slovenia

Faculty of Mathematics and Computer Science, University of Bucharest

“Simion Stoilow” Institute of Mathematics of the Romanian Academy, organizes the conference

A new approach in theoretical and applied methods in algebra and analysis

Constanta, 4-6 April 2013

This conference is supported by the CNCS-UEFISCDI grant PN-II-ID-WE-2012-4-169

Director of the grant: Cristina FLAUT

Details on

http://math.univ-ovidius.ro/default.aspx?cat=Evenimente
The aim of this conference is to bring together mathematicians from some European countries in order to exchange their research experience in studying algebra and their applications in analysis. More precisely, some connections between algebra and analysis will be presented in the following research directions:

a) The study of the algebras of hypercomplex numbers. Some mathematicians from Russia, USA, UK, Germany, Italy, Belgium, Poland, Mexico, Ukraine, and Romania have a long experience and important results in this research area.

b) Applications of these algebras in solving PDEs, in studying codes, in combinatorics, etc. Hypercomplex analysis provides effective methods for solving some partial differential equations, like for instance the three-dimensional Laplace equation, the biharmonic equation, and also some other classical equations that appear in mathematical physics.

c) The hyperstructures (such as hypergroups, hyperalgebras, and so on) with emphasis on fuzzy sets and systems, as well as on finite geometries, hypergraphs, etc. There are some specialists in this research field in Constanta and Iasi, and there is a fruitful cooperation of the algebra schools in Iasi, Constanta and Italy. The theory of algebraic hyperstructures is a natural generalization of the theory of classical algebraic structures such as groups, rings, fields and vector spaces. In a hyperstructure, the operations are multivalued functions that associate with any couple of elements a subset of the support set. They are studied in connection with binary or n-ary relations, fuzzy sets, rough sets, probabilities, code theory, cryptography, and social sciences. In geometry, they are useful to redefine from an algebraic point of view the classical geometries, or in the study of algebraic geometry, tropical geometry and number theory. From an analytic point of view, the hypergroups can be studied through their topological properties. The concepts of pseudotopological and strong topological hypergroups have been obtained as a generalization of topological groups, and were recently extended to the fuzzy case. Besides, several actions of hypergroups have interesting applications in the theories of metric spaces and of partial differential equations.

d) Special classes of rings, modules and algebras with many applications with a high degree of interdisciplinarity: in number theory (such as, for instance, the levels and sublevels of algebras), coding theory, etc.

e) Hopf algebras and other topics in non-commutative algebras. Hopf algebras have connections with and applications to many branches of mathematics and physics, such as number theory (formal groups), algebraic geometry (affine group schemes), Galois theory (Hopf algebra actions), graded rings (Hopf algebra coactions), Lie theory (universal enveloping algebras), operator theory (Hopf *-algebras), representation theory, combinatorics, category theory, topology, non-commutative geometry, statistical mechanics, conformal and quantum field theories, etc. Many times, Hopf algebras unified results from different fields. Several talks illustrating the ubiquity of Hopf algebras and the usefulness of techniques related to them in different research areas will be presented.

Young researchers in algebra and analysis attending this conference will see the state-of-the-art and also some new trends in these research areas, and will benefit from exchanging some new research methods.

We hope that this conference will establish new scientific contacts in order to present and develop some new algebraic and topological methods in hypercomplex analysis, to give new applications of the above mentioned theories, and to indicate some innovative procedures to obtain new hyperstructures connected with binary relations, hypercomplex numbers,
and metric spaces.

On this occasion, we also intend to celebrate the appearance of the twentieth volume of our journal Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica (http://www.anstuocmath.ro/) and its founder, Professor Mirela Stefanescu.

Faculty of Mathematics and Computer Science, "Ovidius" University of Constanta, Romania, in partnership withInstitute of Mathematics of the National Academy of Sciences of UkraineCentre for Systems and Information Technologies, University of Nova Gorica, SloveniaFaculty of Mathematics and Computer Science, University of Bucharest“Simion Stoilow” Institute of Mathematics of the Romanian Academy,organizes the conferenceA new approach in theoretical and applied methods in algebra and analysis## Constanta, 4-6 April 2013

This conference is supported by the CNCS-UEFISCDI grant PN-II-ID-WE-2012-4-169Director of the grant: Cristina FLAUT

http://math.univ-ovidius.ro/default.aspx?cat=EvenimenteDetails onThe aim of this conference is to bring together mathematicians from some European countries in order to exchange their research experience in studying algebra and their applications in analysis. More precisely, some connections between algebra and analysis will be presented in the following research directions:

a) The study of the algebras of hypercomplex numbers. Some mathematicians from Russia, USA, UK, Germany, Italy, Belgium, Poland, Mexico, Ukraine, and Romania have a long experience and important results in this research area.

b) Applications of these algebras in solving PDEs, in studying codes, in combinatorics, etc. Hypercomplex analysis provides effective methods for solving some partial differential equations, like for instance the three-dimensional Laplace equation, the biharmonic equation, and also some other classical equations that appear in mathematical physics.

c) The hyperstructures (such as hypergroups, hyperalgebras, and so on) with emphasis on fuzzy sets and systems, as well as on finite geometries, hypergraphs, etc. There are some specialists in this research field in Constanta and Iasi, and there is a fruitful cooperation of the algebra schools in Iasi, Constanta and Italy. The theory of algebraic hyperstructures is a natural generalization of the theory of classical algebraic structures such as groups, rings, fields and vector spaces. In a hyperstructure, the operations are multivalued functions that associate with any couple of elements a subset of the support set. They are studied in connection with binary or n-ary relations, fuzzy sets, rough sets, probabilities, code theory, cryptography, and social sciences. In geometry, they are useful to redefine from an algebraic point of view the classical geometries, or in the study of algebraic geometry, tropical geometry and number theory. From an analytic point of view, the hypergroups can be studied through their topological properties. The concepts of pseudotopological and strong topological hypergroups have been obtained as a generalization of topological groups, and were recently extended to the fuzzy case. Besides, several actions of hypergroups have interesting applications in the theories of metric spaces and of partial differential equations.

d) Special classes of rings, modules and algebras with many applications with a high degree of interdisciplinarity: in number theory (such as, for instance, the levels and sublevels of algebras), coding theory, etc.

e) Hopf algebras and other topics in non-commutative algebras. Hopf algebras have connections with and applications to many branches of mathematics and physics, such as number theory (formal groups), algebraic geometry (affine group schemes), Galois theory (Hopf algebra actions), graded rings (Hopf algebra coactions), Lie theory (universal enveloping algebras), operator theory (Hopf *-algebras), representation theory, combinatorics, category theory, topology, non-commutative geometry, statistical mechanics, conformal and quantum field theories, etc. Many times, Hopf algebras unified results from different fields. Several talks illustrating the ubiquity of Hopf algebras and the usefulness of techniques related to them in different research areas will be presented.

Young researchers in algebra and analysis attending this conference will see the state-of-the-art and also some new trends in these research areas, and will benefit from exchanging some new research methods.

We hope that this conference will establish new scientific contacts in order to present and develop some new algebraic and topological methods in hypercomplex analysis, to give new applications of the above mentioned theories, and to indicate some innovative procedures to obtain new hyperstructures connected with binary relations, hypercomplex numbers,

and metric spaces.

On this occasion, we also intend to celebrate the appearance of the twentieth volume of our journal Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica(http://www.anstuocmath.ro/) and its founder, Professor Mirela Stefanescu.For other details, please see:http://math.univ-ovidius.ro/default.aspx?cat=Evenimente