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R E P O R T about the International Scientific Conference GRADED STRUCTURES IN ALGEBRA AND THEIR APPLICATIONS Dedicated to the Memory of Professor Marc Krasner Dubrovnik, 22-24 September 2016 http://www.iuc.hr/conference-details.php?id=283

At the Conference organized by the Department of Natural Sciences and Mathematics of the Academy of Sciences and Arts of Bosnia and Herzegovina (ANUBiH) in cooperation with the Institute Fourier of the University Joseph Fourier in Grenoble, France and the Faculty of Natural Sciences and Mathematics of the University of Maribor, Slovenia, welcoming speeches were given on behalf of the Conference organizer, President of ANUBiH academician Prof. Dr. Miloš Trifkovi ć, and on behalf of the International University Centre, Dubrovnik (IUC Dubrovnik), Prof. Dr. Krunoslav Pisk, director of the Center.

As the first of the three coordinators of the Conference, Prof. Dr. Mirjana Vuković, corresponding member of ANUBiH addressed the conference participants with a short welcoming speech and speech „About Mark Krasner (1912-1985)“ – the famous French mathematician of Russian-Jewish origin, who was a professor and professor emeritus of the Pierre and Marie Curie University in Paris, a holder of the title Officier des Palmes Académiques and the first laureate of the Doisteau-Blutet Award of the French Academy of Science, who has contributed greatly to the development of different areas of mathematics.

Thematically, the Conference was dedicated, primarily, to the graded structures, which were introduced first by N. Bourbaki, and the final form of the definition was given by M. Krasner. Therefore, the name Bourbaki-Krasner graded structures, as natural in itself, imposes for them on one side, and on the other there are the paragraded structures (groups, rings, modules), which have emerged as a natural generalization of the first, and which were introduced by M. Krasner and the organizer of the Conference M. Vuković, from where the name KrasnerVuković paragraded structures appeared. The aim of this Conference was more far-reaching than the presentation of the latest scientific results. It consisted of finding connections between this fundamental theoretical branch of mathematics and other fields of mathematics, applied mathematics, and science in general, as well as the introduction of top scientists with paragraded structures, which would lead to the connection and cooperation of scientists working in various fields of abstract algebra and algebraic theory of numbers, ultrametric and p-adic analysis, as well as in graph theory and mathematical logic. And, of course, another no less important objective of the Conference was to mark the 30 th anniversary of the death of Mark Krasner, an eminent scientist of world renown, to remind the scientific community on the importance and size of his scientific works and contribution to the development of overall scientific thought in the aforementioned fields of mathematics, as well as in the history and philosophy of science, especially mathematical logic for which, according to Krasner, the abstract Galois theory represented the essence, the substance - being! The conference was designed on the lectures of 16 invited speakers (from 10 different countries), but has received a total of 11 scientific papers, which were presented, although due to some unpredicted circumstances only nine speakers from eight different countries arrived: Bosnia and Herzegovina, Canada, England, France, Germany, Poland, Serbia and Slovenia. Conference participants belong to the world's most famous and highly acknowledged - top

mathematicians. This was noted by director of IUC Prof. Dr. Krunoslav Pisk who said that for a long time there was not a stronger Conference in IUC regarding the composition of the participants. It can freely be said that what was set as the aim of this Conference has in great extent already been implemented or is in the course of implementation. 1. The interest for paragraded structures has increased. 2. There was a connection of paragraded structures with other fields of mathematics: thus, both articles presented at the Conference in which paragraded structures are associated with modular forms and the mathematical logic have already been written (A. Pantchishkine and M. Džamonja) which contributed to the growth of citations in the field of paragraded structures. 3. In addition, preparation of the scientific monograph with A. Pantchishkine is planned, in which paragraded structures will be connected with modular forms. Scientific papers presented at the Conference will be published in a supplement of ANU BiH's journal Sarajevo Journal of Mathematics, which will be dedicated to Professor Marc Krasner. IN V ITED SP EA KE RS Mirjana Vuković, corresponding member of ANUBiH, Sarajevo, BA & Emil Ilić-Georgijević. University of Sarajevo, Sarajevo, BA “A note on radicals of paragraded rings” Emil Ilić-Georgijević, University of Sarajevo, Sarajevo, BA Mirjana Vuković, corresponding member of ANUBiH, Sarajevo, BA “A note on general radicals of paragraded rings” Vlastimil Dlab, F. R. S. C. Carleton University, Ottawa, Ontario, CA “Towers of semisimple algebras, their graphs and Jones index” Nadiya Gubareni, Czestochowa University of Technology, Częstochowa, PL “Tensor algebras and their representations” Elena Bunina, Lomonosov Moscow State University, Ru & Aleksander Mikhalev, Lomonosov Moscow State University, Ru “Elementary Equivalence of Linear Groups over Graded Rings with Finite” Dušan Pagon, University of Maribor, Maribor, SI “On codimension growth of graded PI-algebras” Mirna Džamonja, University of East Anglia, Norfolk, GB “Paragraded structures inspired by mathematical logic” Academician Stevan Pilipović, University of Novi Sad, Novi Sad, RS et al. “Spaces of ultradistributions of Beurling type over R d + through Laguerre Expansion” Alexei Pantchishkine, University Joseph Fourier, Grenoble, FR “Graded structures and differential operators on nearly holomorphic and quasimodular forms on classical groups” Siegfried Böcherer, University of Mannheim, Mannheim, DE “Quasimodular Siegel modular forms as p-adic modular forms” Prof. Dr. Alain Escassut, et al., University Clairmont-Ferrand, FR “Order, type and cotype of growth for p-adic entire functions”

Academic Miloš Trifković, president of ANUBiH, welcaming speach of Conference IUC-2016 Dubrovnik, September 22 – 24, 2016

1st row: from left to right: Academician Stevan Pilipović, Professor Alexei Pantchishkine, Professor Siegfried Böcherer, Mirjana Vuković, corresponding member of ANUBiH, Professor Vlastimil Dlab, F.R.S.C., Professor Mirna Džamonja, and 2nd row: Professor Dušan Pagon, Assist. Professor Emil Ilić-Georgijević

M. Vuković, corresponding member of ANUBiH, President of the Organizing Committee