Biography: T. M. G. Ahsanullah, born at a remote village of a tiny district Bogra in the northern part of Bangladesh in 1954. Obtained his Master of Science degree in pure Mathematics with honors from Dhaka University in 1979. Ahsanullah studied at the Vrije Universiteit Brussel, Belgium during 1979-1984, obtaining in 1984 Doctor of Science degree (Ph.D.) in Mathematical Sciences, specializing Fuzzy Topological Structures on Groups and Semigroups generalizing Topological Groups and Semigroups. He served Dhaka University (DU, 1985-2002), before taking early retirement as Professor of Mathematics, and joined King Saud University (KSU) in 2002 as Professor (2002-). He supervised several Master Thesis students at DU, and Ph. D. students at KSU. He is a member of Editorial Board of New Mathematics and Natural Computation (Mathematics of Uncertainty). He is a reviewer of more than 30 journals including Mathematical Reviews and Zentralblat fur Mathematik and member of serval Mathematical Societies including American Math. Soc., London Math Soc., Canadian Math. Soc., and the Society for the Mathematics of Uncertainty, Department of Electrical and Computer Engineering, Duke University, USA. He published more than 50 research papers in various journals. His research area includes Lattice valued convergence groups, Approach convergence groups, Probabilistic metric spaces, Probabilistic convergence groups, Topological category theory. Recently, he has become interested in transformations groups, probabilistic convergence transformation groups, and domain theory.
Speech Title: Lattice-valued Convergence Groups and Various Lattice-valued Transformation Groups
Abstract: Since the inception of Zadeh's seminal paper on fuzzy sets, enormous work has been undertaken over more than 50 years both from theoretical and application point of view. Fuzzy convergence spaces or in terms of present day terminology Lattice-valued convergence spaces/Many-valued convergence spaces, a supercategory of the category of topological spaces, where a good amount of research being done over the years by many authors. Following a notion of L-fuzzy convergence spaces, L being a complete Heyting algebra, attributed to G. Jaeger, we reached to a category of enriched lattice-valued convergence groups and most recently, arrived a step forward to an article entitled Stratified LMN-convergence tower groups and their stratified LMN-uniform convergence tower structures, where L, M are frames and N is a quantale. In this present talk, first, we give an overview of the recent development of lattice-valued convergence theories in conjunction with algebraic structures, and secondly, we focus on L-continuity groups, where the idea of continuity is due to R. Flagg’s quantales and continuity, and their various connection to L-convergence groups, L being a value quantale. Finally, we explore the possible link of some of the preceding items, such as, quantale-valued convergence structures as well as quantale-valued metric spaces in conjunction with algebraic structures to theoretical computer science en route to domain theory.