snowy river

Akita Mathematical Sciences Interest Group (AMSIG) Seminar series




Abstract: The main objective of this presentation is to show that closure space theory can be used as a uniform conceptual framework for a wide range of mathematical theories. The emphasis will be on logic, algebraic systems, topology, geometry, convexity theory, formalism for quantum mechanics, but the list of mathematical theories conceptualized with closure spaces is much longer. Closure space formulation of theories was frequently utilized for the purpose of generalization. Some dangers of generalization will be discussed.

Abstract: The topic is repetitions in the context of combinatorics on words. First, I will introduce basic concepts and tools used in the combinatorial study of sequences over finite alphabets. I will address the two main question sets regarding repetitions: avoidability and upper/lower bounds. After the introductory part, I will present some results about bounding repetitions and the ideas along which I am trying to create a framework for unified upper bounds on different types of repetitions.

Abstract: In this talk, I will introduce the foundations of Formal Concept Analysis (FCA) based on the notion of order. I will start with basic concepts related with orders as binary relations to lattices, before introducing their uses in data mining. I will finish the talk with some brief presentation of two of my research themes, the first one on FCA on orders, in phylogenetic, and the second one on orders on FCA, with pattern structures for semantic analysis.

Abstract: The talk will introduce semigroups as abstract algebraic structures and their natural representation as sets of transformations closed under function composition. Transformation semigroups have a nice visual representation, where multiplication corresponds to stacking diagrams. This diagrammatic approach can be extended for a larger class of semigroups. The talk will go through the applications of diagram semigroups and the current open questions, with special emphasis on their recent computational enumeration. The talk contains elementary definitions and intuitive operations only, therefore it is suitable for a wider audience.