Dear colleagues,

Next week on Tuesday Yoshihiro Maruyama, a finishing master student at Department of Humanistic Informatics, Kyoto University is making a talk at RIMS, Kyoto University. No registration necessary. See you there!

Best regards, Ichiro Hasuo --- RIMS-CS website http://www.kurims.kyoto-u.ac.jp/~cs/

===== Speaker: Yoshihiro Maruyama (Department of Humanistic Informatics, Kyoto University) http://researchmap.jp/ymaruyama/

Title: Duality in Logic, Algebraic Geometry, and Computer Science

Date: 11.00 - 12.00, Tue 8 Mar 2011

Place: Room 478, "Research Bldg. No. 2 (Sougou Kenkyu 2-Goukan)" http://www.kyoto-u.ac.jp/en/access/campus/main.htm (Next to our CS Lab) 総合研究2号館 478号室 (CS室のとなりです) http://www.kyoto-u.ac.jp/ja/access/campus/map6r_y.htm

Abstract:

Categorical duality often arises between ontological and epistemological aspects of concepts.　Indeed, we can find a number of such dualities in diverse fields: duality between models and theories in logic; duality between computer systems and their properties in computer science; duality between states and observables in quantum physics; duality between varieties and rings in algebraic geometry. In this talk, we briefly attempt to clarify the relationships between these dualities (especially, dualities in logic and algebraic geometry in relation to logical completeness and Hilbert Nullstellensatz), and develop a moderately general theory of dualities between modal logics and coalgebras (representations of the above-mentioned duality in computer science), extending the theory of natural dualities (a general theory of Stone-type dualities based on universal algebra) via a new concept of modal power. For the latter part, a preprint "Natural Duality, Modality and Coalgebra" is available in: http://researchmap.jp/ymaruyama/