• Honam Mathematical Journal
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• v.35 no.1
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• pp.1-15
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• 2013

In this paper, we study a sheaf-theoretic analysis of the convolution algebra on quiver varieties. As by-products, we reinterpret the results of H. Nakajima. We also produce a refined form of the BBD decomposition theorem for quiver varieties. Finally, we study a construction of highest weight modules through constructible functions.

• Journal of the Korean Institute of Educational Facilities
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• v.21 no.4
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• pp.31-40
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• 2014

The modern day architectural giant, Maki Fumihiko, has lived through both the early and the more recent modernism, Contemporary. In the 1950's he was faithful to the spirit that was founded on the early modernity, Metabolism. In his later years in the 2000's, his style can be distinguished into Neo-Modernism which was based on local influence. The educational system at Washington University and the modern city of Saint Louis carries the continuation of Fumihiko Maki's early and later architectural career. Steinberg Hall and Kemper Art Museum have been built adjacent to each other in an extended period of time. These two projects encompass the changes in the era that has gone through modernism, transformation of an architect's career, and the maturation of the university. Steinberg Hall carries the ideal and the spirit of young Fumihiko Maki, therefore, the basic platform of experimentation of the early Metabolist has been applied. Spatial theory that concentrates on the integration of relations is also evident in this project. In contrast, Kemper Art Museum expresses the work of a 78 year-old veteran from the perspective of Neo-Modernism. This piece focuses on the internal space through the coexistence of a variety of space, and with that it notably interprets the integration of the pieces to the whole as a set theory. The partial change that we see is the evidence of the change in the early and the later modernism, while maintaining the innocence and the spirit of it. This is to highlight the fact that, ultimately, the goal of architecture is to secure the human race's honesty and their freedom expressed through space.