SELECTED VIOLIN REPERTOIRE BY CONTEMPORARY KOREAN COMPOSERS

This dissertation deals with violin repertoire of current Korean composers. A survey of this music illustrates the various ways in which Korean composers dealt with their native musical traits on the one hand, and their studies of western techniques on the other hand. This music is rarely performed due to its unavailability and also its complexity. The initial task was one of identifying the Korean composers who write contemporary violin music in order to contact them. This was mostly accomplished with extensive long distance telephone and also a few instances of written or faxed correspondence. Since literature pertaining to the present topic is practically nonexistent in the United States, the generous offerings in the form of books and magazine articles sent by the composers greatly aided in the research. Challenges in the nature of interpretation, unusual violinistic demands, and complex ensemble considerations became the next stage ,of the project once the scores arrived. Performance preparation included stimulating sessions with Dr. Gerald Fischbach who offered many illuminating ideas and ingenious advice in some very unorthodox violin writing. Coachings from members of the Guarneri Quartet also resulted in excellent suggestions. The traditional elements which the composers have at their disposal include Korean scales of three to five tones, rhythmic patterns which are largely based on triplets and triple meter, sonorities of traditional instruments such as the Kaya-gum, and characteristics such as very sustained tempi. The works considered in this study illustrate how these traits are interspersed within twentieth century fabrics of free atonality, the twelve-tone system, quarter-steps, and the intervallic series. Some compositions avoid contemporary techniques by adhering to simple forms and show strong tendencies towards tonality. Still others are highly westernized and only exhibit a few instances of Korean characteristics. The experience of studying and performing this repertoire has culminated in the affirmation that the philosophies of Korean traditional and western musical cultures has been assimilated by contemporary Korean composers to create a musical language that is convincing in its own way

End-periodic homeomorphisms and volumes of mapping tori

Given an irreducible, end-periodic homeomorphism f of a surface S with finitely many ends, all accumulated by genus, the mapping torus is the interior of a compact, irreducible, atoroidal 3-manifold with incompressible boundary. Our main result is an upper bound on the infimal hyperbolic volume of the compactified mapping torus in terms of the translation length of f on the pants graph of S. This builds on work of Brock and Agol in the finite-type setting. We also construct a broad class of examples of irreducible, end-periodic homeomorphisms and use them to show that our bound is asymptotically sharp.Comment: 42 pages, 9 figure

Surface Houghton groups

For every $n\ge 2$, the {\em surface Houghton group} $\mathcal B_n$ is defined as the asymptotically rigid mapping class group of a surface with exactly $n$ ends, all of them non-planar. The groups $\mathcal B_n$ are analogous to, and in fact contain, the braided Houghton groups. These groups also arise naturally in topology: every monodromy homeomorphisms of a fibered component of a depth-1 foliation of closed 3-manifold is conjugate into some $\mathcal B_n$. As countable mapping class groups of infinite type surfaces, the groups $\mathcal B_n$ lie somewhere between classical mapping class groups and big mapping class groups. We initiate the study of surface Houghton groups proving, among other things, that $\mathcal B_n$ is of type $F_{n-1}$, but not of type $FP_n$, analogous to the braided Houghton groups.Comment: 19 pages, 1 figur