In topology loop spaces can be understood combinatorially using algebraic theories. This approach can be extended to work for certain model structures on categories of presheaves over a site with functorial unit interval objects, such as topological spaces and simplicial sheaves of smooth schemes at finite type. For such model categories a new category of algebraic theories with a proper cellular simplicial model structure can be defined. This model structure can be localized in a way compatible with left Bousfield localizations of the underlying category of presheaves to yield a Motivic model structure for algebraic theories. As in the topological context, the model structure is Quillen equivalent to a category of loop spaces in the underlying category.

In this thesis, I examined how practicing and studying musical motifs affect a jazz musician’s way of improvising.   The main purpose was to investigate how I could get away from old habits and discover new paths in my improvisations with the help of repetition and withholding of ideas.    In the project, I transcribed some of my musical heroes and analyzed their solos on different recordings. I developed ways of practicing with the transcribed material to get motivic development into my playing. I also did a lot of active listening to recordings in search for other musicians’ ways of using musical motifs. During the concert, I played my compositions and compositions written by other musicians. I transcribed and analyzed specific parts from the concert to hear my development.     Practicing and transcribing led to an overall understanding of the concept of motivic development. The actual progress was made through focused listening to recordings and committing to a specific part of improvisation for a more extended amount of time. / <p>Kalle Johansson - Piano</p><p>Olle Lannér Risenfors - Bas</p><p>Johan Förnell - Trummor</p><p>Floater - Carla Bley</p><p>Tautology - Lee Konitz</p><p>Jigsaw - Kalle Johansson</p><p>Cheryl - Charlie Parker</p><p>Ned - Kalle Johansson</p><p>Grew - Kalle Johansson</p>

The lecture recital was given on July 2, 1984. The Megalith Trilogy was performed following a lecture which examined the internal structure of the work. The main body of the lecture focused on motivic and tonal considerations and included motivic and pitch reductions of the three movements. In addition to the lecture recital three other public solo recitals were performed. The four programs were recorded on magnetic tape and are filed with the written version of the lecture as a part of the dissertation.

Russian-born American composer, Lera Auerbach (b. 1973), is a pianist and composer with a growing reputation. She has written nearly a dozen works for solo piano in addition to ballets, operas, chamber works, and other solo instrumentations. Her solo piano work 24 Preludes for Piano, op. 41 (1998) is the first of three prelude sets she has written; op. 41 is scored for solo piano, op. 46 is composed for violin and piano, and op. 47 is written for cello and piano. Throughout her works, Auerbach's compositional language is intuitively polystylistic, tonally centered, and couched in traditional forms. In her 24 Preludes for Piano, op. 41, Auerbach creates a polystylistic and motivically cohesive large-scale work of the individual preludes. In this document, three aspects of the 24 Preludes for Piano, op. 41 are discussed in two parts: form, most significant polystylistic influences, and most prominent motivic connections. The first part of the document investigates two aspects: the form of each prelude and several polystylistic influences. Auerbach uses form to give each short prelude structure; ABA and Arch forms are most often used. Each of the preludes demonstrates different polystylistic elements; she refers to various genres such as the ricercar and chorale prelude as well as various techniques including stretto and additive rhythms. Additionally, Auerbach pays polystylistic homage to different composers including Bartók, Debussy, Mussorgsky, Purcell, Ravel and others. The second part of the document demonstrates several of the underlying motivic connections that unify the collection. The cohesion is created through self-referencing motivic connections that are best heard when the set of twenty-four is performed in its entirety. Auerbach's series of polystylistic miniatures is also an organically unified large-scale work.

<p>Arising from permutation representations of finite groups, Brauer-Kuroda relations are relations between Dedekind zeta functions of certain intermediate fields of a Galois extension of number fields. Let E be a totally real number field and let n ≥ 2 be an even integer. Taking s = 1 − n in the Brauer-Kuroda relations then gives a correspondence between orders of certain motivic and Galois cohomology groups. Following the works of Voevodsky and Wiles (cf. [33], [36]), we show that these relations give a direct relation on the motivic cohomology groups, allowing one to easily compute the higher class numbers, the orders of these motivic cohomology groups, of fields of high degree over Q from the corresponding values of its subfields. This simplifies the process by restricting the computations to those of fields of much smaller degree, which we are able to compute through Sage ([30]). We illustrate this with several extensive examples.</p> / Master of Science (MSc)

Cette thèse est consacrée à définir et étudier des invariants motiviques associés aux ensembles semi-algébriques dans les corps valués. Ceux-ci sont les combinaisons booléennes d'ensembles définis par des inégalités valuatives. L'outil principal que nous utilisons est l'intégration motivique, une forme de théorie de la mesure à valeurs dans le groupe de Grothendieck des variétés définies sur le corps résiduel. Dans une première partie, on définit la notion de densité locale motivique. C'est un analogue valuatif du nombre de Lelong complexe, de la densité réelle de Kurdyka-Raby et de la densité p-adique de Cluckers-Comte-Loeser. C'est un invariant métrique à valeurs dans un localisé du groupe de Grothendieck des variétés. Notre résultat principal est que cet invariant se calcule sur le cône tangent muni de multiplicités motiviques. On établit un analogue de la formule de Cauchy-Crofton locale. On montre enfin que dans le cas d'une courbe plane, la densité motivique est égale à la somme des inverses des multiplicités des branches. L'objet de la seconde partie est de définir un morphisme d'anneau du groupe de Grothendieck des ensembles semi-algébriques sur un corps valué K vers le groupe de Grothendieck de la catégorie d'Ayoub des motifs rigides analytiques sur K. On montre qu'il étend le morphisme qui envoie la classe d'une variété algébrique sur la classe de son motif cohomologique à support compact. Cela fournit donc une notion virtuelle de motif cohomologique à support compact pour les variétés rigides analytiques. On montre également un théorème de dualité permettant de comparer le motif cohomologique de la fibre de Milnor analytique avec la fibre de Milnor motivique. / This thesis is devoted to define and study some motivic invariants associated to semialgebraic sets in valued fields. They are boolean combinations of sets defined by valuative inequalities. Our main tool is the theory of motivic integration, which is a kind of measure theory with values in the Grothendieck group of varieties defined over the residue field. In the first part, we define the notion of motivic local density. It is a valuative analog of complex Lelong number, Kurdyka-Raby real density and p-adic density of Cluckers- Comte-Loeser. It is a metric invariant with values in a localization of the Grothendieck group of varieties. Our main result is that it can be computed on the tangent cone with motivic multiplicities. We also establish an analog of the local Cauchy-Crofton formula. We finally show that the density of a germ of plane curve defined over the residue field is equal to the sum of the inverses of the multiplicities of the formal branches of the curve. The goal of the second part is to define a ring morphism from the Grothendieck group of semi-algebraic sets defined over a valued field K to the Grothendieck group of Ayoub’s categoryof rigid analytic motives over K. We show that it extends the morphism sending the class of an algebraic variety to the class of its cohomological motive with compact support. This gives a notion of virtual cohomological motive with compact support for rigid analytic varieties. We also show a duality theorem allowing us to compare the cohomological motive of the analytic Milnor fiber with the motivic Milnor fiber.

xxv, 492 p. ： music / This study applies Schenkerian theory to Chet Baker's jazz improvisations in order to uncover the melodic, harmonic, and contrapuntal hallmarks of his style. Analyses of short excerpts taken from multiple recorded improvisations reveal Baker's improvisational vocabulary, which includes recurring underlying structures that Baker embellishes in a wide variety of ways and places in a wide variety of harmonic contexts. These analyses also explore other traits (rhythmic, timbral, etc.) that appear in Baker's improvisations throughout his career. The dissertation culminates in three illustrative analyses that demonstrate the ways in which Baker constructs single, unified improvisations by masterfully controlling the long-range voice-leading tendencies of his improvised lines. As he weaves his vocabulary into these lines, he creates improvisations that unfold in a way that is logical, satisfying in the fulfillment of expectations, and motivically cohesive on multiple levels of structure. / Committee in charge: Steve Larson， Co-Chair； Jack Boss， Co-Chair； Stephen Rodgers， Member Anne Dhu McLucas Member； George Rowe， Outside Member； Timothy Clarke， External Contributing Member

Im Mittelpunkt der Untersuchungen stehen Grundlagen für äquivariante motivische Homotopietheorie. Für eine neue Grothendieck-Topologie auf einer Kategorie von äquivarianten glatten k-Schemata werden unstabile und stabile motivische Homotopietheorie entwickelt. Im zweiten Teil der Arbeit wird als Anwendung der stabilen Theorie eine Adams-Spektralsequenz mit motivischer Borel-Kohomologie konstruiert.

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