Tannakian Formalism Applied to the Category of Mixed Hodge Structures

Many problems in analysis have been solved using the theory of Hodge structures. P. Deligne started to treat these structures in a categorical way. Following him, we introduce the categories of mixed real and complex Hodge structures. Category of mixed Hodge structures over the field of real or complex numbers is a rigid abelian tensor category, and in fact, a neutral Tannakian category. Therefore it is equivalent to the category of representations of an affine group scheme. The direct sums of pure Hodge structures of different weights over real or complex numbers can be realized as a representation of the torus group, whose complex points is the Cartesian product of two punctured complex planes. Mixed Hodge structures turn out to consist of information of a direct sum of pure Hodge structures of different weights and a nilpotent automorphism. Therefore mixed Hodge structures correspond to the representations of certain semidirect product of a nilpotent group and the torus group acting on it.

Socialist Realism instead of Formalism : the Formation and Development of the Soviet Music Control System 1932-1950

Whereas it has been widely assumed in the public that the Soviet music policy system had a “top-down” structure of control and command that directly affected musical creativity, in fact my research shows that the relations between the different levels of the music policy system were vague, and the viewpoints of its representatives differed from each other. Because the representatives of the party and government organs controlling operas could not define which kind of music represented Socialist Realism, the system as it developed during the 1930s and 1940s did not function effectively enough in order to create such a centralised control of Soviet music, still less could Soviet operas fulfil the highly ambiguous aesthetics of Socialist Realism. I show that musical discussions developed as bureaucratic ritualistic arenas, where it became more important to reveal the heretical composers, making scapegoats of them, and requiring them to perform self-criticism, than to give directions on how to reach the artistic goals of Socialist Realism. When one opera was found to be unacceptable, this lead to a strengthening of control by the party leadership, which lead to more operas, one after the other, to be revealed as failures. I have studied the control of the composition, staging and reception of the opera case-studies, which remain obscure in the West despite a growing scholarly interest in them, and have created a detailed picture of the foundation and development of the Soviet music control system in 1932-1950. My detailed discussion of such case-studies as Ivan Dzerzhinskii’s The Quiet Don, Dmitrii Shostakovich’s Lady Macbeth of Mtsensk District, Vano Muradeli’s The Great Friendship, Sergei Prokofiev’s Story of a Real Man, Tikhon Khrennikov’s Frol Skobeev and Evgenii Zhukovskii’s From All One’s Heart backs with documentary precision the historically revisionist model of the development of Soviet music. In February 1948, composers belonging to the elite of the Union of Soviet Composers, e.g. Dmitri Shostakovich and Sergei Prokofiev, were accused in a Central Committee Resolution of formalism, as been under the influence of western modernism. Accusations of formalism were connected to the criticism of the conciderable financial, material and social privileges these composers enjoyed in the leadership of the Union. With my new archival findings I give a more detailed picture of the financial background for the 1948 campaign. The independent position of the music funding organization of the Union of Soviet Composers (Muzfond) to decide on its finances was an exceptional phenomenon in the Soviet Union and contradicted the strivings to strengthen the control of Soviet music. The financial audits of the Union of Soviet Composers did not, however, change the elite status of some of its composers, except for maybe a short duration in some cases. At the same time the independence of the significal financial authorities of Soviet theatres was restricted. The cuts in the governmental funding allocated to Soviet theatres contradicted the intensified ideological demands for Soviet operas.

Käsitteellisestä ruumiilliseen, sitaatiosta paikkaan - maalaustaide ja nykytaiteen historia

The dissertation "From Conceptual to Corporeal, from Quotation to Site: Painting and History of Contemporary Art" explores the state of painting in contemporary art and art theory since the 1960s. The purpose of the study is to re-consider the dominant "end of painting" -narrative in contemporary art history, which goes back to the modernist ideology of painting as a reductive, medium-specific form of art. Drawing on Michel Foucault´s concepts of discursive formation and archive, as well as Jean-Luc Nancy´s post-phenomenological philosophy on corporeality, I suggest that contemporary painting can be redefined as a discursive-sensuous practice. Instead of seeing painting as obsolete or over as an avantgarde art genre, I show that there have been alternative, neo-avantgardist ways of defining painting since the end of the 1960s, such as French artist Daniel Buren´s early writings on painting as "theoretical practice". Consequently, the tendency of the canonical Anglo-American contemporary art narratives to underestimate the historical and institutional codes of art can be questioned. This tendency can be seen, for example, in Rosalind Krauss´s influential theory on index. The study also reflects the relations between conceptual art and painting since the 1960s and maps recent theories of painting, which re-examine the genre´s possibilities after the modernist rhetoric. Concepts of "flatbed", "painting in the extended field", "as painting" and so on are compared critically with the idea of painting as discursive practice. It is also shown that the issues in painting arise from the contemporary critical art debate while the dematerialisation paradigm of conceptual art has dissolved. The study focuses on the corporeal-material-sensuous -cluster of meanings attached to painting and searches for its avantgardist possibilities as redefined by postfeminist and post-phenomenological discourse. The ideas of hierarchy of the senses and synesthesia are developed within the framework of Jean-Luc Nancy´s and Luce Irigaray´s thought. The parameters for the study have been Finnish painting from 1990 to 2002. On the Finnish art scene there has been no "end of painting" ideology, strictly speaking. The mythology and medium-specificity of modernism have been deconstructed since the mid-1980s, but "the archive" of painting, like themes of abstraction, formalism and synesthesia have been re-worked by the discursive practice of painting, for example, in the works of Nina Roos, Tarja Pitkänen-Walter and Jussi Niva.

On Toponymic Constructions as an Alternative to Naming Patterns in Describing Finnish Lake Names

This thesis combines a computational analysis of a comprehensive corpus of Finnish lake names with a theoretical background in cognitive linguistics. The combination results on the one hand in a description of the toponymic system and the processes involved in analogy-based naming and on the other hand some adjustments to Construction Grammar. Finnish lake names are suitable for this kind of study, as they are to a large extent semantically transparent even when relatively old. There is also a large number of them, and they are comprehensively collected in a computer database. The current work starts with an exploratory computational analysis of co-location patterns between different lake names. Such an analysis makes it possible to assess the importance of analogy and patterns in naming. Prior research has suggested that analogy plays an important role, often also in cases where there are other motivations for the name, and the current study confirms this. However, it also appears that naming patterns are very fuzzy and that their nature is somewhat hard to define in an essentially structuralist tradition. In describing toponymic structure and the processes involved in naming, cognitive linguistics presents itself as a promising theoretical basis. The descriptive formalism of Construction Grammar seems especially well suited for the task. However, now productivity becomes a problem: it is not nearly as clear-cut as the latter theory often assumes, and this is even more apparent in names than in more traditional linguistic material. The varying degree of productivity is most naturally described by a prototype-based theory. Such an approach, however, requires some adjustments to onstruction Grammar. Based on all this, the thesis proposes a descriptive model where a new name -- or more generally, a new linguistic expression -- can be formed by conceptual integration from either a single prior example or a construction generalised from a number of different prior ones. The new model accounts nicely for various aspects of naming that are problematic for the traditional description based on analogy and patterns.

Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.

Spin and relativistic motion of bound states

The wave functions of moving bound states may be expected to contract in the direction of motion, in analogy to a rigid rod in classical special relativity, when the constituents are at equal (ordinary) time. Indeed, the Lorentz contraction of wave functions is often appealed to in qualitative discussions. However, only few field theory studies exist of equal-time wave functions in motion. In this thesis I use the Bethe-Salpeter formalism to study the wave function of a weakly bound state such as a hydrogen atom or positronium in a general frame. The wave function of the e^-e^+ component of positronium indeed turns out to Lorentz contract both in 1+1 and in 3+1 dimensional quantum electrodynamics, whereas the next-to-leading e^-e^+\gamma Fock component of the 3+1 dimensional theory deviates from classical contraction. The second topic of this thesis concerns single spin asymmetries measured in scattering on polarized bound states. Such spin asymmetries have so far mainly been analyzed using the twist expansion of perturbative QCD. I note that QCD vacuum effects may give rise to a helicity flip in the soft rescattering of the struck quark, and that this would cause a nonvanishing spin asymmetry in \ell p^\uparrow -> \ell' + \pi + X in the Bjorken limit. An analogous asymmetry may arise in p p^\uparrow -> \pi + X from Pomeron-Odderon interference, if the Odderon has a helicity-flip coupling. Finally, I study the possibility that the large single spin asymmetry observed in p p^\uparrow -> \pi(x_F,k_\perp) + X when the pion carries a high momentum fraction x_F of the polarized proton momentum arises from coherent effects involving the entire polarized bound state.

Non-Gaussian Cosmological Perturbations from Hybrid Inflation and Preheating

This thesis consists of four research papers and an introduction providing some background. The structure in the universe is generally considered to originate from quantum fluctuations in the very early universe. The standard lore of cosmology states that the primordial perturbations are almost scale-invariant, adiabatic, and Gaussian. A snapshot of the structure from the time when the universe became transparent can be seen in the cosmic microwave background (CMB). For a long time mainly the power spectrum of the CMB temperature fluctuations has been used to obtain observational constraints, especially on deviations from scale-invariance and pure adiabacity. Non-Gaussian perturbations provide a novel and very promising way to test theoretical predictions. They probe beyond the power spectrum, or two point correlator, since non-Gaussianity involves higher order statistics. The thesis concentrates on the non-Gaussian perturbations arising in several situations involving two scalar fields, namely, hybrid inflation and various forms of preheating. First we go through some basic concepts -- such as the cosmological inflation, reheating and preheating, and the role of scalar fields during inflation -- which are necessary for the understanding of the research papers. We also review the standard linear cosmological perturbation theory. The second order perturbation theory formalism for two scalar fields is developed. We explain what is meant by non-Gaussian perturbations, and discuss some difficulties in parametrisation and observation. In particular, we concentrate on the nonlinearity parameter. The prospects of observing non-Gaussianity are briefly discussed. We apply the formalism and calculate the evolution of the second order curvature perturbation during hybrid inflation. We estimate the amount of non-Gaussianity in the model and find that there is a possibility for an observational effect. The non-Gaussianity arising in preheating is also studied. We find that the level produced by the simplest model of instant preheating is insignificant, whereas standard preheating with parametric resonance as well as tachyonic preheating are prone to easily saturate and even exceed the observational limits. We also mention other approaches to the study of primordial non-Gaussianities, which differ from the perturbation theory method chosen in the thesis work.

Non-Gaussianities and Preheating from N-flation and Magnetogenesis via rotating cosmic string loops

In this thesis we examine multi-field inflationary models of the early Universe. Since non-Gaussianities may allow for the possibility to discriminate between models of inflation, we compute deviations from a Gaussian spectrum of primordial perturbations by extending the delta-N formalism. We use N-flation as a concrete model; our findings show that these models are generically indistinguishable as long as the slow roll approximation is still valid. Besides computing non-Guassinities, we also investigate Preheating after multi-field inflation. Within the framework of N-flation, we find that preheating via parametric resonance is suppressed, an indication that it is the old theory of preheating that is applicable. In addition to studying non-Gaussianities and preheatng in multi-field inflationary models, we study magnetogenesis in the early universe. To this aim, we propose a mechanism to generate primordial magnetic fields via rotating cosmic string loops. Magnetic fields in the micro-Gauss range have been observed in galaxies and clusters, but their origin has remained elusive. We consider a network of strings and find that rotating cosmic string loops, which are continuously produced in such networks, are viable candidates for magnetogenesis with relevant strength and length scales, provided we use a high string tension and an efficient dynamo.

Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.

The Problem of Implementation and its Relation to the Philosophy of Cognitive Science

According to certain arguments, computation is observer-relative either in the sense that many physical systems implement many computations (Hilary Putnam), or in the sense that almost all physical systems implement all computations (John Searle). If sound, these arguments have a potentially devastating consequence for the computational theory of mind: if arbitrary physical systems can be seen to implement arbitrary computations, the notion of computation seems to lose all explanatory power as far as brains and minds are concerned. David Chalmers and B. Jack Copeland have attempted to counter these relativist arguments by placing certain constraints on the definition of implementation. In this thesis, I examine their proposals and find both wanting in some respects. During the course of this examination, I give a formal definition of the class of combinatorial-state automata , upon which Chalmers s account of implementation is based. I show that this definition implies two theorems (one an observation due to Curtis Brown) concerning the computational power of combinatorial-state automata, theorems which speak against founding the theory of implementation upon this formalism. Toward the end of the thesis, I sketch a definition of the implementation of Turing machines in dynamical systems, and offer this as an alternative to Chalmers s and Copeland s accounts of implementation. I demonstrate that the definition does not imply Searle s claim for the universal implementation of computations. However, the definition may support claims that are weaker than Searle s, yet still troubling to the computationalist. There remains a kernel of relativity in implementation at any rate, since the interpretation of physical systems seems itself to be an observer-relative matter, to some degree at least. This observation helps clarify the role the notion of computation can play in cognitive science. Specifically, I will argue that the notion should be conceived as an instrumental rather than as a fundamental or foundational one.

Coherent quantum Boltzmann equations from cQPA

We reformulate and extend our recently introduced quantum kinetic theory for interacting fermion and scalar fields. Our formalism is based on the coherent quasiparticle approximation (cQPA) where nonlocal coherence information is encoded in new spectral solutions at off-shell momenta. We derive explicit forms for the cQPA propagators in the homogeneous background and show that the collision integrals involving the new coherence propagators need to be resummed to all orders in gradient expansion. We perform this resummation and derive generalized momentum space Feynman rules including coherent propagators and modified vertex rules for a Yukawa interaction. As a result we are able to set up self-consistent quantum Boltzmann equations for both fermion and scalar fields. We present several examples of diagrammatic calculations and numerical applications including a simple toy model for coherent baryogenesis.