Kemian ylioppilaskokeen tehtävät summatiivisen arvioinnin välineenä

The main purpose of the research was to illustrate chemistry matriculation examination questions as a summative assessment tool, and represent how the questions have evolved over the years. Summative assessment and its various test item classifications, Finnish goal-oriented curriculum model, and Bloom’s Revised Taxonomy of Cognitive Objectives formed the theoretical framework for the research. The research data consisted of 257 chemistry questions from 28 matriculation examinations between 1996 and 2009. The analysed test questions were formulated according to the national upper secondary school chemistry curricula 1994, and 2003. Qualitative approach and theory-driven content analysis method were employed in the research. Peer review was used to guarantee the reliability of the results. The research was guided by the following questions: (a) What kinds of test item formats are used in chemistry matriculation examinations? (b) How the fundamentals of chemistry are included in the chemistry matriculation examination questions? (c) What kinds of cognitive knowledge and skills do the chemistry matriculation examination questions require? The research indicates that summative assessment was used diversely in chemistry matriculation examinations. The tests included various test item formats, and their combinations. The majority of the test questions were constructed-response items that were either verbal, quantitative, or experimental questions, symbol questions, or combinations of the aforementioned. The studied chemistry matriculation examinations seldom included selected-response items that can be either multiple-choice, alternate choice, or matching items. The relative emphasis of the test item formats differed slightly depending on whether the test was a part of an extensive general studies battery of tests in sciences and humanities, or a subject-specific test. The classification framework developed in the research can be applied in chemistry and science education, and also in educational research. Chemistry matriculation examinations are based on the goal-oriented curriculum model, and cover relatively well the fundamentals of chemistry included in the national curriculum. Most of the test questions related to the symbolism of chemical equation, inorganic and organic reaction types and applications, the bonding and spatial structure in organic compounds, and stoichiometry problems. Only a few questions related to electrolysis, polymers, or buffer solutions. None of the test questions related to composites. There were not any significant differences in the emphasis between the tests formulated according to the national curriculum 1994 or 2003. Chemistry matriculation examinations are cognitively demanding. The research shows that the majority of the test questions require higher-order cognitive skills. Most of the questions required analysis of procedural knowledge. The questions that only required remembering or processing metacognitive knowledge, were not included in the research data. The required knowledge and skill level varied slightly between the test questions in the extensive general studies battery of tests in sciences and humanities, and subject-specific tests administered since 2006. The proportion of the Finnish chemistry matriculation examination questions requiring higher-order cognitive knowledge and skills is very large compared to what is discussed in the research literature.

Ionic Liquids and Microwaves in Promotion of Organic Synthesis : Friedel-Crafts reaction, deuterolabelling and O-Demethylation

The use of ionic liquids in chemical research has gained considerable interest and activity in recent years. Due to their unique and varied physicochemical properties, in comparison to molecular solvents, the potential applications for ionic liquids are enormous. The use of microwave irradiation, as a powerful dielectric heating technique, in synthetic organic chemistry has been known since 1986. Since then, it has gained significant recognition for its research and application in both academia and industry. The use of either ionic liquids or microwave irradiation in synthetic organic chemistry has been known to afford improved, alternative or complimentary selectivities, in comparison to traditional processes. In this study, the use of ionic liquids as solvents, co-solvents and catalytic media was explored in Friedel-Crafts, deuterolabelling and O-demethylation reactions. Alternative methods for the production of a variety of aromatic ketones using the Friedel-Crafts acylation methodology were investigated using ionic liquid catalyst or ionic liquid acidic additive systems. The disclosed methods, i.e. metal bistriflamides and chloroindate ionic liquids systems, possessed good catalytic activity in the synthesis of typical benzophenones. These catalytic systems were also recyclable. Microwave irradiation was found to be useful in the synthesis of various polyhydroxydeoxybenzoins and arylpropanones as synthetic precursors to naturally occurring or potentially bioactive compounds. Under optimized condition, the reaction occurred in only four minutes using systems such as [bmim][NTf2]/HNTf2 and [bmim][BF4]/BF3·OEt2. Naturally occurring polyphenols, such as isoflavones, can possess various types of biological or pharmacological activity. In particular, some are noted for their beneficial effects on human health. Isotopically labelled analogues of polyphenols are valuable as analytical standards in the quantification of these compounds from biological matrices. A new strategy for deuterolabelling of polyphenols was developed using ionic liquids as co-solvents and 35% DCl/D2O, as a cheap deuterium source, under microwave irradiation. Under these conditions, perdeuterated compounds were achieved in short reaction times, in high isotopic purity and in excellent yields. An O-demethylation reaction was developed, using an ionic liquid reaction medium with BBr3 for the deprotection of a variety methyl protected polyphenolic compounds, such as isoflavons and lignans. This deprotection procedure was found to be very practical as the reaction occurred under mild reaction conditions and in short reaction times. The isolation and purification steps were particularly straightforward and high yielding, in comparison to traditional methods.

Schiff Base Complexes and their Assemblies on Surfaces

Schiff bases and their transition metal complexes are of significant current interest even though they have been prepared for decades. They have been used in various applications such as catalysis, corrosion protection, and molecular sensors. In this study, N-aryl Schiff base ketimine ligands as well as numerous new, differently substituted salen and salophen-type ligands and their cobalt(II), copper(II), iron(II), manganese(II), and nickel(II) complexes were synthesised. New solid state structures of the above compounds and the dioxygen coordination properties of cobalt(II) complexes and catalytic properties of three synthesised binuclear complexes were examined. The prepared complexes were applied in the formation of self-assembled layers on a polycrystalline gold surface and liquid-graphite interface. The effect of metal ion and ligand structure on the as-formed patterns was studied. When studying gold surfaces, a unique thiol-assisted dissolution of elemental gold was observed and a new thin gold foil preparation method was introduced. In the summary, synthesis, structures, and properties of Schiff base ligands and their transition metal complexes are described in detail and the applications of these reviewed. Assemblies of other complexes on a liquid-graphite interface and on a gold surface are also presented, and the surface characterisation methods and surfaces employed are described.

Intermolecular Interactions of Noble-Gas-Containing Species

The importance of intermolecular interactions to chemistry, physics, and biology is difficult to overestimate. Without intermolecular forces, condensed phase matter could not form. The simplest way to categorize different types of intermolecular interactions is to describe them using van der Waals and hydrogen bonded (H-bonded) interactions. In the H-bond, the intermolecular interaction appears between a positively charged hydrogen atom and electronegative fragments and it originates from strong electrostatic interactions. H-bonding is important when considering the properties of condensed phase water and in many biological systems including the structure of DNA and proteins. Vibrational spectroscopy is a useful tool for studying complexes and the solvation of molecules. Vibrational frequency shift has been used to characterize complex formation. In an H-bonded system A∙∙∙H-X (A and X are acceptor and donor species, respectively), the vibrational frequency of the H-X stretching vibration usually decreases from its value in free H-X (red-shift). This frequency shift has been used as evidence for H-bond formation and the magnitude of the shift has been used as an indicator of the H-bonding strength. In contrast to this normal behavior are the blue-shifting H-bonds, in which the H-X vibrational frequency increases upon complex formation. In the last decade, there has been active discussion regarding these blue-shifting H-bonds. Noble-gases have been considered inert due to their limited reactivity with other elements. In the early 1930 s, Pauling predicted the stable noble-gas compounds XeF6 and KrF6. It was not until three decades later Neil Bartlett synthesized the first noble-gas compound, XePtF6, in 1962. A renaissance of noble-gas chemistry began in 1995 with the discovery of noble-gas hydride molecules at the University of Helsinki. The first hydrides were HXeCl, HXeBr, HXeI, HKrCl, and HXeH. These molecules have the general formula of HNgY, where H is a hydrogen atom, Ng is a noble-gas atom (Ar, Kr, or Xe), and Y is an electronegative fragment. At present, this class of molecules comprises 23 members including both inorganic and organic compounds. The first and only argon-containing neutral chemical compound HArF was synthesized in 2000 and its properties have since been investigated in a number of studies. A helium-containing chemical compound, HHeF, was predicted computationally, but its lifetime has been predicted to be severely limited by hydrogen tunneling. Helium and neon are the only elements in the periodic table that do not form neutral, ground state molecules. A noble-gas matrix is a useful medium in which to study unstable and reactive species including ions. A solvated proton forms a centrosymmetric NgHNg+ (Ng = Ar, Kr, and Xe) structure in a noble-gas matrix and this is probably the simplest example of a solvated proton. Interestingly, the hypothetical NeHNe+ cation is isoelectronic with the water-solvated proton H5O2+ (Zundel-ion). In addition to the NgHNg+ cations, the isoelectronic YHY- (Y = halogen atom or pseudohalogen fragment) anions have been studied with the matrix-isolation technique. These species have been known to exist in alkali metal salts (YHY)-M+ (M = alkali metal e.g. K or Na) for more than 80 years. Hydrated HF forms the FHF- structure in aqueous solutions, and these ions participate in several important chemical processes. In this thesis, studies of the intermolecular interactions of HNgY molecules and centrosymmetric ions with various species are presented. The HNgY complexes show unusual spectral features, e.g. large blue-shifts of the H-Ng stretching vibration upon complexation. It is suggested that the blue-shift is a normal effect for these molecules, and that originates from the enhanced (HNg)+Y- ion-pair character upon complexation. It is also found that the HNgY molecules are energetically stabilized in the complexed form, and this effect is computationally demonstrated for the HHeF molecule. The NgHNg+ and YHY- ions also show blue-shifts in their asymmetric stretching vibration upon complexation with nitrogen. Additionally, the matrix site structure and hindered rotation (libration) of the HNgY molecules were studied. The librational motion is a much-discussed solid state phenomenon, and the HNgY molecules embedded in noble-gas matrices are good model systems to study this effect. The formation mechanisms of the HNgY molecules and the decay mechanism of NgHNg+ cations are discussed. A new electron tunneling model for the decay of NgHNg+ absorptions in noble-gas matrices is proposed. Studies of the NgHNg+∙∙∙N2 complexes support this electron tunneling mechanism.

Copper Diffusion Barrier Deposition on Integrated Circuit Devices by Atomic Layer Deposition Technique

Transfer from aluminum to copper metallization and decreasing feature size of integrated circuit devices generated a need for new diffusion barrier process. Copper metallization comprised entirely new process flow with new materials such as low-k insulators and etch stoppers, which made the diffusion barrier integration demanding. Atomic Layer Deposition technique was seen as one of the most promising techniques to deposit copper diffusion barrier for future devices. Atomic Layer Deposition technique was utilized to deposit titanium nitride, tungsten nitride, and tungsten nitride carbide diffusion barriers. Titanium nitride was deposited with a conventional process, and also with new in situ reduction process where titanium metal was used as a reducing agent. Tungsten nitride was deposited with a well-known process from tungsten hexafluoride and ammonia, but tungsten nitride carbide as a new material required a new process chemistry. In addition to material properties, the process integration for the copper metallization was studied making compatibility experiments on different surface materials. Based on these studies, titanium nitride and tungsten nitride processes were found to be incompatible with copper metal. However, tungsten nitride carbide film was compatible with copper and exhibited the most promising properties to be integrated for the copper metallization scheme. The process scale-up on 300 mm wafer comprised extensive film uniformity studies, which improved understanding of non-uniformity sources of the ALD growth and the process-specific requirements for the ALD reactor design. Based on these studies, it was discovered that the TiN process from titanium tetrachloride and ammonia required the reactor design of perpendicular flow for successful scale-up. The copper metallization scheme also includes process steps of the copper oxide reduction prior to the barrier deposition and the copper seed deposition prior to the copper metal deposition. Easy and simple copper oxide reduction process was developed, where the substrate was exposed gaseous reducing agent under vacuum and at elevated temperature. Because the reduction was observed efficient enough to reduce thick copper oxide film, the process was considered also as an alternative method to make the copper seed film via copper oxide reduction.

Aminopyridinato Complexes as Possible Alternatives for Metallocenes in Ethylene Polymerization

Polyethylene is the most widely used synthetic polymer in the world. Most polyethylene is made with Ziegler-Natta catalysts. Polyethylenes for special applications are made with metallocenes, which are nowadays heavily patented. It is laborious therefore, to develop new metallocenes. The aim of this work was to investigate the feasibility of replacing the cyclopentadienyl ligands of metallocenes by aminopyridinato ligands without losing the good properties of the metallocenes, such as high activity and formation of linear polymer. The subject was approached by studying what kind of catalysts the metallocenes are and how they catalyze polyethylene. The polymerization behavior of metallocenes was examined by synthesizing a piperazino substituted indenyl zirconocene catalyst and comparing its polymerization data with that of the indenyl zirconocene catalyst. On the basis of their isolobality, it was thought that aminopyridinato ligands might replace cyclopentadienyl ligands. It was presumed that the polymerization mechanism and the active center in ethylene polymerization would be similar for aminopyridinato and metallocene catalysts. Titanium aminopyridinato complexes were prepared and their structures determined to clarify the relationship between structure of the catalyst precursor and polymerization results. The ethylene polymerization results for titanium 2-phenylaminopyridinato catalysts and titanocene catalysts were compared.

Traditionally Protected Forests and Sacred Forests of Zigua and Gweno Ethnic Groups in Tanzania

In Tanzania, indigenous forests can still be found whose existence is based on the management systems of precolonial society. This study covers material from over 900 forests. There are similar types of forests elsewhere in Africa, and similar forests can also be found in indigenous cultures on every continent. In this study they are called traditionally protected forests (TPFs). They have a high level of endemism and a rich biodiversity. The field study was carried out during the years 1997-2003 using participatory methods. An active debate is going on concerning the capacity of local communities to manage their environment. The role of indigenous people and their institutions in the development of the physical environment is a central issue in the debate. This study discusses the opportunities that the local people have had to decide on how to conserve, maintain, utilise, and manage their environment during different political periods. The study explains what kinds of changes have taken place in these forests and institutions in northeastern Tanzania among the matrilinear Zigua and patrilinear Gweno ethnic groups. About 2% of the land area of the communities was still protected by the precolonial structures. The communities have established their protection systems for different reasons, not only because of their beliefs but also because of different secular and clearly environmentally motivated reasons. There are different TPF types. Less than half of them are directly related to spirituality, and more than half are not. In earlier research elsewhere, it has been commonly understood that spiritual reasons played the main role in the protection of these environments. This study is also part of the postcolonial geographical discussion on the precolonial landscape and environmental management which was started by Carl Sauer. In the Zigua case study villages, only two out of five first comer clans have performed rain rituals in the past 30 years. Many of the most respected sacred sites do not have a ritual maker or even a person who knows how to perform rituals any longer. The same is happening with male initiation rites. In all case study villages there have been illegal cuts in the TPFs, but variations can be seen between the communities. The number of those who neither respect indigenous regulations nor accept indigenous penalties is growing. Positive developments have also taken place. Nowadays, the Forest Act of 2002 is in effect, which works as a cornerstone of community-based land ownership and also allows elders to protect TPFs, and by-laws are created with the support of different projects. Moreover, during the field study it was found that many young people are ignorant about their village's TPF sites, but interested in learning about their history and values.

Host Rock Classification (HRC) system for nuclear waste disposal in crystalline bedrock

A new rock mass classification scheme, the Host Rock Classification system (HRC-system) has been developed for evaluating the suitability of volumes of rock mass for the disposal of high-level nuclear waste in Precambrian crystalline bedrock. To support the development of the system, the requirements of host rock to be used for disposal have been studied in detail and the significance of the various rock mass properties have been examined. The HRC-system considers both the long-term safety of the repository and the constructability in the rock mass. The system is specific to the KBS-3V disposal concept and can be used only at sites that have been evaluated to be suitable at the site scale. By using the HRC-system, it is possible to identify potentially suitable volumes within the site at several different scales (repository, tunnel and canister scales). The selection of the classification parameters to be included in the HRC-system is based on an extensive study on the rock mass properties and their various influences on the long-term safety, the constructability and the layout and location of the repository. The parameters proposed for the classification at the repository scale include fracture zones, strength/stress ratio, hydraulic conductivity and the Groundwater Chemistry Index. The parameters proposed for the classification at the tunnel scale include hydraulic conductivity, Q´ and fracture zones and the parameters proposed for the classification at the canister scale include hydraulic conductivity, Q´, fracture zones, fracture width (aperture + filling) and fracture trace length. The parameter values will be used to determine the suitability classes for the volumes of rock to be classified. The HRC-system includes four suitability classes at the repository and tunnel scales and three suitability classes at the canister scale and the classification process is linked to several important decisions regarding the location and acceptability of many components of the repository at all three scales. The HRC-system is, thereby, one possible design tool that aids in locating the different repository components into volumes of host rock that are more suitable than others and that are considered to fulfil the fundamental requirements set for the repository host rock. The generic HRC-system, which is the main result of this work, is also adjusted to the site-specific properties of the Olkiluoto site in Finland and the classification procedure is demonstrated by a test classification using data from Olkiluoto. Keywords: host rock, classification, HRC-system, nuclear waste disposal, long-term safety, constructability, KBS-3V, crystalline bedrock, Olkiluoto

The Miocene of Western Asia; Fossil mammals at the crossroads of faunal provinces and climate regimes

Being at the crossroads of the Old World continents, Western Asia has a unique position through which the dispersal and migration of mammals and the interaction of faunal bioprovinces occurred. Despite its critical position, the record of Miocene mammals in Western Asia is sporadic and there are large spatial and temporal gaps between the known fossil localities. Although the development of the mammalian faunas in the Miocene of the Old World is well known and there is ample evidence for environmental shifts in this epoch, efforts toward quantification of habitat changes and development of chronofaunas based on faunal compositions were mostly neglected. Advancement of chronological, paleoclimatological, and paleogeographical reconstruction tools and techniques and increased numbers of new discoveries in recent decades have brought the need for updating and modification of our level of understanding. We under took fieldwork and systematic study of mammalian trace and body fossils from the northwestern parts of Iran along with analysis of large mammal data from the NOW database. The data analysis was used to study the provinciality, relative abundance, and distribution history of the closed- and open-adapted taxa and chronofaunas in the Miocene of the Old World and Western Asia. The provinciality analysis was carried out, using locality clustering, and the relative abundance of the closed- and open-adapted taxa was surveyed at the family level. The distribution history of the chronofaunas was studied, using faunal resemblance indices and new mapping techniques, together with humidity analysis based on mean ordinated hypsodonty. Paleoichnological studies revealed the abundance of mammalian footprints in several parts of the basins studied, which are normally not fossiliferous in terms of body fossils. The systematic study and biochronology of the newly discovered mammalian fossils in northwestern Iran indicates their close affinities with middle Turolian faunas. Large cranial remains of hipparionine horses, previously unknown in Iran and Western Asia, are among the material studied. The initiation of a new field project in the famous Maragheh locality also brings new opportunities to address questions regarding the chronology and paleoenvironment of this classical site. Provinciality analysis modified our previous level of understandings, indicating the interaction of four provinces in Western Asia. The development of these provinces was apparently due to the presence of high mountain ranges in the area, which affected the dispersal of mammals and also climatic patterns. Higher temperatures and possibly higher co2 levels in the Middle Miocene Climatic Optimum apparently favored the development of the closed forested environments that supported the dominance of the closed-adapted taxa. The increased seasonality and the progressive cooling and drying of the midlatitudes toward the Late Miocene maintained the dominance of open-adapted faunas. It appears that the late Middle Miocene was the time of transition from a more forested to a less forested world. The distribution history of the closed- and open-adapted chronofaunas shows the presence of cosmopolitan and endemic faunas in Western Asia. The closed-adapted faunas, such as the Arabian chronofauna of the late Early‒early Middle Miocene, demonstrated a rapid buildup and gradual decline. The open-adapted chronofaunas, such as the Late Miocene Maraghean fauna, climaxed gradually by filling the opening environments and moving in response to changes in humidity patterns. They abruptly declined due to demise of their favored environments. The Siwalikan chronofauna of the early Late Miocene remained endemic and restricted through all its history. This study highlights the importance of field investigations and indicates that new surveys in the vast areas of Western Asia, which are poorly sampled in terms of fossil mammal localities, can still be promising. Clustering of the localities supports the consistency of formerly known patterns and augments them. Although the quantitative approach to relative abundance history of the closed- and open-adapted mammals harks back to more than half a century ago, it is a novel technique providing robust results. Tracking the history of the chronofaunas in space and time by means of new computational and illustration methods is also a new practice that can be expanded to new areas and time spans.

Identiteettien maisemat Saskatchewanin Uudessa Suomessa : Uudisasutuksesta uusidentifikaatioon

The present study examines how the landscape of the rural immigrant colony of New Finland (Saskatchewan, Canada) has reflected the Finnish origins of the about 350 settlers and their descendants, their changing ideologies, values, sense of collectiveness and the meanings of the Finnish roots. The study also reveals the reasons and power structures behind the ethnic expressions. Researched time period runs from the beginning of the settlement in 1888 to the turn of the millennium. The research concentrates on buildings, cemeteries, personal names and place names which contain strong visual and symbolic messages and are all important constituents of mundane landscapes. For example, the studied personal names are important identity-political indexes telling about the value of the Finnish nationalism, community spirit, dual Finnish-Canadian identities and also the process of assimilation which, for example, had differences between genders. The study is based on empirical field research, and iconographical and textual interpretations supported by classifications and comparative analyses. Several interviews and literature were essential means of understanding the changing political contexts which influenced the Finnish settlement and its multiple landscape representations. Five historical landscape periods were identified in New Finland. During these periods the meanings and representations of Finnish identity changed along with national and international politics and local power structures. For example, during the Second World War Canada discouraged representations of Finnish culture because Finland and Canada were enemies. But Canada s multicultural policy in the 1980s led to several material and symbolic representations indicating the Finnish settlement after a period of assimilation and deinstitutionalization. The study shows how these representations were indications of the politics of a (selective) memory. Especially Finnish language, cultural traditions and the Evangelical-Lutheran values of the pioneers, which have been passed down to new generations, are highly valued part of the Finnish heritage. Also the work of the pioneers and their participation in the building of Saskatchewan is an important collective narrative. The selectiveness of a memory created the landscape of forgetting which includes deliberately forgotten parts of the history. For example, the occasional disputes between the congregations are something that has been ignored. The results show how the different landscape elements can open up a useful perspective to diaspora colonies or other communities also by providing information which otherwise would be indistinguishable. In this case, for example, two cemeteries close together were a sign of religious distributions among the early settlers.

Boundedness of weakly singular integral operators on domains

The monograph dissertation deals with kernel integral operators and their mapping properties on Euclidean domains. The associated kernels are weakly singular and examples of such are given by Green functions of certain elliptic partial differential equations. It is well known that mapping properties of the corresponding Green operators can be used to deduce a priori estimates for the solutions of these equations. In the dissertation, natural size- and cancellation conditions are quantified for kernels defined in domains. These kernels induce integral operators which are then composed with any partial differential operator of prescribed order, depending on the size of the kernel. The main object of study in this dissertation being the boundedness properties of such compositions, the main result is the characterization of their Lp-boundedness on suitably regular domains. In case the aforementioned kernels are defined in the whole Euclidean space, their partial derivatives of prescribed order turn out to be so called standard kernels that arise in connection with singular integral operators. The Lp-boundedness of singular integrals is characterized by the T1 theorem, which is originally due to David and Journé and was published in 1984 (Ann. of Math. 120). The main result in the dissertation can be interpreted as a T1 theorem for weakly singular integral operators. The dissertation deals also with special convolution type weakly singular integral operators that are defined on Euclidean spaces.

Homoclinic Splitting without Trees

We study a Hamiltonian describing a pendulum coupled with several anisochronous oscillators, giving a simple construction of unstable KAM tori and their stable and unstable manifolds for analytic perturbations. When the coupling takes place through an even trigonometric polynomial in the angle variables, we extend analytically the solutions of the equations of motion, order by order in the perturbation parameter, to a large neighbourhood of the real line representing time. Subsequently, we devise an asymptotic expansion for the splitting (matrix) associated with a homoclinic point. This expansion consists of contributions that are manifestly exponentially small in the limit of vanishing gravity, by a shift-of-countour argument. Hence, we infer a similar upper bound for the splitting itself. In particular, the derivation of the result does not call for a tree expansion with explicit cancellation mechanisms.

Homogeneous model theory of metric structures

This thesis studies homogeneous classes of complete metric spaces. Over the past few decades model theory has been extended to cover a variety of nonelementary frameworks. Shelah introduced the abstact elementary classes (AEC) in the 1980s as a common framework for the study of nonelementary classes. Another direction of extension has been the development of model theory for metric structures. This thesis takes a step in the direction of combining these two by introducing an AEC-like setting for studying metric structures. To find balance between generality and the possibility to develop stability theoretic tools, we work in a homogeneous context, thus extending the usual compact approach. The homogeneous context enables the application of stability theoretic tools developed in discrete homogeneous model theory. Using these we prove categoricity transfer theorems for homogeneous metric structures with respect to isometric isomorphisms. We also show how generalized isomorphisms can be added to the class, giving a model theoretic approach to, e.g., Banach space isomorphisms or operator approximations. The novelty is the built-in treatment of these generalized isomorphisms making, e.g., stability up to perturbation the natural stability notion. With respect to these generalized isomorphisms we develop a notion of independence. It behaves well already for structures which are omega-stable up to perturbation and coincides with the one from classical homogeneous model theory over saturated enough models. We also introduce a notion of isolation and prove dominance for it.

On Random Planar Curves and Their Scaling Limits

Planar curves arise naturally as interfaces between two regions of the plane. An important part of statistical physics is the study of lattice models. This thesis is about the interfaces of 2D lattice models. The scaling limit is an infinite system limit which is taken by letting the lattice mesh decrease to zero. At criticality, the scaling limit of an interface is one of the SLE curves (Schramm-Loewner evolution), introduced by Oded Schramm. This family of random curves is parametrized by a real variable, which determines the universality class of the model. The first and the second paper of this thesis study properties of SLEs. They contain two different methods to study the whole SLE curve, which is, in fact, the most interesting object from the statistical physics point of view. These methods are applied to study two symmetries of SLE: reversibility and duality. The first paper uses an algebraic method and a representation of the Virasoro algebra to find common martingales to different processes, and that way, to confirm the symmetries for polynomial expected values of natural SLE data. In the second paper, a recursion is obtained for the same kind of expected values. The recursion is based on stationarity of the law of the whole SLE curve under a SLE induced flow. The third paper deals with one of the most central questions of the field and provides a framework of estimates for describing 2D scaling limits by SLE curves. In particular, it is shown that a weak estimate on the probability of an annulus crossing implies that a random curve arising from a statistical physics model will have scaling limits and those will be well-described by Loewner evolutions with random driving forces.

On the Geometry of Infinite-Dimensional Grassmannian Manifolds and Gauge Theory

This PhD Thesis is about certain infinite-dimensional Grassmannian manifolds that arise naturally in geometry, representation theory and mathematical physics. From the physics point of view one encounters these infinite-dimensional manifolds when trying to understand the second quantization of fermions. The many particle Hilbert space of the second quantized fermions is called the fermionic Fock space. A typical element of the fermionic Fock space can be thought to be a linear combination of the configurations m particles and n anti-particles . Geometrically the fermionic Fock space can be constructed as holomorphic sections of a certain (dual)determinant line bundle lying over the so called restricted Grassmannian manifold, which is a typical example of an infinite-dimensional Grassmannian manifold one encounters in QFT. The construction should be compared with its well-known finite-dimensional analogue, where one realizes an exterior power of a finite-dimensional vector space as the space of holomorphic sections of a determinant line bundle lying over a finite-dimensional Grassmannian manifold. The connection with infinite-dimensional representation theory stems from the fact that the restricted Grassmannian manifold is an infinite-dimensional homogeneous (Kähler) manifold, i.e. it is of the form G/H where G is a certain infinite-dimensional Lie group and H its subgroup. A central extension of G acts on the total space of the dual determinant line bundle and also on the space its holomorphic sections; thus G admits a (projective) representation on the fermionic Fock space. This construction also induces the so called basic representation for loop groups (of compact groups), which in turn are vitally important in string theory / conformal field theory. The Thesis consists of three chapters: the first chapter is an introduction to the backround material and the other two chapters are individually written research articles. The first article deals in a new way with the well-known question in Yang-Mills theory, when can one lift the action of the gauge transformation group on the space of connection one forms to the total space of the Fock bundle in a compatible way with the second quantized Dirac operator. In general there is an obstruction to this (called the Mickelsson-Faddeev anomaly) and various geometric interpretations for this anomaly, using such things as group extensions and bundle gerbes, have been given earlier. In this work we give a new geometric interpretation for the Faddeev-Mickelsson anomaly in terms of differentiable gerbes (certain sheaves of categories) and central extensions of Lie groupoids. The second research article deals with the question how to define a Dirac-like operator on the restricted Grassmannian manifold, which is an infinite-dimensional space and hence not in the landscape of standard Dirac operator theory. The construction relies heavily on infinite-dimensional representation theory and one of the most technically demanding challenges is to be able to introduce proper normal orderings for certain infinite sums of operators in such a way that all divergences will disappear and the infinite sum will make sense as a well-defined operator acting on a suitable Hilbert space of spinors. This research article was motivated by a more extensive ongoing project to construct twisted K-theory classes in Yang-Mills theory via a Dirac-like operator on the restricted Grassmannian manifold.