Geometry of BV quantization and Mathai-Quillen formalism

Il formalismo Mathai-Quillen (MQ) è un metodo per costruire la classe di Thom di un fibrato vettoriale attraverso una forma differenziale di profilo Gaussiano. Lo scopo di questa tesi è quello di formulare una nuova rappresentazione della classe di Thom usando aspetti geometrici della quantizzazione Batalin-Vilkovisky (BV). Nella prima parte del lavoro vengono riassunti i formalismi BV e MQ entrambi nel caso finito dimensionale. Infine sfrutteremo la trasformata di Fourier “odd" considerando la forma MQ come una funzione definita su un opportuno spazio graduato.

Frobenius polynomials for Calabi-Yau equations

Sei $\pi:X\rightarrow S$ eine \"uber $\Z$ definierte Familie von Calabi-Yau Varietaten der Dimension drei. Es existiere ein unter dem Gauss-Manin Zusammenhang invarianter Untermodul $M\subset H^3_{DR}(X/S)$ von Rang vier, sodass der Picard-Fuchs Operator $P$ auf $M$ ein sogenannter {\em Calabi-Yau } Operator von Ordnung vier ist. Sei $k$ ein endlicher K\"orper der Charaktetristik $p$, und sei $\pi_0:X_0\rightarrow S_0$ die Reduktion von $\pi$ \uber $k$. F\ur die gew\ohnlichen (ordinary) Fasern $X_{t_0}$ der Familie leiten wir eine explizite Formel zur Berechnung des charakteristischen Polynoms des Frobeniusendomorphismus, des {\em Frobeniuspolynoms}, auf dem korrespondierenden Untermodul $M_{cris}\subset H^3_{cris}(X_{t_0})$ her. Sei nun $f_0(z)$ die Potenzreihenl\osung der Differentialgleichung $Pf=0$ in einer Umgebung der Null. Da eine reziproke Nullstelle des Frobeniuspolynoms in einem Teichm\uller-Punkt $t$ durch $f_0(z)/f_0(z^p)|_{z=t}$ gegeben ist, ist ein entscheidender Schritt in der Berechnung des Frobeniuspolynoms die Konstruktion einer $p-$adischen analytischen Fortsetzung des Quotienten $f_0(z)/f_0(z^p)$ auf den Rand des $p-$adischen Einheitskreises. Kann man die Koeffizienten von $f_0$ mithilfe der konstanten Terme in den Potenzen eines Laurent-Polynoms, dessen Newton-Polyeder den Ursprung als einzigen inneren Gitterpunkt enth\alt, ausdr\ucken,so beweisen wir gewisse Kongruenz-Eigenschaften unter den Koeffizienten von $f_0$. Diese sind entscheidend bei der Konstruktion der analytischen Fortsetzung. Enth\alt die Faser $X_{t_0}$ einen gew\ohnlichen Doppelpunkt, so erwarten wir im Grenz\ubergang, dass das Frobeniuspolynom in zwei Faktoren von Grad eins und einen Faktor von Grad zwei zerf\allt. Der Faktor von Grad zwei ist dabei durch einen Koeffizienten $a_p$ eindeutig bestimmt. Durchl\auft nun $p$ die Menge aller Primzahlen, so erwarten wir aufgrund des Modularit\atssatzes, dass es eine Modulform von Gewicht vier gibt, deren Koeffizienten durch die Koeffizienten $a_p$ gegeben sind. Diese Erwartung hat sich durch unsere umfangreichen Rechnungen best\atigt. Dar\uberhinaus leiten wir weitere Formeln zur Bestimmung des Frobeniuspolynoms her, in welchen auch die nicht-holomorphen L\osungen der Gleichung $Pf=0$ in einer Umgebung der Null eine Rolle spielen.

Symplectic Lagrangian fibrations

In this work we investigate the deformation theory of pairs of an irreducible symplectic manifold X together with a Lagrangian subvariety Y in X, where the focus is on singular Lagrangian subvarieties. Among other things, Voisin's results [Voi92] are generalized to the case of simple normal crossing subvarieties; partial results are also obtained for more complicated singularities.rnAs done in Voisin's article, we link the codimension of the subspace of the universal deformation space of X parametrizing those deformations where Y persists, to the rank of a certain map in cohomology. This enables us in some concrete cases to actually calculate or at least estimate the codimension of this particular subspace. In these cases the Lagrangian subvarieties in question occur as fibers or fiber components of a given Lagrangian fibration f : X --> B. We discuss examples and the question of how our results might help to understand some aspects of Lagrangian fibrations.

L-2-Kohomologie von Calabi-Yau-Familien über Kurven

Ist $f: X \to S$ eine glatte Familie von Calabi-Yau-Mannigfaltigkeiten der Dimension $m$ über einer quasiprojektiven Kurve, so trägt nach einem Resultat von Zucker die erste $L^2$-Kohomologiegruppe $H^1_{(2)}(S, R^m f_* \mathbb{C}_X)$ eine reine Hodgestruktur vom Gewicht $m+1$. In dieser Arbeit berechnen wir die Hodgezahlen solcher Hodgestrukturen für $m= 1, 2, 3$ und verallgemeinern dabei Formeln aus einem Artikel von del Angel, Müller-Stach, van Straten und Zuo auf den Fall, in dem die lokalen Monodromiematrizen bei Unendlich nicht unipotent, sondern echt quasi-unipotent sind. Wir verwenden dazu den $L^2$-Higgs-Komplex nach Jost, Yang und Zuo. Für Familien von Kurven führt dies auf eine bereits bekannte Formel von Cox und Zucker. Schließlich wenden wir die Ergebnisse im Fall $m=3$ auf 14 Familien von Calabi-Yau-Mannigfaltigkeiten an, die eine Rolle in der Spiegelsymmetrie spielen, sowie auf eine von Rohde konstruierte Familie ohne Punkte mit maximal unipotenter Monodromie.

Hearing Delzant Polytopes From the Equivariant Spectrum

Let M^{2n} be a symplectic toric manifold with a fixed T^n-action and with a toric K\"ahler metric g. Abreu asked whether the spectrum of the Laplace operator $\Delta_g$ on $\mathcal{C}^\infty(M)$ determines the moment polytope of M, and hence by Delzant's theorem determines M up to symplectomorphism. We report on some progress made on an equivariant version of this conjecture. If the moment polygon of M^4 is generic and does not have too many pairs of parallel sides, the so-called equivariant spectrum of M and the spectrum of its associated real manifold M_R determine its polygon, up to translation and a small number of choices. For M of arbitrary even dimension and with integer cohomology class, the equivariant spectrum of the Laplacian acting on sections of a naturally associated line bundle determines the moment polytope of M.

ARIS-Campaign: Intercomparison of three ground based 22 GHz radiometers for middle atmospheric water vapor at the Zugspitze in winter 2009

This paper presents the Alpine Radiometer Intercomparison at the Schneefernerhaus (ARIS), which took place in winter 2009 at the high altitude station at the Zugspitze, Germany (47.42° N, 10.98° E, 2650 m). This campaign was the first direct intercomparison between three new ground based 22 GHz water vapor radiometers for middle atmospheric profiling with the following instruments participating: MIRA 5 (Karlsruhe Institute of Technology), cWASPAM3 (Max Planck Institute for Solar System Research, Katlenburg-Lindau) and MIAWARA-C (Institute of Applied Physics, University of Bern). Even though the three radiometers all measure middle atmospheric water vapor using the same rotational transition line and similar fundamental set-ups, there are major differences between the front ends, the back ends, the calibration concepts and the profile retrieval. The spectrum comparison shows that all three radiometers measure spectra without severe baseline artifacts and that the measurements are in good general agreement. The measurement noise shows good agreement to the values theoretically expected from the radiometer noise formula. At the same time the comparison of the noise levels shows that there is room for instrumental and calibration improvement, emphasizing the importance of low elevation angles for the observation, a low receiver noise temperature and an efficient calibration scheme. The comparisons of the retrieved profiles show that the agreement between the profiles of MIAWARA-C and cWASPAM3 with the ones of MLS is better than 0.3 ppmv (6%) at all altitudes. MIRA 5 has a dry bias of approximately 0.5 ppm (8%) below 0.1 hPa with respect to all other instruments. The profiles of cWASPAM3 and MIAWARA-C could not be directly compared because the vertical region of overlap was too small. The comparison of the time series at different altitude levels show a similar evolution of the H2O volume mixing ratio (VMR) for the ground based instruments as well as the space borne sensor MLS.

Tracks of immigrant political incorporation

Models of Immigrant Political Incorporation brings together a multidisciplinary group of scholars to consider pathways by which immigrants may be incorporated into the political processes of western democracies. It builds on a rich tradition of studying immigrant incorporation, but each chapter innovates by moving beyond singular accounts of particular groups and locations toward a general causal model with the scope and breadth to apply across groups, places, and time. Models of Immigrant Political Incorporation addresses three key analytic questions: what, if anything, are the distinctive features of immigrants or immigrant groups? How broadly should one define and study politics? What are the initial premises for analyzing pathways toward incorporation; does one learn more by starting from an assumption of racialization and exclusion or from an assumption of engagement and inclusion? While all models engage with all three key analytic questions, chapters vary in their relative focus on one or another, and in the answers they provide. Most include graphical illustrations of the model, as well as extended examples applying the model to one or more immigrant populations. At a time when research on immigrant political incorporation is rapidly accumulating - and when immigrants are increasingly significant political actors in many democratic polities — this volume makes a timely and valuable intervention by pushing researchers to articulate causal dynamics, provide clear definitions and measurable concepts, and develop testable hypotheses. Furthermore, the wide array of frameworks examining how immigrants become part of a polity or are shunted aside ensure that activists and analysts alike will find useful insights. By including historians, sociologists, and political scientists, by ranging across North America and Western Europe, by addressing successful and failed incorporative efforts, this handbook offers guides for anyone seeking to develop a dynamic, unified, and supple model of immigrant political incorporation.

(Table 1) Ice thickness at lake Nam Co, Tibet, during 2008-2009

Lake ice change is one of the sensitive indicators of regional and global climate change. Different sources of data are used in monitoring lake ice phenology nowadays. Visible and Near Infrared bands of imagery (VNIR) are well suited for the observation of freshwater ice change, for example data from AVHRR and MODIS. Active and passive microwave data are also used for the observation of lake ice, e.g., from satellite altimetry and radiometry, backscattering coefficient from QuickSCAT, brightness temperature (Tb) from SSM/I, SMMR, and AMSR-E. Most of the studies are about lake ice cover phenology, while few studies focus on lake ice thickness. For example, Hall et al. using 5 GHz (6 cm) radiometer data showed a good relationship between Tb and ice thickness. Kang et al. found the seasonal evolution of Tb at 10.65 GHz and 18.7 GHz from AMSR-E to be strongly influenced by ice thickness. Many studies on lake ice phenology have been carried out since the 1970s in cold regions, especially in Canada, the USA, Europe, the Arctic, and Antarctica. However, on the Tibetan Plateau, very little research has focused on lake ice-cover change; only a small number of published papers on Qinghai Lake ice observations. The main goal of this study is to investigate the change in lake ice phenology at Nam Co on the Tibetan Plateau using MODIS and AMSR-E data (monitoring the date of freeze onset, the formation of stable ice cover, first appearance of water, and the complete disappearance of ice) during the period 2000-2009.

A genetic method for dissecting the mechanism of transcriptional activator synergy by identical activators

Pairs of transcriptional activators in prokaryotes have been shown to activate transcription synergistically from promoters with two activator binding sites. In some cases, such synergistic effects result from cooperative binding, but in other cases each DNA-bound activator plays a direct role in the activation process by interacting simultaneously with separate surfaces of RNA polymerase. In such cases, each DNA-bound activator must possess a functional activating region, the surface that mediates the interaction with RNA polymerase. When transcriptional activation depends on two or more identical activators, it is not straightforward to test the requirement of each activator for a functional activating region. Here we describe a method for directing a mutationally altered activator to either one or the other binding site, and we demonstrate the use of this method to examine the mechanism of transcriptional activator synergy by the Escherichia coli cyclic AMP receptor protein (CRP) working at an artificial promoter bearing two CRP-binding sites.

Mechanism for a transcriptional activator that works at the isomerization step

Transcriptional activators in prokaryotes have been shown to stimulate different steps in the initiation process including the initial binding of RNA polymerase (RNAP) to the promoter and a postbinding step known as the isomerization step. Evidence suggests that activators that affect initial binding can work by a cooperative binding mechanism by making energetically favorable contacts with RNAP, but the mechanism by which activators affect the isomerization step is unclear. A well-studied example of an activator that normally exerts its effect exclusively on the isomerization step is the bacteriophage λ cI protein (λcI), which has been shown genetically to interact with the C-terminal region of the σ70 subunit of RNAP. We show here that the interaction between λcI and σ can stimulate transcription even when the relevant portion of σ is transplanted to another subunit of RNAP. This activation depends on the ability of λcI to stabilize the binding of the transplanted σ moiety to an ectopic −35 element. Based on these and previous findings, we discuss a simple model that explains how an activator's ability to stabilize the binding of an RNAP subdomain to the DNA can account for its effect on either the initial binding of RNAP to a promoter or the isomerization step.

The structure of Selmer groups

The purpose of this article is to describe certain results and conjectures concerning the structure of Galois cohomology groups and Selmer groups, especially for abelian varieties. These results are analogues of a classical theorem of Iwasawa. We formulate a very general version of the Weak Leopoldt Conjecture. One consequence of this conjecture is the nonexistence of proper Λ-submodules of finite index in a certain Galois cohomology group. Under certain hypotheses, one can prove the nonexistence of proper Λ-submodules of finite index in Selmer groups. An example shows that some hypotheses are needed.

Integrality of Tate-cycles

We explain a technical result about p-adic cohomology and apply it to the study of Shimura varieties. The technical result applies to algebraic varieties with torsion-free cohomology, but for simplicity we only treat abelian varieties.

Congruences between modular forms: Raising the level and dropping Euler factors

We discuss the relationship among certain generalizations of results of Hida, Ribet, and Wiles on congruences between modular forms. Hida’s result accounts for congruences in terms of the value of an L-function, and Ribet’s result is related to the behavior of the period that appears there. Wiles’ theory leads to a class number formula relating the value of the L-function to the size of a Galois cohomology group. The behavior of the period is used to deduce that a formula at “nonminimal level” is obtained from one at “minimal level” by dropping Euler factors from the L-function.

Reminiscences after thirty years in the ministry /

Mode of access: Internet.

On Selmer groups and factoring p-adic L-functions

Thesis (Ph.D.)--University of Washington, 2016-06