1,721,034 research outputs found
Bundle gerbes and moduli spaces
Full text linkIn this paper, we construct the index bundle gerbe of a family of self-adjoint Dirac-type operators, refining a construction of Segal. In a special case, we construct a geometric bundle gerbe called the caloron bundle gerbe, which comes with a natural connection and curving, and show that it is isomorphic to the analytically constructed index bundle gerbe. We apply these constructions to certain moduli spaces associated to compact Riemann surfaces, constructing on these moduli spaces, natural bundle gerbes with connection and curving, whose 3-curvature represent Dixmier-Douady classes that are generators of the third de Rham cohomology groups of these moduli spaces. © 2011 Elsevier B.V.Peter Bouwknegt, Varghese Mathai and Siye Wuhttp://www.journals.elsevier.com/journal-of-geometry-and-physics
T-duality simplifies bulk-boundary correspondence: the parametrised case
Full text linkWe state a general conjecture that T-duality simplifies a model for the bulk-boundary correspondence in the parametrised context. We give evidence that it is valid by proving it in a special interesting case, which is relevant both to String Theory and to the study of topological insulators with defects in Condensed Matter Physics.Keith C. Hannabuss, Varghese Mathai, and Guo Chuan Thian
Absence of evidence for the ultimate regime in two-dimensional Rayleigh-Benard convection reply
Full text linkIn their Comment [1] Doering et al. question our numerically found [2] onset of a transition to the ultimate regime of 2D Rayleigh-Bénard (RB) convection. We disagree with their reasoning
On the Chern character in Higher Twisted K-theory and spherical T-duality
Full text linkPublished online: 5May 2021In this paper, we construct for higher twists that arise from cohomotopy classes, the Chern character in higher twisted K-theory, that maps into higher twisted cohomology. We show that it gives rise to an isomorphism between higher twisted K-theory and higher twisted cohomology over the reals. Finally we compute spherical T-duality in higher twisted K-theory and higher twisted cohomology in very general cases.Lachlan Macdonald, Varghese Mathai, Hemanth Saratchandra
Homotopy invariance of Novikov-Shubin invariants and L2 Betti numbers
No full textWe give short proofs of the Gromov-Shubin theorem on the homotopy invariance of the Novikov-Shubin invariants and of the Dodziuk theorem on the homotopy invariance of the Betti numbers of the universal covering of a closed manifold in this paper. We show that the homotopy invariance of these invariants is no more difficult to prove than the homotopy invariance of ordinary homology theory.Jonathan Block, Varghese Mathai and Shmuel Weinberger
Higher Tannaka duality
Full text linkDans cette thèse, nous prouvons un théorème de dualité de Tannaka pour les (infini, 1)-catégories. La dualité classique de Tannaka est une dualité entre certains groupes et catégories monoïdales munies d'une structure particulière. La dualité de Tannaka supérieure renvoie, elle, à une dualité entre certains champs en groupes dérivés et certaines (infini, 1)-catégories monoïdales munies d'une structure particulière. Cette dualité supérieure est définie sur les anneaux dérivés et englobe la théorie de dualité classique. Nous comparons la dualité de Tannaka supérieure à la théorie de dualité de Tannaka classique et portons une attention particulière à la dualité de Tannaka sur les corps. Dans ce dernier cas, cette théorie a une relation étroite avec la théorie des types d'homotopie schématique de Toën. Nous décrivons également trois applications de la théorie : les complexes parfaits, les motifs et leur analogue non-commutatif dû à Kontsevich.In this thesis we prove a Tannaka duality theorem for (infini, 1)-categories. Classical Tannaka duality is a duality between certain groups and certain monoidal categories endowed with particular structure. Higher Tannaka duality refers to a duality between certain derived group stacks and certain monoidal (infini, 1)-categories endowed with particular structure. This higher duality theorem is defined over derived rings and subsumes the classical statement. We compare the higher Tannaka duality to the classical theory and pay particular attention to higher Tannaka duality over fields. In the later case this theory has a close relationship with the theory of schematic homotopy types of Toën. We also describe three applications of our theory : perfect complexes and that of both motives and its non-commutative analogue due to Kontsevich
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Hitchin's projectively flat connection and the moduli space of Higgs bundles
Full text linkIn this thesis we investigate the geometric quantization of moduli spaces of vector bundles over compact Riemann surfaces. In particular we will recall the geometric quantization of the moduli space of stable holomorphic vector bundles carried out by Hitchin, and study the generalisation of this problem for the moduli space of stable holomorphic Higgs bundles. The geometric quantization of Higgs moduli spaces presents new difficulties, since these moduli spaces are non-compact. However, they come with natural C+ actions, and this has implications for the geometric quantization: the quantum spaces for the Higgs moduli spaces split into finite-dimensional weight spaces for the C+ action, which can be identified with spaces of sections of certain bundles over the compact stable bundle moduli space. In the first part of this thesis, we review necessary background in differential geometry. Chapter 1 reviews the standard theory of connections on smooth vector bundles. Chapter 2 serves as an introduction to symplectic geometry, symplectic quotients, and their relationship to geometric invariant theory. Chapter 3 reviews the fundamental ideas in complex di
erential geometry, and in particular in Kahler geometry, as well as the basic theory of holomorphic vector bundles required later. In the second part of this thesis, we introduce the moduli spaces of stable bundles and Higgs bundles, formally defining them as infinite-dimensional Kahler quotients. In Chapter 4 the stable bundle space is considered, and we review its important properties and interpretations. Chapter 5 concerns the Higgs bundle moduli space and the ways it generalises and compares to the stable bundle moduli space. In the third and final part of this thesis, we recall the process of geometric quantization via Kahler polarisations, and apply it to the moduli space of Higgs bundles. In Chapter 6 we define geometric quantization, and state a theorem of Andersen on the existence of Hitchin connections for compact symplectic manifolds. In Chapter 7 we geometrically quantize the Higgs line bundle moduli space, and investigate the difficulties of generalising the techniques used to the higher rank spaces. In particular we construct a projectively at Hitchin connection on the bundle of quantum spaces over Teichmuller space. As far as the author is aware, this is an original result.Thesis (MPhil) -- University of Adelaide, School of Mathematical Sciences, 201
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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