Constructs a map from stable extensions to irreducible metrics on Riemann surfaces.
problem Understanding and constructing cone spherical metrics on Riemann surfaces.
method Using the theory of indigenous bundles, the construction involves developing maps and stable extensions of two line bundles.
result Generically injective map from stable extensions to irreducible metrics, with properties about effective divisors.
The paper develops a theory of Ehresmann structures in positive characteristic.
problem Developing a theory for Ehresmann structures in positive characteristic.
method Comparing Frobenius-Ehresmann structures with Cartan geometries and studying their equivalence.
result Formulating and proving the Ehresmann-Weil-Thurston principle for Frobenius-Ehresmann structures.
Introduces challenges and techniques for creating machine translation for indigenous languages.
problem Limited data for machine translation of indigenous languages.
method Introduction to challenges, concepts, and techniques for creating MT systems.
result Discussion of recent advances and open questions in NLP for these languages.
This paper reviews sentiment analysis on Indian languages.
problem Understanding sentiment in multilingual web data.
method Reviews and discusses approaches for sentiment analysis on Indian languages.
result Challenges in sentiment analysis on indigenous languages.
We investigate the Brazilian personal income distribution using data from National Household Sample Survey (PNAD), an annual research available by the Brazilian Institute of Geography and Statistics (IBGE). It provides general characteristics of the country's population. Using PNAD data background we also confirm the e…
Amharic is the official language of the Federal Democratic Republic of Ethiopia. There are lots of historic Amharic and Ethiopic handwritten documents addressing various relevant issues including governance, science, religious, social rules, cultures and art works which are very reach indigenous knowledge. The Amharic …
Footfall based biometric system is perhaps the only person identification technique which does not hinder the natural movement of an individual. This is a clear edge over all other biometric systems which require a formidable amount of human intervention and encroach upon an individual's privacy to some extent or the o…
In many developing countries intellectual property infringement and the commerce of pirate goods is an entrepreneurial activity. Digital piracy is very often the only media for having access to music, cinema, books and software. At the same time, bio-prospecting and infringement of indigenous knowledge rights by intern…
Decision tool helps manage biofouling risks for ships in the Baltic Sea.
problem Biofouling of ships causes environmental and economic issues.
method Bayesian networks to identify biofouling management strategies.
result Optimal biofouling management includes biocidal-free coating and in-water cleaning.
Deep learning automates biofouling detection in ship hull images.
problem Automating biofouling assessment from ship hull images.
method Deep learning model trained on expert-annotated images.
result Deep learning model agrees with expert annotations.
The study of quotient structures in multi-graded bundles, including double vector bundles.
problem Understanding quotients of multi-graded bundles, especially double vector bundles.
method Analyzing quotients as towers of affine bundles and constructing normal bundles.
result Any quotient of multi-graded bundles fits into a tower of affine bundles.
Study of semi-principal bundles using group actions and wreath products.
problem Understanding bundles with fibers as free G-spaces. method Defining semi-principal bundles, bases, and frame bundles; using wreath products and functors.
result Semi-principal bundles can be retracted to principal bundles, preserving parallel transport.
Establishes a framework for stringor bundles, proving their canonical isomorphism to Stolz-Teichner's.
problem Defining and rigorously studying higher differential geometric objects like stringor bundles.
method Developed a framework of 2-Hilbert bundles, including an associated bundle construction.
result Proves the Stolz-Teichner stringor bundle is canonically isomorphic to the 2-Hilbert bundle.
In this study, we generalize double tangent bundles to double jet bundles. We present a secondary vector bundle structure on a 1-jet of a vector bundle. We show that 1-jet of a vector bundle carries two vector bundle structures, namely primary and secondary structures. We also show that the manifold charts induced by p…
This paper shows vector bundles and differential bundles are equivalent in smooth manifolds.
problem Characterizing vector bundles in smooth manifolds.
method Introducing differential bundles in a tangent category and proving equivalence with vector bundles in smooth manifolds.
result Differential bundles in smooth manifolds are equivalent to vector bundles.
Introduces Darboux-Lie derivative for fiber bundles.
problem None explicitly stated; focuses on introducing a new derivative.
method Study of Darboux-Lie derivative for fiber-bundle maps.
result Properties of Darboux-Lie derivative for fiber bundles.
On a complex manifold, a co-Higgs bundle is a holomorphic vector bundle with an endomorphism twisted by the tangent bundle. The notion of generalized holomorphic bundle in Hitchin's generalized geometry coincides with that of co-Higgs bundle when the generalized complex manifold is ordinary complex. Schwarzenberger's r…
A stratified bundle is a fibered space in which strata are classical bundles and in which attachment of strata is controlled by a structure category of fibers. Well known results on fibre bundles are shown to be true for stratified bundles; namely the pull back theorem, the bundle theorem and the principal bundle theor…
We define double principal bundles (DPBs), for which the frame bundle of a double vector bundle, double Lie groups and double homogeneous spaces are basic examples. It is shown that a double vector bundle can be realized as the associated bundle of its frame bundle. Also dual structures, gauge transformations and conne…
Proves every equivariant vector bundle over toric manifolds is a Klyachko bundle.
problem Characterizing equivariant vector bundles over toric manifolds.
method Analyzes topological and smooth equivariant vector bundles over toric manifolds.
result Every equivariant vector bundle is a Klyachko bundle.
Categorical bundles provide a natural framework for gauge theories involving multiple gauge groups. Unlike the case of traditional bundles there are distinct notions of triviality, and hence also of local triviality, for categorical bundles. We study categorical principal bundles that are product bundles in the categor…
Symplectic fillings of prequantization bundles are shown to be disk bundles under certain conditions.
problem Characterizing symplectic fillings of prequantization bundles with finite capacities.
method Analysis of symplectic capacities and diffeomorphisms.
result Symplectic fillings of prequantization bundles are diffeomorphic to disk bundles under finite capacity conditions.
Identifies images of determinant morphism for specific co-Higgs bundles.
problem Determining images of determinant morphism for co-Higgs bundles.
method Identifying images of the determinant morphism of trace-free co-Higgs bundles modeled on rank 2 Schwarzenberger bundles.
result Identified images of the determinant morphism for specific co-Higgs bundles.
Bundling of graph edges (node-to-node connections) is a common technique to enhance visibility of overall trends in the edge structure of a large graph layout, and a large variety of bundling algorithms have been proposed. However, with strong bundling, it becomes hard to identify origins and destinations of individual…
The paper defines and explores vector bundles that can be turned and their properties.
problem Understanding which vector bundles can be turned and their properties.
method Defining and investigating vector bundles that can be turned, and developing their theory and obstructions.
result Rank-2k bundles over the 2k-sphere are turnable, and this implies orientability. Study projective flat vector bundles over Riemann surfaces using Wronskian line bundles.
problem Understanding projective flat holomorphic vector bundles over Riemann surfaces.
method Assigning Wronskian line bundles to vector bundles and interpreting Abel's identity.
result Abel's identity is the first Chern class of the Wronskian line bundle.
The paper generalizes bundle gerbes over groupoids and their correspondence with PB groupoids.
problem Generalizing bundle gerbes over groupoids and their properties.
method Developed a functorial correspondence between PB groupoids and bundle gerbes over groupoids.
result Built a correspondence between PB groupoids and bundle gerbes over groupoids, including partial quotients.
Study geometric characterization of asymptotic pseudodifferential calculus on spinor bundles.
problem Geometric characterization of asymptotic pseudodifferential calculus on spinor bundles.
method Groupoid approach to pseudodifferential calculus, rescaled bundle.
result Rescaled bundle provides geometric characterization to asymptotic pseudodifferential calculus on spinor bundles.
Generalizes Higgs bundles theory using a vector bundle twist.
problem Extending Higgs bundles theory to incorporate vector bundle twists.
method Defined a Hitchin map and spectral correspondence, stated Hitchin-Kobayashi correspondence.
result Established a theory halfway between curve and higher-dimensional variety Higgs bundles.
Study of generalized vector bundles and their geometric tools.
problem Extension of differential geometric tools to infinite dimensional vector bundles.
method Analysis of automorphisms, frame bundle, connection 1-forms, and covariant derivatives in diffeological vector pseudo-bundles.
result Non-isomorphism between connection 1-forms and covariant derivatives in infinite dimensional cases.
The paper extends orthogonal decomposition results to hermitian Higgs bundles.
problem Classical propositions on holomorphic vector bundles do not always extend to Higgs bundles.
method The approach involves extending propositions on orthogonal decompositions and the second fundamental form to hermitian Higgs bundles.
result Extended propositions concerning orthogonal decompositions and the second fundamental form have applications in Higgs bundles.
Introduces generalized principal bundles and connections, linking them to standard gauge theories.
problem Generalized principal bundles and connections in field theories.
method Local coordinate transformation laws and horizontal lifts.
result Generalized principal connections are associated to Lie group fiber bundle connections.
We present the notion of a filtered bundle as a generalisation of a graded bundle. In particular, we weaken the necessity of the transformation laws for local coordinates to exactly respect the weight of the coordinates by allowing more general polynomial transformation laws. The key examples of such bundles include af…
Study proves existence of precotangent bundles for Grassmannians.
problem Existence of precotangent bundles for Grassmannians.
method Proof for Grassmannians of reflexive Banach spaces and p-restricted Grassmannians of polarized Hilbert space. result Existence of bundle predual to tangent bundle (precotangent bundle).
Investigates connections in Lie group bundles, focusing on geometric reduction.
problem Geometric reduction of gauge field theories.
method Definition and analysis of equivariant connections in Lie group bundles.
result Provides conditions for the existence and properties of equivariant connections.
Study of Pascal algebra matrices and their jet bundle map for vector bundles.
problem Defining and studying Pascal algebra matrices and their map on jet bundles.
method Identifying Pascal algebra matrices, showing generator well defines Pascal map, using it for intrinsic contact definition.
result Intrinsic definition of point-wise contact between Hermitian vector bundles using unitary equivalence of Pascal maps.
A bundle gerbe is constructed from an oriented smooth vector bundle of even rank with a fiberwise inner product, over a compact connected orientable smooth manifold with Riemannian metric. From a trivialization of the bundle gerbe is constructed an irreducible Clifford module bundle, a spinor bundle over the smooth fre…
We develop the theory of smooth principal bundles for a smooth group G, using the framework of diffeological spaces. After giving new examples showing why arbitrary principal bundles cannot be classified, we define D-numerable bundles, the smooth analogs of numerable bundles from topology, and prove that pulling ba…
In \cite{BR1}, \cite{BR2}, a parabolic determinant line bundle on a moduli space of stable parabolic bundles was constructed, along with a Hermitian structure on it. The construction of the Hermitian structure was indirect: The parabolic determinant line bundle was identified with the pullback of the determinant line b…
Study on topological rigidity of ALE vector bundles with specific conditions.
problem Classifying ALE vector bundles with asymptotically conical total spaces.
method Topological classification and geometric analysis of ALE vector bundles.
result Only 2-sphere, projective plane, and open contractible manifolds admit ALE tangent bundles.
Defines connections for singularly foliated bundles.
problem Understanding connections in bundles with singular foliations.
method Introduces connections compatible with singular foliations, defines holonomy groupoids.
result Holonomy groupoids of trivial bundles are quotients of Androulidakis-Skandalis groupoids.
Extends Higgs fields theory to complex fiber bundles.
problem Characterize nonlinear flat connections on complex fiber bundles.
method Representation of extension class by curvature, nonlinear Higgs bundles, and nonabelian Hodge structure.
result Established a faithful functor from nonlinear flat bundles to nonlinear Higgs bundles.
Graded bundles are a class of graded manifolds which represent a natural generalisation of vector bundles and include the higher order tangent bundles as canonical examples. We present and study the concept of the linearisation of graded bundle which allows us to define the notion of the linear dual of a graded bundle.…
Study improves Simpson's estimate for cyclic harmonic bundles.
problem Improving Simpson's estimate for cyclic harmonic bundles.
method Applying to the classification of Toda type G-harmonic bundles.
result Enhanced estimate for cyclic harmonic bundles.
This masters thesis reviews bundle gerbe theory and the well-known basic bundle gerbe over SU(n). We introduce the cup product bundle gerbe, and show it is stably isomorphic to the pullback of the basic bundle gerbe by the Weyl map. This result enriches our understanding of the basic bundle gerbe, which has numerous ap…
Study shows some biquotients have non-biquotient tangent bundles.
problem Characterizing when the tangent bundle of a biquotient is a biquotient vector bundle.
method Examined infinite families of biquotients and manifolds, using Hirzebruch's signature-Euler characteristic relation.
result Found infinite families of biquotients whose tangent bundles are not biquotient vector bundles.
Decomposes bundle gerbes on supermanifolds into simpler components.
problem Classifying bundle gerbes on supermanifolds.
method Proves decomposition theorem and cohomological classification theorems.
result Bundle gerbes on supermanifolds decompose into a gerbe over the manifold and a 2-form.
Theory of 2-vector bundles for smooth manifolds developed.
problem Developing a comprehensive theory for 2-vector bundles over smooth manifolds.
method Based on bicategory of algebras, bimodules, and intertwiners; symmetric monoidal structures; classification via Cech cohomology.
result Unified framework for bundle gerbes and algebra bundles.