arXiv research

Paper proposes a voting method to improve acoustic scene classification.

The paper develops a theory of $C^\infty$-superrings and their superschemes.

In this paper we analyze supergeometric locally covariant quantum field theories. We develop suitable categories SLoc of super-Cartan supermanifolds, which generalize Lorentz manifolds in ordinary quantum field theory, and show that, starting from a few representation theoretic and geometric data, one can construct a f…

This work interprets supergravity as a super Cartan geometry linking it to Yang-Mills theory.

We use super $q$-Howe duality to provide diagrammatic presentations of an idempotented form of the Hecke algebra and of categories of $\mathfrak{gl}_N$-modules (and, more generally, $\mathfrak{gl}_{N|M}$-modules) whose objects are tensor generated by exterior and symmetric powers of the vector representations. As an ap…

We derive the canonical forms of super Riemannian metrics and the local isometry groups of such metrics. For certain super metrics we also compute the simply connected covering groups of the local isometry groups and interpret these as local spin groups of the super metric. Using a generalization of a Theorem of Rogers…

The paper defines a category of Lagrangian correspondences in super Hilbert spaces and constructs a functorial field theory.

Vector bundles and double vector bundles, or $2$-fold vector bundles, arise naturally for instance as base spaces for algebraic structures such as Lie algebroids, Courant algebroids and double Lie algebroids. It is known that all these structures possess a unified description using the language of super\-geometry and g…

Scheme resolves super-brane topology via equivariant structures.

In his recent investigation of a super Teichmüller space, Sachse (2007), based on work of Molotkov (1984), has proposed a theory of Banach supermanifolds using the `functor of points' approach of Bernstein and Schwarz. We prove that the the category of Berezin-Kostant-Leites supermanifolds is equivalent to the category…

It is known that there exists a natural functor $Φ$ from Lie supergroups to super Harish-Chandra pairs. A functor going backwards, that associates a Lie supergroup with each super Harish-Chandra pair, yielding an equivalence of categories, was found by Koszul [18]; this result was later extended by other authors, to di…

Mathematical theory of super fiber bundles and connections developed.

Study classifies super vector bundles and proves universality.

A key open problem in M-theory is the identification of the degrees of freedom that are expected to be hidden at ADE-singularities in spacetime. Comparison with the classification of D-branes by K-theory suggests that the answer must come from the right choice of generalized cohomology theory for M-branes. Here we show…

Proposes a multi-resolution model for prostate cancer classification using mpMRI.

This is the second in a series of papers laying the foundations for a differential graded approach to derived differential geometry (and other geometries in characteristic zero). In this paper, we extend the classical notion of a dg-algebra to define, in particular, the notion of a differential graded algebra in the wo…

This is the first in a series of papers laying the foundations for a differential graded approach to derived differential geometry (and other geometries in characteristic zero). In this paper, we study theories of supercommutative algebras for which infinitely differentiable functions can be evaluated on elements. Such…

Constructs 2-vector bundles and 2K-theory for Lie groupoids and 2-equivariant settings.

We introduce mappings between spaces of functions on (super)manifolds that generalize pullbacks with respect to smooth maps but are, in general, nonlinear (actually, formal). The construction is based on canonical relations and generating functions. (The underlying structure is a formal category, which is a "thickening…

Defines odd Khovanov homology via categorification of q-Schur algebra.

We construct and study a new family of TQFTs based on nilpotent highest weight representations of quantum sl(2) at a root of unity indexed by generic complex numbers. This extends to cobordisms the non-semi-simple invariants defined in (arXiv:1202.3553) including the Kashaev invariant of links. Here the modular categor…

Extends supersymmetry to include exotic $\mathbb{Z}_2^n$-graded spinors.

A classical theorem states that the group of automorphisms of a manifold $M$ preserving a $G$-structure of finite type is a Lie group. We generalize this statement to the category of $cs$ manifolds and give some examples, some of which being generalizations of classical notions, others being particular to the super cas…

Mathematical study supports connection between 3D manifolds and modular tensor categories.

We propose a novel, projection based way to incorporate the conditional information into the discriminator of GANs that respects the role of the conditional information in the underlining probabilistic model. This approach is in contrast with most frameworks of conditional GANs used in application today, which use the …

Explains basics of supersymmetry and supergeometry.

In the 90s, based on presentations of 3-manifolds by Heegaard diagrams, Kuperberg associated a scalar invariant of 3-manifolds to each finite dimensional involutory Hopf algebra over a field. We generalize this construction to the case of involutory Hopf algebras in arbitrary symmetric monoidal categories admitting cer…

Smooth $\mathbb{Z}_2^n$-supermanifolds have been introduced and studied recently. The corresponding sign rule is given by the "scalar product" of the involved $\mathbb{Z}_2^n$-degrees. It exhibits interesting changes in comparison with the sign rule using the parity of the total degree. With the new rule, nonzero degre…

Develops Hermitian TQFTs from quantum groups, defining new topological phases.

Study super cluster algebras from super Plücker and Ptolemy relations.

The paper defines and analyzes curvature tensors on super twisted product spaces.

With the usual definition of a super Hilbert space and a super unitary representation, it is easy to show that there are lots of super Lie groups for which the left-regular representation is not super unitary. I will argue that weakening the definition of a super Hilbert space (by allowing the super scalar product to b…

We establish a higher generalization of super L-infinity-algebraic T-duality of super WZW-terms for super p-branes. In particular, we demonstrate spherical T-duality of super M5-branes propagating on exceptional-geometric 11d super spacetime.

Unified super-symmetry and higher fluxes using super-Lie-infinity algebras.

Researchers create holographic super-embeddings for M5 and M2 branes.

Develops Riemannian geometry for noncommutative super surfaces.

Defines super stable maps and proves quotient superorbifolds for genus zero.

Defines semi-symmetric metric connection on super warped products.

Authors derive McShane identity for super tori.

Riemann surfaces are two-dimensional manifolds with a conformal class of metrics. It is well known that the harmonic action functional and harmonic maps are tools to study the moduli space of Riemann surfaces. Super Riemann surfaces are an analogue of Riemann surfaces in the world of super geometry. After a short intro…

New theorem disproves Angle Defect for super triangles.

Constructs the moduli space of super J-holomorphic curves.

The underlying even manifold of a super Riemann surface is a Riemann surface with a spinor valued differential form called gravitino. Consequently infinitesimal deformations of super Riemann surfaces are certain infinitesimal deformations of the Riemann surface and the gravitino. Furthermore the action functional of no…

The paper studies special warped products with a specific connection on super Riemannian manifolds.

Super tau-covers extend bihamiltonian hierarchies' symmetries.

A super Lie group is a group whose operations are $G^{\infty}$ mappings in the sense of Rogers. Thus the underlying supermanifold possesses an atlas whose transition functions are $G^{\infty}$ functions. Moreover the images of our charts are open subsets of a graded infinite-dimensional Banach space since our space of …

Defines a super analog of Plücker embedding for Grassmannian.

Unified solution to M-theory problems using super-exceptional geometry.