A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New symmetry dimensions for higher order ODEs are identified.
Study of symmetries in 2D Yang-Mills theory, including orbifolds and higher forms.
New proof shows symmetry for certain curved surfaces in higher dimensions.
Higher Gauge Flow Models integrate higher geometry and symmetries into Generative Flow Models.
We construct in projective differential geometry of the real dimension higher symmetry algebra of the symplectic Dirac operator ${D}\kern-0.5em\raise0.22ex\hbox{/}_s$ acting on symplectic spinors. The higher symmetry differential operators correspond to the solution space of a class of projectively invariant overde…
We find a remarkable subalgebra of higher symmetries of the elliptic Euler-Darboux equation. To this aim we map such equation into its hyperbolic analogue already studied by Shemarulin. Taking into consideration how symmetries and recursion operators transform by this complex contact transformation, we explicitly give …
By developing a generalized cobordism theory, we explore the higher global symmetries and higher anomalies of quantum field theories and interacting fermionic/bosonic systems in condensed matter. Our essential math input is a generalization of Thom-Madsen-Tillmann spectra, Adams spectral sequence, and Freed-Hopkins's t…
We develop a new approach, based on quantization methods, to study higher symmetries of invariant differential operators. We focus here on conformally invariant powers of the Laplacian over a conformally flat manifold and recover results of Eastwood, Leistner, Gover and Šilhan. In particular, conformally equivariant qu…
The paper studies higher geometric structures and connections on manifolds, constructing moduli stacks and proving equivalence criteria.
We explore 4d Yang-Mills gauge theories (YM) living as boundary conditions of 5d gapped short/long-range entangled (SRE/LRE) topological states. Specifically, we explore 4d time-reversal symmetric pure YM of an SU(2) gauge group with a second-Chern-class topological term at (SU(2) YM), by turning on backg…
This work presents a geometrical formulation of the Clairin theory of conditional symmetries for higher-order systems of partial differential equations (PDEs). We devise methods for obtaining Lie algebras of conditional symmetries from known conditional symmetries, and unnecessary previous assumptions of the theory are…
Introduces new connections in higher geometry.
The geometrical theory of partial differential equations in the absolute sense, without any additional structures, is developed. In particular the symmetries need not preserve the hierarchy of independent and dependent variables. The order of derivatives can be changed and the article is devoted to the higher--order in…
Improves hypergraph link prediction by breaking symmetry.
Study quantum aspects of 1-form symmetries using BV-BRST cohomology and gerbes.
We survey the role of symmetry in diffeomorphic registration of landmarks, curves, surfaces, images and higher-order data. The infinite dimensional problem of finding correspondences between objects can for a range of concrete data types be reduced resulting in compact representations of shape and spatial structure. Th…
Using the AdS/CFT correspondence, we identify the symmetry algebra of the Laplacian on Euclidean space as an explicit quotient of the universal enveloping algebra of the Lie algebra of conformal motions. We construct analogues of these symmetries on a general conformal manifold.
Hidden symmetries of the Goryachev-Chaplygin and Kovalevskaya gyrostats spacetimes, as well as the Brdička-Eardley-Nappi-Witten pp-waves are studied. We find out that these spacetimes possess higher rank Stäckel-Killing tensors and that in the case of the pp-wave spacetimes the symmetry group of the Stäckel-Killing ten…
We describe mirror symmetry on higher dimensional tori, paying special attention to the behaviour of D-branes under mirror symmetry. To find the mirror D-branes the description of mirror symmetry on D-branes due to Ooguri, Oz en Yin is used. This method allows us to deal with the coisotropic D-branes recently introduce…
Study quantum aspects of 1-form symmetries using BV-BRST cohomology.
The paper connects orbifold singularities to higher symmetries in SQFTs.
We prove sharp blow up rates of solutions of higher order conformally invariant equations in a bounded domain with an isolated singularity, and show the asymptotic radial symmetry of the solutions near the singularity. This is an extension of the celebrated theorem of Caffarelli-Gidas-Spruck for the second order Yamabe…
A framework for reducing PDEs by symmetry, preserving key structures.
The mathematical physicists Bershadsky-Cecotti-Ooguri-Vafa (BCOV) proposed, in a seminal article from '94, a conjecture extending genus zero mirror symmetry to higher genera. With a view towards a refined formulation of the Grothendieck-Riemann-Roch theorem, we offer a mathematical description of the BCOV conjecture at…
A BV algebra is a formal framework within which the BV quantization algorithm is implemented. In addition to the gauge symmetry, encoded in the BV master equation, the master action often exhibits further global symmetries, which may be in turn gauged. We show how to carry this out in a BV algebraic set up. Depending o…
The symmetry operators for the Laplacian in flat space were recently described and here we consider the same question for the square of the Laplacian. Again, there is a close connection with conformal geometry. There are three main steps in our construction. The first is to show that the symbol of a symmetry is constra…
Higher-dimensional spacetimes have well-behaved boundaries.
New rigidity results for manifolds with maximal symmetry rank and positive intermediate Ricci curvature.
Summarizes quantum field theories with discrete symmetry, classifying representations and anomalies.
The aim of this work is to develop a systematic manner to close overdetermined systems arising from conformal Killing tensors (CKT). The research performs this action for 1-tensor and 2-tensors. This research makes it possible to develop a new general method for any rank of CKT. This method can also be applied to other…
Generically an almost complex structure has no symmetries at all, but there exist symmetric structures. In this paper we describe how to guarantee that the pseudogroup of local symmetries is small (finite-dimensional). It will be indicated that a large symmetry pseudogroup (infinite-dimensional) is a signature of some …
On locally conformally flat manifolds we describe a construction which maps generalised conformal Killing tensors to differential operators which may act on any conformally weighted tensor bundle; the operators in the range have the property that they are symmetries of any natural conformally invariant differential ope…
The paper shows that almost every path structure is not variational.
New geometric approach realizes 5D bulk theories with 4D edge modes.
Extended symmetries and anomalies in compactified 6d SCFTs on various internal manifolds.
Reductions of higher tangent bundles of Lie groupoids provide natural examples of geometric structures which we would like to call higher algebroids. Such objects can be also constructed abstractly starting from an arbitrary almost Lie algebroid. A higher algebroid is, in principle, a graded bundle equipped with a diff…
Solvable structures, likewise solvable algebras of local symmetries, can be used to integrate scalar ODEs by quadratures. Solvable structures, however, are particularly suitable for the integration of ODEs with a lack of local symmetries. In fact, under regularity assumptions, any given ODE always admits solvable struc…
New methods reveal symmetries in Chern-Simons theory.
Classifies charge-3 monopoles with symmetry, identifying new spectral curves.
We study SYZ mirror symmetry in the context of non-Kaehler Calabi-Yau manifolds. In particular, we study the six-dimensional Type II supersymmetric systems with Ramond-Ramond fluxes, and generalize them to higher dimensions. We show that Fourier-Mukai transform provides the mirror map between these Type IIA and…
This research introduces Lie brackets on spaces of biderivations in Lie algebras.
We study the equation E_fc of flat connections in a fiber bundle and discover a specific geometric structure on it, which we call a flat representation. We generalize this notion to arbitrary PDE and prove that flat representations of an equation E are in 1-1 correspondence with morphisms f: E\to E_fc, where E and E_fc…
Develops a new framework for anomaly description in quantum field theories.
Classifies hypersurfaces with positive constant mean curvature in hyperbolic space.
Symmetric hypersurfaces and boundaries in R^n+1 with group actions.
New symmetries found for scalar and vector ODEs of arbitrary dimensions.
The article explores symmetric maps on surfaces, focusing on semi-equivelar maps.
We propose an extension of the structure equation for constant mean curvature (CMC) surfaces in a three dimensional Riemannian space form to the associated CMC hierarchy of evolution equations by the higher-order commuting symmetries. Via the canonical formal Killing field, considered as an infinitely prolonged and loo…