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.
The paper studies surface quotients of Fuchsian buildings.
Covering space theory is used to construct new examples of buildings.
AI helps build particle physics theories more efficiently.
We describe rules for building 2d theories labeled by 4-manifolds. Using the proposed dictionary between building blocks of 4-manifolds and 2d N=(0,2) theories, we obtain a number of results, which include new 3d N=2 theories T[M_3] associated with rational homology spheres and new results for Vafa-Witten partition fun…
This survey is a brief introduction to the theory of hyperbolic buildings and their lattices, with a focus on recent results.
Maps from buildings to spaces study K-theory of Hecke algebras.
We classify compact 2-connected homogeneous spaces with the same rational cohomology as a product of spheres. This classification relies on spectral sequences, homotopy theory, and representation theory. We then apply this classification to two geometric problems. The first problem is the classification of all isoparam…
Researchers develop methods to construct Lagrangian cobordisms between Legendrian knots.
Deep learning networks are approximated using dynamical systems theory.
Reductive (or semisimple) algebraic groups, Lie groups and Lie algebras have a rich geometry determined by their parabolic subgroups and subalgebras, which carry the structure of a building in the sense of J. Tits. We present herein an elementary approach to the geometry of parabolic subalgebras, over an arbitrary fiel…
New trick builds hyperbolic manifolds from compact ones, proving some don't virtually fiber.
New framework constructs holographic tensor networks using hyperbolic buildings.
By using Random Matrix Theory, we build covariance matrices between stocks of the BM&F-Bovespa (Bolsa de Valores, Mercadorias e Futuros de São Paulo) which are cleaned of some of the noise due to the complex interactions between the many stocks and the finiteness of available data. We also use a regression model in ord…
We build a variational theory of geodesics of the Tanaka-Webster connection on a strictly pseudoconvex CR manifold.
The relationship between minimal algebraic Kac-Moody groups and twin buildings is well known as is the relationship between formal completions in one direction and affine buildings. Nevertheless, as the completion of a Kac-Moody group in one direction destroys the opposite BN-pair, there exists no longer a twin buildin…
We build an elementary analytico-geometric theory of Segre chains and their jets.
Knot theory applied to quantum computing models.
Let I(p,v) be Bourdon's building, the unique simply-connected 2-complex such that all 2-cells are regular right-angled hyperbolic p-gons and the link at each vertex is the complete bipartite graph K(v,v). We investigate and mostly determine the set of triples (p,v,g) for which there exists a uniform lattice Γ in Aut(I(…
We propose a general notion of algebraic gauge theory obtained via extracting the main properties of classical gauge theory. Building on a recent work on transferring curved -structures we show that, under certain technical conditions, algebraic gauge theories can be transferred along chain contractions. Sp…
Paper builds a physical model of a foliation theory concept.
This is the second paper in a series of papers aimed at providing a geometric construction of modular functors and topological quantum field theories from conformal field theory building on the constructions in [TUY] and [KNTY]. We give a geometric construct of a modular functor for any simple Lie-algebra and any level…
The geometry of symmetric spaces, polar actions, isoparametric submanifolds and spherical buildings is governed by spherical Weyl groups and simple Lie groups. A natural generalization of semisimple Lie groups are affine Kac-Moody groups as they mirror their structure theory and have good explicitely known representati…
We present some ideas for a possible Noncommutative Floer Homology. The geometric motivation comes from an attempt to build a theory which applies to practically every 3-manifold (closed, oriented and connected) and not only to homology 3-spheres. There is also a physical motivation: one would like to construct a nonco…
We present about twenty conjectures, problems and questions about flat manifolds. Many of them build the bridges between the flat world and representation theory of the finite groups, hyperbolic geometry and dynamical systems.
The paper studies fibering properties of RACGs and random subcomplexes of buildings.
A transfer learning method builds high-dimensional models using disparate datasets.
Paper proposes new methods for improving interatomic potentials.
A Smale flow is a structurally stable flow with one dimensional invariant sets. We use information from homology and template theory to construct, visualize and in some cases, classify, nonsingular Smale flows in the 3-sphere.
Tutorials on preference learning with Gaussian Processes.
The classical Beauville-Bogomolov Decomposition Theorem asserts that any compact Kähler manifold with numerically trivial canonical bundle admits an étale cover that decomposes into a product of a torus, and irreducible, simply-connected Calabi-Yau-- and holomorphic-symplectic manifolds. The decomposition of the simply…
Develops theory of relatively Anosov representations using flow examples.
Conservation laws, heirarchies, scattering theory and Bäcklund transformations are known to be the building blocks of integrable partial differential equations. We identify these as facets of a theory of Poisson group actions, and apply the theory to the ZS-AKNS nxn heirarchy (which includes the non-linear Schrödinger …
Construct M-Theory lifts of type IIA orientifolds.
Building on the universal covering group of the general linear group, we introduce the composite spinor bundle whose subbundles are Lorentz spin structures associated with different gravitational fields. General covariant transformations of this composite spinor bundle are canonically defined.
Paper builds neural networks on matrix manifolds using gyrovector spaces.
We develop the structure theory of full isometry groups of locally compact non-positively curved metric spaces. Amongst the discussed themes are de Rham decompositions, normal subgroup structure and characterising properties of symmetric spaces and Bruhat--Tits buildings. Applications to discrete groups and further dev…
We give a Thurston-like definition for laminations on higher Teichmuller spaces associated to a surface and a semi-simple group for and . The case or corresponds to the classical theory of laminations. Our construction involves positive configurations of points in the affine bui…
Considering a Hamiltonian Dynamical System describing the motion of charged particle in a Tokamak or a Stellarator, we build a change of coordinates to reduce its dimension. This change of coordinates is in fact an intricate succession of mappings that are built using Hyperbolic Partial Differential Equations, Differen…
Study builds non-bi-orderable groups without generalized torsion.
A well known conjecture in the theory of transformation groups states that if p is a prime and (Z/p)^r acts freely on a product of k spheres, then r is less than or equal to k. We prove this assertion if p is large compared to the dimension of the product of spheres. The argument builds on tame homotopy theory for non …
The paper analyzes optimal stock position-building strategies in competitive markets.
Study Morse complexity of manifolds and homology classes, proving bounds and implications.
As in a symmetric space of noncompact type, one can associate to an oriented geodesic segment in a Euclidean building a vector valued length in the Euclidean Weyl chamber; in addition to the metric length it contains information on the direction of the segment. We study in this paper restrictions on the vector valued s…
The study restricts groups in graph of groups structures.
Abstract: Linking field theory to Floer theory via regularization.
Projection maps which appear in the theory of buildings and oriented matroids are closely related to the notion of shellability. This was first observed by Bj{ö}rner. In this paper, we give an axiomatic treatment of either concept and show their equivalence. We also axiomatize duality in this setting. As applications o…
Enhances knot Floer homology with algebraic representation theory.
We prove an Hersch's type isoperimetric inequality for the third positive eigenvalue on . Our method builds on the theory we developped to construct extremal metrics on Riemannian surfaces in conformal classes for any eigenvalue.