Zobrazeno 1 - 10
of 4 003
pro vyhledávání: '"Runkel, A."'
The skein module for a d-dimensional manifold is a vector space spanned by embedded framed graphs decorated by a category A with suitable extra structure depending on the dimension d, modulo local relations which hold inside d-balls. For a full subca
Externí odkaz:
http://arxiv.org/abs/2407.09302
Autor:
Gröne, Jannik, Runkel, Ingo
From the input of an oriented three-dimensional TFT with framed line defects and a commutative $\Delta$-separable Frobenius algebra $A$ in the ribbon category of these line defects, we construct a three-dimensional spin TFT. The framed line defects o
Externí odkaz:
http://arxiv.org/abs/2406.17336
Autor:
Hofer, Aaron, Runkel, Ingo
Given a not necessarily semisimple modular tensor category C, we use the corresponding 3d TFT defined in [arXiv:1912.02063] to explicitly describe a modular functor as a symmetric monoidal 2-functor from a 2-category of oriented bordisms to a 2-categ
Externí odkaz:
http://arxiv.org/abs/2405.18038
Neural ordinary differential equations (Neural ODEs) propose the idea that a sequence of layers in a neural network is just a discretisation of an ODE, and thus can instead be directly modelled by a parameterised ODE. This idea has had resounding suc
Externí odkaz:
http://arxiv.org/abs/2405.02478
This is a survey article for the Encyclopedia of Mathematical Physics, 2nd Edition. Topological defects are described in the context of the 2-dimensional Ising model on the lattice, in 2-dimensional quantum field theory, in topological quantum field
Externí odkaz:
http://arxiv.org/abs/2311.02449
Recently, large degeneracy based on product eigenstates has been found in spin ladders, Kagome-like lattices, and motif magnetism, connected to spin liquids, anyonic phases, and quantum scars. We unify these systems by a complete classification of pr
Externí odkaz:
http://arxiv.org/abs/2310.13158
Autor:
Romaidis, Iordanis, Runkel, Ingo
Mapping class group averages appear in the study of 3D gravity partition functions. In this paper, we work with 3D topological field theories to establish a bulk-boundary correspondence between such averages and correlators of 2D rational CFTs whose
Externí odkaz:
http://arxiv.org/abs/2309.14000
Levin-Wen models are a class of two-dimensional lattice spin models with a Hamiltonian that is a sum of commuting projectors, which describe topological phases of matter related to Drinfeld centres. We generalise this construction to lattice systems
Externí odkaz:
http://arxiv.org/abs/2309.05755
We consider the link and three-manifold invariants in [DGGPR], which are defined in terms of certain non-semisimple finite ribbon categories $\mathcal{C}$ together with a choice of tensor ideal and modified trace. If the ideal is all of $\mathcal{C}$
Externí odkaz:
http://arxiv.org/abs/2307.06069
Autor:
Cheng, Chun-Wun, Runkel, Christina, Liu, Lihao, Chan, Raymond H, Schönlieb, Carola-Bibiane, Aviles-Rivero, Angelica I
Image segmentation is a fundamental task in image analysis and clinical practice. The current state-of-the-art techniques are based on U-shape type encoder-decoder networks with skip connections, called U-Net. Despite the powerful performance reporte
Externí odkaz:
http://arxiv.org/abs/2302.00626