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Modular conjugations in 2D conformal field theory and holographic bit threads
We study the geometric action of some modular conjugations in two dimensional (2D) conformal field theories. We investigate the bipartition given by...
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Weil–Petersson geodesics on the modular surface
We consider the Weil–Petersson (WP) metric on the modular surface. We lift WP geodesics to the universal cover of the modular surface, and analyse...
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An observable in Classical Pure AdS3 Gravity: the twist along a geodesic
In this paper, we consider a little-studied observable in classical pure AdS 3 gravity: the twist along a geodesic. The motivation is that the twist...
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Holomorphic Retractions of Bounded Symmetric Domains onto Totally Geodesic Complex Submanifolds
Given a bounded symmetric domain Ω the author considers the geometry of its totally geodesic complex submanifolds S ⊂ Ω. In terms of the...
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Modular geodesics and wedge domains in non-compactly causal symmetric spaces
We continue our investigation of the interplay between causal structures on symmetric spaces and geometric aspects of Algebraic Quantum Field Theory....
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Cycle integrals of meromorphic modular forms and Siegel theta functions
We study meromorphic modular forms associated with positive definite binary quadratic forms and their cycle integrals along closed geodesics in the...
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Modular flow in JT gravity and entanglement wedge reconstruction
It has been shown in recent works that JT gravity with matter with two boundaries has a type II ∞ algebra on each side. As the bulk spacetime between...
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Analyticity of replica correlators and modular ETH
We study the two point correlation function of a local operator on an n -sheeted replica manifold corresponding to the half-space in the vacuum state...
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Modular parallel transport of multiple intervals in 1+1-dimensional free fermion theory
Modular parallel transport is a generalization of Berry phases, applied to modular (entanglement) Hamiltonians. Here we initiate the study of modular...
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Causal shadow and non-local modular flow: from degeneracy to perturbative genesis by correlation
Causal shadows are bulk space-time regions between the entanglement wedges and the causal wedges, their existence encodes deep aspects of the...
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Extended-cycle integrals of modular functions for badly approximable numbers
Cycle integrals of modular functions are expected to play a role in real quadratic analogue of singular moduli. In this paper, we extend the...
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An adaptive model order reduction technique for parameter-dependent modular structures
This work is concerned with an adaptive reduced order model of modular structures assembled from parameter-dependent substructures. The substructures...
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The Eisenstein and winding elements of modular symbols for odd square-free level
We explicitly write down the Eisenstein elements inside the space of modular symbols for Eisenstein series with integer coefficients for the...
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A closure operator respecting the modular j-function
We prove some unconditional cases of the Existential Closedness problem for the modular j -function. For this, we show that for any finitely generated...
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Modular Operator for Null Plane Algebras in Free Fields
We consider the algebras generated by observables in quantum field theory localized in regions in the null plane. For a scalar free field theory, we...
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Weak modular Zilber–Pink with derivatives
In unpublished notes Pila proposed a Modular Zilber–Pink with derivatives (MZPD) conjecture, which is a Zilber–Pink type statement for the modular j -f...
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A nonpositive curvature property of modular semilattices
The orthoscheme complex of a graded poset is a metrization of its order complex such that the simplex of each maximal chain is isometric to the...
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Riemann-DTI Geodesic Tractography Revisited
Clinical tractography is a challenging problem in diffusion tensor imaging (DTI) due to persistent validation issues. Geodesic tractography, based on...