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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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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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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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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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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In unpublished notes Pila proposed a Modular Zilber–Pink with derivatives (MZPD) conjecture, which is a Zilber–Pink type statement for the modular j -f...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...
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On the dimension of totally geodesic submanifolds in the Prym loci
In this paper we give a bound on the dimension of a totally geodesic submanifold of the moduli space of polarised abelian varieties of a given...
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On the Linear Dilatation of the Map**s Satisfying an Inverse Poletsky Modular Inequality in Metric Spaces
We study the linear dilatation of the map**s satisfying an inverse Poletsky inequality in metric spaces. We also show that under certain conditions...
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Classical Modular Symbols, Modular Forms, L-functions
We introduce the classical modular symbols, which are modular symbols with coefficients polynomials of bounded degree. We explain their close...
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On certain orbits of geodesic flow and \(\pmb {(a,b)}\)-continued fractions
In this article, we characterize two kinds of exceptional orbits of the geodesic flow associated with the modular surface in terms of a two-parameter...
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Classical modular group
In this chapter, we introduce the classical modular group...
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Knot Invariants in Geodesic Flows
The mean value of an asymptotic invariant of a knotted trajectory of a Ghys-Dehornoy geodesic flow is calculated. The result is important for...
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Translates of rational points along expanding closed horocycles on the modular surface
We study the limiting distribution of the rational points under a horizontal translation along a sequence of expanding closed horocycles on the...
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Homeomorphisms between Finsler manifolds satisfying the Rohde condition
We study the main features of homeomorphisms between two Finsler manifolds satisfying the Rohde condition, i.e. the difference between the moduli of...
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On Effective Upper Bound for Huber’s Constant
We determine an effective upper bound for Huber’s constant in the prime geodesic theorem on cofinite Fuchsian groups in the previously uncovered case...