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Coxeter Quotients of Knot Groups through 16 Crossings Exp. Math. (IF 0.5) Pub Date : 2024-03-12 Ryan Blair, Alexandra Kjuchukova, Nathaniel Morrison
We find explicit maximal rank Coxeter quotients for the knot groups of 595,515 out of the 1,701,936 knots through 16 crossings. We thus calculate the bridge numbers and verify Cappell and Shaneson’...
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Crepant Resolutions, Mutations, and the Space of Potentials Exp. Math. (IF 0.5) Pub Date : 2024-02-11 Mary Barker, Benjamin Standaert, Ben Wormleighton
The McKay correspondence has had much success in studying resolutions of 3-fold quotient singularities through a wide range of tools coming from geometry, combinatorics, and representation theory. ...
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Open Covers and Lex Points of Hilbert Schemes Over Quotient Rings via Relative Marked Bases Exp. Math. (IF 0.5) Pub Date : 2024-02-01 Cristina Bertone, Francesca Cioffi, Matthias Orth, Werner M. Seiler
We introduce the notion of a relative marked basis over quasi-stable ideals, together with constructive methods and a functorial interpretation, developing computational methods for the study of Hi...
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Structures in HOMFLY-PT Homology Exp. Math. (IF 0.5) Pub Date : 2024-01-07 Alex Chandler, Eugene Gorsky
We study the structure of triply graded Khovanov-Rozansky homology using both the data recently computed by Nakagane and Sano for knots up to 11 crossings, and the sl(2) action defined by the secon...
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Earthquakes on the Once-Punctured Torus Exp. Math. (IF 0.5) Pub Date : 2024-01-04 Grace S. Garden
We study earthquake deformations on Teichmüller space associated with simple closed curves of the once-punctured torus. We describe two methods to get an explicit form of the earthquake deformation...
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A Cable Knot and BPS-Series II Exp. Math. (IF 0.5) Pub Date : 2024-01-04 John Chae
This is a companion paper to earlier work of the author, which generalizes to an infinite family of (2,2w+1)-cabling of the figure eight knot (|w|>3) and proposes general formulas for the two-varia...
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Continued Fraction Expansions Towards Zaremba’s Conjecture Exp. Math. (IF 0.5) Pub Date : 2023-12-26 Khalil Ayadi, Takao Komatsu
In this article, we show that Zaremba’s conjecture holds for positive integers that appear as values of polynomials resulting from a recurrence formula and their powers of two. For example, Zaremba...
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On the Arithmetic of Generalized Fekete Polynomials Exp. Math. (IF 0.5) Pub Date : 2023-12-21 Ján Mináč, Tung T. Nguyen, Nguyễn Duy Tân
For each prime number p one can associate a Fekete polynomial with coefficients–1 or 1 except the constant term, which is 0. These are classical polynomials that have been studied extensively in th...
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No Eleventh Conditional Ingleton Inequality Exp. Math. (IF 0.5) Pub Date : 2023-12-21 Tobias Boege
A rational probability distribution on four binary random variables X,Y,Z,U is constructed which satisfies the conditional independence relations [X⊥⊥Y],[X⊥⊥Z|U],[Y⊥⊥U|Z] and [Z⊥⊥U|XY] but whose ...
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A Family of Iterated Maps on Natural Numbers Exp. Math. (IF 0.5) Pub Date : 2023-12-19 Angsuman Das
In this paper, we introduce and study the iterates of the following family of functions φk defined on natural numbers which exhibits nice properties.φk(x)={x+k, if x is prime;largest prime divisor ...
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Intersection Numbers on Fibrations and Catalan Numbers Exp. Math. (IF 0.5) Pub Date : 2023-12-19 Rimma Hämäläinen, Jason Lo, Edward Morales
On an elliptic surface or threefold, Catalan numbers appear when one tries to compute the autoequivalence group action on the Bridgeland stability manifold. We explain why this happens by identifyi...
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Self-Dual Matroids from Canonical Curves Exp. Math. (IF 0.5) Pub Date : 2023-08-08 Alheydis Geiger, Sachi Hashimoto, Bernd Sturmfels, Raluca Vlad
Abstract Self-dual configurations of 2n points in a projective space of dimension n – 1 were studied by Coble, Dolgachev–Ortland, and Eisenbud–Popescu. We examine the self-dual matroids and self-dual valuated matroids defined by such configurations, with a focus on those arising from hyperplane sections of canonical curves. These objects are parametrized by the self-dual Grassmannian and its tropicalization
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Orbits on K3 Surfaces of Markoff Type Exp. Math. (IF 0.5) Pub Date : 2023-08-03 Elena Fuchs, Matthew Litman, Joseph H. Silverman, Austin Tran
Abstract Let W⊂P1×P1×P1W⊂P1×P1×P1 be a surface given by the vanishing of a (2, 2, 2)-form. These surfaces admit three involutions coming from the three projections W→P1×P1W→P1×P1 , so we call them tri-involutive K3 (TIK3) surfaces. By analogy with the classical Markoff equation, we say that WW is of Markoff type (MK3) if it is symmetric in its three coordinates and invariant under double sign changes
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Correction Exp. Math. (IF 0.5) Pub Date : 2023-08-03
Published in Experimental Mathematics (Vol. 32, No. 3, 2023)
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Higher Rademacher Symbols Exp. Math. (IF 0.5) Pub Date : 2023-07-21 W. Duke
Abstract Certain higher Rademacher symbols are defined that give class functions on the modular group. Their basic properties are derived via a two-variable reformulation of Eichler-Shimura cohomology. This reformulation better explains the role of cycle integrals and also yields new results, about the integrality of the values of the symbols. The Rademacher symbols determine the values at non-positive
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Heuristics for Anti-cyclotomic ℤp-extensions Exp. Math. (IF 0.5) Pub Date : 2023-06-15 Debanjana Kundu, Lawrence C. Washington
Abstract This paper studies Iwasawa invariants in anti-cyclotomic towers. We do this by proposing two heuristics supported by computations. First we propose the Intersection Heuristics: these model “how often” the p-Hilbert class field of an imaginary quadratic field intersects the anti-cyclotomic tower and to what extent. Second we propose the Invariants Heuristics: these predict that the Iwasawa
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A Numerical Stability Analysis of Mean Curvature Flow of Noncompact Hypersurfaces with Type-II Curvature Blowup: II Exp. Math. (IF 0.5) Pub Date : 2023-05-31 David Garfinkle, James Isenberg, Dan Knopf, Haotian Wu
Abstract In previous work, we have presented evidence from numerical simulations that the Type-II singularities of mean curvature flow (MCF) of rotationally symmetric, complete, noncompact embedded hypersurfaces, constructed by the second and the fourth authors of this paper, are stable. In this work, we again use numerical simulations to show that MCF subject to initial perturbations that are not
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Crossing the Transcendental Divide: From Translation Surfaces to Algebraic Curves Exp. Math. (IF 0.5) Pub Date : 2023-05-24 Türkü Özlüm Çelik, Samantha Fairchild, Yelena Mandelshtam
Abstract We study constructing an algebraic curve from a Riemann surface given via a translation surface, which is a collection of finitely many polygons in the plane with sides identified by translation. We use the theory of discrete Riemann surfaces to give an algorithm for approximating the Jacobian variety of a translation surface whose polygon can be decomposed into squares. We first implement
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Discontinuities of the Integrated Density of States for Laplacians Associated with Penrose and Ammann–Beenker Tilings Exp. Math. (IF 0.5) Pub Date : 2023-05-22 David Damanik, Mark Embree, Jake Fillman, May Mei
Abstract Aperiodic substitution tilings provide popular models for quasicrystals, materials exhibiting aperiodic order. We study the graph Laplacian associated with four tilings from the mutual local derivability class of the Penrose tiling, as well as the Ammann–Beenker tiling. In each case we exhibit locally-supported eigenfunctions, which necessarily cause jump discontinuities in the integrated
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Homology Representations of Compactified Configurations on Graphs Applied to 𝓜2,n Exp. Math. (IF 0.5) Pub Date : 2023-05-22 Christin Bibby, Melody Chan, Nir Gadish, Claudia He Yun
Abstract We obtain new calculations of the top weight rational cohomology of the moduli spaces M2,n, equivalently the rational homology of the tropical moduli spaces Δ2,nΔ2,n , as a representation of Sn. These calculations are achieved fully for all n≤11n≤11 , and partially—for specific irreducible representations of Sn—for n≤22n≤22 . We also present conjectures, verified up to n = 22, for the multiplicities
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Computing Heights via Limits of Hodge Structures Exp. Math. (IF 0.5) Pub Date : 2023-04-13 Spencer Bloch, Robin de Jong, Emre Can Sertöz
Abstract We consider the problem of explicitly computing Beilinson–Bloch heights of homologically trivial cycles on varieties defined over number fields. Recent results have established a congruence, up to the rational span of logarithms of primes, between the height of certain limit mixed Hodge structures and certain Beilinson–Bloch heights obtained from odd-dimensional hypersurfaces with a node.
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Explicit Computations with Cubic Fourfolds, Gushel–Mukai Fourfolds, and their Associated K3 Surfaces Exp. Math. (IF 0.5) Pub Date : 2023-04-10 Giovanni Staglianò
Abstract We present some applications of the Macaulay2 software package SpecialFanoFourfolds, a package for working with Hodge-special cubic fourfolds and Hodge-special Gushel–Mukai fourfolds. In particular, we show how to construct new examples of such fourfolds, some of which turn out to be rational. We also describe how to calculate K3 surfaces associated with cubic or Gushel-Mukai fourfolds, which
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Topological Bounds on Hyperkähler Manifolds Exp. Math. (IF 0.5) Pub Date : 2023-04-10 Justin Sawon
Abstract We conjecture that certain curvature invariants of compact hyperkähler manifolds are positive/negative. We prove the conjecture in complex dimension four, give an “experimental proof” in higher dimensions, and verify it for all known hyperkähler manifolds up to dimension eight. As an application, we show that our conjecture leads to a bound on the second Betti number in all dimensions.
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An Algorithm to Find Ribbon Disks for Alternating Knots Exp. Math. (IF 0.5) Pub Date : 2023-03-15 Brendan Owens, Frank Swenton
Abstract We describe an algorithm to find ribbon disks for alternating knots, and the results of a computer implementation of this algorithm. The algorithm is underlain by a slice link obstruction coming from Donaldson’s diagonalization theorem. It successfully finds ribbon disks for slice two-bridge knots and for the connected sum of any alternating knot with its reverse mirror, as well as for 662
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Convolution and Square in Abelian Groups I Exp. Math. (IF 0.5) Pub Date : 2023-02-28 Yves Benoist
Abstract We prove that the functional equation f⋆f(2 t)=λf(t)2, for t in Z/dZ with d odd, admits a nonzero solution f if λ=a+ib with a, b positive integers such that a+b=d and a≡(d+1)24 mod 4. The proof involves theta functions on elliptic curves with complex multiplication.
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On Subgroups Finite Index in Complex Hyperbolic Lattice Triangle Groups Exp. Math. (IF 0.5) Pub Date : 2023-02-22 Martin Deraux
Abstract We study several explicit finite index subgroups in the known complex hyperbolic lattice triangle groups, and show some of them are neat, some of them have positive first Betti number, some of them have a homomorphisms onto a non-Abelian free group. For some lattice triangle groups, we determine the minimal index of a neat subgroup. Finally, we answer a question raised by Stover and describe
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Hard Diagrams of the Unknot Exp. Math. (IF 0.5) Pub Date : 2023-02-07 Benjamin A. Burton, Hsien-Chih Chang, Maarten Löffler, Clément Maria, Arnaud de Mesmay, Saul Schleimer, Eric Sedgwick, Jonathan Spreer
Abstract We present three “hard” diagrams of the unknot. They require (at least) three extra crossings before they can be simplified to the trivial unknot diagram via Reidemeister moves in S2. Two of them are constructed by applying previously proposed methods. The proof of their hardness uses significant computational resources. We also determine that no small “standard” example of a hard unknot diagram
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Confirming Brennan’s Conjecture Numerically on a Counterexample to Thurston’s K = 2 Conjecture Exp. Math. (IF 0.5) Pub Date : 2022-12-28 Ognjen Tošić
Abstract It was shown by Bishop that if Thurston’s K = 2 conjecture holds for some planar domain, then Brennan’s conjecture holds for the Riemann map of that domain as well. In this paper we show numerically that the original counterexample to Thurston’s K = 2 conjecture given by Epstein, Marden and Marković is not a counterexample to Brennan’s conjecture.
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Band-Limited Maximizers for a Fourier Extension Inequality on the Circle, II Exp. Math. (IF 0.5) Pub Date : 2022-11-24 James Barker, Christoph Thiele, Pavel Zorin-Kranich
Abstract Among the class of functions on the circle with Fourier modes up to degree 120, constant functions are the unique real-valued maximizers for the endpoint Tomas-Stein inequality.
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Cohomology fractals, Cannon–Thurston maps, and the geodesic flow Exp. Math. (IF 0.5) Pub Date : 2022-09-15 David Bachman, Matthias Goerner, Saul Schleimer, Henry Segerman
Abstract Cohomology fractals are images naturally associated to cohomology classes in hyperbolic three-manifolds. We generate these images for cusped, incomplete, and closed hyperbolic three-manifolds in real-time by ray-tracing to a fixed visual radius. We discovered cohomology fractals while attempting to illustrate Cannon–Thurston maps without using vector graphics; we prove a correspondence between
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Equations at Infinity for Critical-Orbit-Relation Families of Rational Maps Exp. Math. (IF 0.5) Pub Date : 2022-09-03 Rohini Ramadas, Rob Silversmith
Abstract We develop techniques for using compactifications of Hurwitz spaces to study families of rational maps P1→P1 defined by critical orbit relations. We apply these techniques in two settings: We show that the parameter space Perd,4 of degree-d bicritical maps with a marked 4-periodic critical point is a d2-punctured Riemann surface of genus (d−1)(d−2)2. We also recover a result of Canci and Vishkautsan
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A Computational View on the Non-degeneracy Invariant for Enriques Surfaces Exp. Math. (IF 0.5) Pub Date : 2022-08-29 Riccardo Moschetti, Franco Rota, Luca Schaffler
Abstract For an Enriques surface S, the non-degeneracy invariant nd(S) retains information on the elliptic fibrations of S and its polarizations. In the current paper, we introduce a combinatorial version of the non-degeneracy invariant which depends on S together with a configuration of smooth rational curves, and gives a lower bound for nd(S). We provide a SageMath code that computes this combinatorial
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Systolic Geometry of Translation Surfaces Exp. Math. (IF 0.5) Pub Date : 2022-08-18 Tobias Columbus, Frank Herrlich, Bjoern Muetzel, Gabriela Weitze-Schmithüsen
Abstract In this paper we investigate the systolic landscape of translation surfaces for fixed genus and fixed angles of their cone points. We furthermore study how the systoles of a translation surface relate to the systoles of its graph of saddle connections. This allows us to develop an algorithm to compute the systolic ratio of origamis in the stratum H(1,1). We compute the maximal systolic ratio
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Algebraic Number Starscapes Exp. Math. (IF 0.5) Pub Date : 2022-08-01 Edmund Harriss, Katherine E. Stange, Steve Trettel
Abstract We study the geometry of algebraic numbers in the complex plane, and their Diophantine approximation, aided by extensive computer visualization. Motivated by the resulting images, which we have called algebraic starscapes, we describe the geometry of the map from the coefficient space of polynomials to the root space, focusing on the quadratic and cubic cases. The geometry describes and explains
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On Projective Evolutes of Polygons Exp. Math. (IF 0.5) Pub Date : 2022-07-28 Maxim Arnold, Richard Evan Schwartz, Serge Tabachnikov
Abstract The evolute of a curve is the envelope of its normals. In this note we consider a projectively natural discrete analog of this construction: we define projective perpendicular bisectors of the sides of a polygon in the projective plane, and study the map that sends a polygon to the new polygon formed by the projective perpendicular bisectors of its sides. We consider this map acting on the
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Representations of Deligne-Mostow lattices into Exp. Math. (IF 0.5) Pub Date : 2022-07-07 E. Falbel, I. Pasquinelli, A. Ucan-Puc
ABSTRACT We classify representations of a class of Deligne-Mostow lattices into PGL(3,C). In particular, we show local rigidity for the representations (of Deligne-Mostow lattices with three-fold symmetry and of type one) where the generators we chose are of the same type as the generators of Deligne-Mostow lattices. We also show local rigidity without constraints on the type of generators for six
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Universality of Nodal Count Distribution in Large Metric Graphs Exp. Math. (IF 0.5) Pub Date : 2022-07-04 Lior Alon, Ram Band, Gregory Berkolaiko
Abstract An eigenfunction of the Laplacian on a metric (quantum) graph has an excess number of zeros due to the graph’s non-trivial topology. This number, called the nodal surplus, is an integer between 0 and the graph’s first Betti number β. We study the distribution of the nodal surplus values in the countably infinite set of the graph’s eigenfunctions. We conjecture that this distribution converges
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Ray-Marching Thurston Geometries Exp. Math. (IF 0.5) Pub Date : 2022-06-25 Rémi Coulon, Elisabetta A. Matsumoto, Henry Segerman, Steve J. Trettel
Abstract We describe algorithms that produce accurate real-time interactive in-space views of the eight Thurston geometries using ray-marching. We give a theoretical framework for our algorithms, independent of the geometry involved. In addition to scenes within a geometry X, we also consider scenes within quotient manifolds and orbifolds X/Γ. We adapt the Phong lighting model to non-euclidean geometries
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Foreword to: Special Issue on Interactive Theorem Provers Exp. Math. (IF 0.5) Pub Date : 2022-06-25 Alex Kontorovich
Published in Experimental Mathematics (Vol. 31, No. 2, 2022)
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Multiple Extremal Disc-Packings in Compact Hyperbolic Surfaces Exp. Math. (IF 0.5) Pub Date : 2022-06-08 Ernesto Girondo, Cristian Reyes
Abstract The radius of a packing of metric discs embedded in a compact hyperbolic surface is bounded by an extremal value dependent upon the topology of the surface and the number of discs in the packing. In this paper we discuss the possibility of finding multiple extremal disc-packings within a given surface, determining the combinatorial-arithmetic conditions on the topology of the surface and the
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Density of Binary Disc Packings: Lower and Upper Bounds Exp. Math. (IF 0.5) Pub Date : 2022-05-19 Thomas Fernique
Abstract We provide, for any r∈(0,1), lower and upper bounds on the maximal density of a packing in the Euclidean plane of discs of radius 1 and r. The lower bounds are mostly folk, but the upper bounds improve the best previously known ones for any r∈[0.11,0.74]. For many values of r, this gives a fairly good idea of the exact maximum density. In particular, we get new intervals for r which does not
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Discrete Dynamical Systems From Real Valued Mutation Exp. Math. (IF 0.5) Pub Date : 2022-05-12 John Machacek, Nicholas Ovenhouse
Abstract We introduce a family of discrete dynamical systems which includes, and generalizes, the mutation dynamics of rank two cluster algebras. These systems exhibit behavior associated with integrability, namely preservation of a symplectic form, and in the tropical case, the existence of a conserved quantity. We show in certain cases that the orbits are unbounded. The tropical dynamics are related
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Large-Time Series Expansion of the Wave Front Length in the Euclidean Disk Exp. Math. (IF 0.5) Pub Date : 2022-05-09 Yves Colin de Verdière, David Vicente
Abstract In the paper [4 Vicente, D. (2020). Une goutte d’eau dans un bol. Quadrature 117. [Google Scholar]], the second author proves that the length |St| of the wave front St at time t of a wave propagating in an Euclidean disk D of radius 1, starting from a source q, admits a linear asymptotics as t→+∞: |St|=λ(q)t+o(t) with λ(q)=2arcsina and a=d(0,q). We will give a more direct proof and compute
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The Groups and Nilpotent Lie Rings of Order p8 with Maximal Class Exp. Math. (IF 0.5) Pub Date : 2022-05-02 Seungjai Lee, Michael Vaughan-Lee
Abstract We classify and count the nilpotent Lie rings of order p8 with maximal class for p≥5. This also provides a classification of the groups of order p8 with maximal class for p≥11 via the Lazard correspondence. We also record the number of nilpotent Lie rings/groups of order pn with maximal class for n≤7 from currently known data and discuss its asymptotic behavior as n grows and its potential
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Real and Complex Multiplication on K3 Surfaces via Period Integration Exp. Math. (IF 0.5) Pub Date : 2022-05-02 Andreas-Stephan Elsenhans, Jörg Jahnel
Abstract We report on a new approach, as well as some related experiments, to construct families of K3 surfaces having real or complex multiplication. The approach is based on an explicit description of the transcendental part of the cohomology in a topological way, using topological tori. Fundamental ideas include considering the period space of marked K3 surfaces, determining the periods by numerical
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Recovery from Power Sums Exp. Math. (IF 0.5) Pub Date : 2022-04-23 Hana Melánová, Bernd Sturmfels, Rosa Winter
Abstract We study the problem of recovering a collection of n numbers from the evaluation of m power sums. This yields a system of polynomial equations, which can be underconstrained (m < n), square (m = n), or overconstrained (m > n). Fibers and images of power sum maps are explored in all three regimes, and in settings that range from complex and projective to real and positive. This involves surprising
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Simple Type Theory is not too Simple: Grothendieck’s Schemes Without Dependent Types Exp. Math. (IF 0.5) Pub Date : 2022-04-25 Anthony Bordg, Lawrence Paulson, Wenda Li
Abstract Church’s simple type theory is often deemed too simple for elaborate mathematical constructions. In particular, doubts were raised whether schemes could be formalized in this setting and a challenge was issued. Schemes are sophisticated mathematical objects in algebraic geometry introduced by Alexander Grothendieck in 1960. In this article we report on a successful formalization of schemes
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Real-Time Visualization in Anisotropic Geometries Exp. Math. (IF 0.5) Pub Date : 2022-04-06 Eryk Kopczyński, Dorota Celińska-Kopczyńska
Abstract We present novel methods for real-time native geodesic rendering of anisotropic geometries ℍ2×ℝ, S2×ℝ, Solv and similar geometries, Nil, twisted ℍ2×ℝ. We also include partial results for the Berger sphere and explain why such real-time rendering of this geometry is difficult. Current approaches are not applicable for rendering complex shapes in these geometries, such as traditional 3D models
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Algorithmic Symplectic Packing Exp. Math. (IF 0.5) Pub Date : 2022-03-31 Greta Fischer, Jean Gutt, Michael Jünger
Abstract In this article we explore a symplectic packing problem where the targets and domains are 2n-dimensional symplectic manifolds. We work in the context where the manifolds have first homology group equal to Zn, and we require the embeddings to induce isomorphisms between first homology groups. In this case, Miller Maley, Mastrangeli, and Traynor showed that the problem can be reduced to a combinatorial
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On the Special Identities of Gelfand–Dorfman Algebras Exp. Math. (IF 0.5) Pub Date : 2022-03-21 P. S. Kolesnikov, B. K. Sartayev
A Gelfand–Dorfman algebra (GD-algebra) is said to be special if it can be embedded into a differential Poisson algebra. In this paper, we prove that the class of all special GD-algebras is closed w...
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Effective Reconstruction of Generic Genus 5 Curves from their Theta Hyperplanes Exp. Math. (IF 0.5) Pub Date : 2022-03-10 David Lehavi
We effectively reconstruct the set of enveloping quadrics of a generic curve C of genus 5 from its theta hyperplanes; for a generic genus 5 curve C this data suffices to effectively reconstruct C. ...
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Positive Plücker tree certificates for non-realizability Exp. Math. (IF 0.5) Pub Date : 2022-01-24 Julian Pfeifle
We introduce a new method for finding a non-realizability certificate of a simplicial sphere Σ: we exhibit a monomial combination of classical 3-term Plücker relations that yields a sum of products...
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Periodic Representations and Approximations of p-adic Numbers Via Continued Fractions Exp. Math. (IF 0.5) Pub Date : 2021-12-30 Stefano Barbero, Umberto Cerruti, Nadir Murru
Continued fractions can be introduced in the field of p-adic numbers Qp , however currently there is not a standard algorithm as in R . Indeed, it is not known how to construct p-adic continued fra...
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diffstrata—A Sage Package for Calculations in the Tautological Ring of the Moduli Space of Abelian Differentials Exp. Math. (IF 0.5) Pub Date : 2021-12-30 Matteo Costantini, Martin Möller, Jonathan Zachhuber
Abstract The boundary of the multi-scale differential compactification of strata of abelian differentials admits an explicit combinatorial description. However, even for low-dimensional strata, the complexity of the boundary requires use of a computer. We give a description of the algorithms implemented in the SageMath package diffstrata to enumerate the boundary components and perform intersection
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Evidence of Random Matrix Corrections for the Large Deviations of Selberg’s Central Limit Theorem Exp. Math. (IF 0.5) Pub Date : 2021-12-20 E. Amzallag, L.-P. Arguin, E. Bailey, K. Hui, R. Rao
Selberg’s central limit theorem states that the values of log |ζ(1/2+iτ)|, where τ is a uniform random variable on [T,2T], are asymptotically distributed like a Gaussian random variable of mean 0 a...
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On Combinatorics of Voronoi Polytopes for Perturbations of the Dual Root Lattices Exp. Math. (IF 0.5) Pub Date : 2021-12-13 Alexey Garber
The Voronoi conjecture on parallelohedra claims that for every convex polytope P that tiles Euclidean d-dimensional space with translations there exists a d-dimensional lattice such that P and the ...
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Schwarzian Versus a Family of Moving Parabolic Points Exp. Math. (IF 0.5) Pub Date : 2021-12-11 Hans Henrik Rugh, Lei Tan, Fei Yang
In this article, the trajectories of meromorphic quadratic differentials whose coefficients are Schwarzian derivatives of rational maps are studied. We conjecture that the graphs consisting of the ...
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Heuristics for 2-class Towers of Cyclic Cubic Fields Exp. Math. (IF 0.5) Pub Date : 2021-12-11 Nigel Boston, Michael R. Bush
We consider the Galois group G2(K) of the maximal unramified 2-extension of K where K/Q is cyclic of degree 3. We also consider the group G2+(K) where ramification is allowed at infinity. In the sp...
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Arithmetic Conjectures Suggested by the Statistical Behavior of Modular Symbols Exp. Math. (IF 0.5) Pub Date : 2021-12-11 Barry Mazur, Karl Rubin
Suppose E is an elliptic curve over Q and χ is a Dirichlet character. We use statistical properties of modular symbols to estimate heuristically the probability that L(E,χ,1)=0 . Via the Birch and...
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Opers and Non-Abelian Hodge: Numerical Studies Exp. Math. (IF 0.5) Pub Date : 2021-11-30 David Dumas, Andrew Neitzke
We present numerical experiments that test the predictions of a conjecture of Gaiotto–Moore–Neitzke and Gaiotto concerning the monodromy map for opers, the non-Abelian Hodge correspondence, and the...