Tanush Shaska
Affiliations:
Algebraic and Arithmetic Geometry
Heights, weighted projective spaces, and rational points
sh-125: Arithmetic Statistics on the Moduli Space of Genus 2 Curves
sh-113: Faltings Heights and Weighted Heights, with A. Obus
sh-112: Stacky Heights and Zeta Functions of Weighted Hypersurfaces, with S. Salami
sh-104: A Canonical Database for Rational Points in the Moduli Space of Genus-Two Curves
sh-94: Arithmetic Sparsity and Cohomological Obstructions in WPS, Int. Journal of Number Theory
sh-91: Rational Points and Zeta Functions of Humbert Surfaces over F_q, NATO Sci. Peace Secur. Ser. D, Vol. 66, pg. 92-122
sh-90: Weighted Heights and GIT Heights, Jour. Algeb. Comb., 2026, no. 3, Paper 41
sh-87: Rational Points of Weighted Hypersurfaces over Finite Fields
2023-01: Vojta's Conjecture on Weighted Projective Varieties, Europ. Jour. Math., 11, 12 (2025)
2022-1: Local and Global Heights on Weighted Projective Varieties, Houston J. Math., Vol. 49, no. 3 (2023), pg. 603-636
2019-1: Weighted Greatest Common Divisors and Weighted Heights, J. Number Theory, 213 (2020), pg. 319-346
2018-4: Computing Heights on Weighted Projective Spaces, Contemporary Math., 724 (2019), pg. 149-160
2016-5: Rational Points in the Moduli Space of Genus Two, Contemp. Math., 703 (2018), pg. 83-115
2014-1: Heights on Algebraic Curves, NATO Sci. Peace Secur. Ser. D, 41 (2015), pg. 137-175
2010-1: The Arithmetic of Genus Two Curves, NATO Sci. Peace Secur. Ser. D, 29 (2011), pg. 59-98
Curves, moduli, and automorphisms
sh-128: Tropical Formula for L_n Loci
sh-127: Hurwitz Spaces, Nielsen Classes, and Projective Degrees
sh-117: The Tropical Moduli Space of Degree-3 Rational Maps, with M. Siadat
sh-116: Shioda Surfaces
2024-01: Equations for Generalized Superelliptic Riemann Surfaces
2021-2: Arithmetic Inflection of Superelliptic Curves, Michigan Math. J., 75 (2025), no. 4, pg. 675-724
2020-1: Reduction of Superelliptic Riemann Surfaces, Contemporary Math., 776 (2022), pg. 227-247
2019-4: From Hyperelliptic to Superelliptic Curves, Albanian J. Math., 13 (2019), pg. 107-200
2019-3: Superelliptic Curves with Many Automorphisms and CM Jacobians, Math. Comp., 90 (2021), pg. 2951-2975
2018-6: On Automorphisms of Algebraic Curves, Contemporary Math., 724 (2019), pg. 175-212
2016-6: On Generalized Superelliptic Riemann Surfaces, Transformation Groups (2025)
2016-3: A Universal Genus-Two Curve from Siegel Modular Forms, SIGMA, 13 (2017), Paper No. 089
2016-1: On the Field of Moduli of Superelliptic Curves, Contemp. Math., 703 (2018), pg. 47-62
2015-4: Theta Functions of Superelliptic Curves, NATO Sci. Peace Secur. Ser. D, 41 (2015), pg. 47-69
2015-2: Weierstrass Points of Superelliptic Curves, NATO Sci. Peace Secur. Ser. D, 41 (2015), pg. 15-46
2015-1: The Case for Superelliptic Curves, NATO Sci. Peace Secur. Ser. D, 41 (2015), pg. 1-14
2014-2: Cyclic Curves over the Reals, NATO Sci. Peace Secur. Ser. D, 41 (2015), pg. 70-83
2013-7: Bielliptic Curves of Genus 3 in Hyperelliptic Moduli, Appl. Algebra Engrg. Comm. Comput., 24 (2013), pg. 387-412
2013-4: 2-Weierstrass Points of Genus 3 Hyperelliptic Curves with Extra Involutions, Comm. Algebra, 45 (2017), pg. 1879-1892
2012-1: Some Remarks on the Hyperelliptic Moduli of Genus 3, Comm. Algebra, 42 (2014), pg. 4110-4130
2011-2: On Superelliptic Curves of Level n and Their Quotients, Albanian J. Math., 5 (2011), pg. 115-137
2009-1: Theta Functions and Algebraic Curves with Automorphisms, with S. Wijesiri, NATO Sci. Peace Secur. Ser. D, 24 (2009), pg. 193-237
2008-3: Determining Equations of Families of Cyclic Curves, Albanian J. Math., 2 (2008), pg. 199-213
2007-3: Thetanulls of Cyclic Curves of Small Genus, Albanian J. Math., 1 (2007), pg. 253-270
2006-4: Subvarieties of the Hyperelliptic Moduli Determined by Group Actions, Serdica Math. J., 32 (2006), pg. 355-374
2005-3: Hyperelliptic Curves of Genus 3 with Prescribed Automorphism Group, Lecture Notes Ser. Comput., 13 (2005), pg. 109-123
2005-2: Hyperelliptic Curves with Reduced Automorphism Group A5, Appl. Algebra Engrg. Comm. Comput., 18 (2007), pg. 3-20
2003-3: Hyperelliptic Curves with Extra Involutions, LMS J. Comput. Math., 8 (2005), pg. 102-115
2003-2: Some Special Families of Hyperelliptic Curves, J. Algebra Appl., 3 (2004), pg. 75-89
2003-1: On the Generic Curve of Genus 3, Contemporary Math., 369 (2005)
2001-2: The Locus of Curves with Prescribed Automorphism Group, Surikaisekikenkyusho Kokyuroku (2002), pg. 112-141
Jacobians, abelian varieties, coverings, and isogenies
sh-98: Hitchin Spinors and Genus 2 Curves, with A. Clingher and A. Malmendier
sh-93: Isogenies, Kummer Surfaces, and Theta Functions, NATO Sci. Peace Secur. Ser. D, Vol. 66, pg. 1-55
2021-1: Geometry of Prym Varieties for Certain Bielliptic Curves of Genus Three and Five, Pure Appl. Math. Q., 17 (2021), pg. 1739-1784
2019-5: The Addition on Jacobian Varieties from a Geometric Viewpoint
2019-2: On Isogenies Among Certain Abelian Surfaces, Michigan Math. J., 71 (2022), pg. 227-269
2017-2: Isogenous Components of Jacobian Surfaces, Europ. Jour. Math., Vol. 6 (2020), pg. 1276-1302
2013-3: Decomposition of Some Jacobian Varieties of Dimension 3, Lect. Notes in Comp. Sci., vol 8884, Springer
2013-1: On Jacobians of Curves with Superelliptic Components, Contemp. Math., 629 (2014), pg. 1-14
2012-2: Genus Two Curves with Many Elliptic Subcovers, Comm. Algebra, 44 (2016), pg. 4450-4466
2008-4: Degree Even Coverings of Elliptic Curves by Genus 2 Curves, Albanian J. Math., 2 (2008), pg. 241-248
2008-1: Degree 4 Coverings of Elliptic Curves by Genus 2 Curves, Albanian J. Math., 2 (2008), pg. 307-318
2005-1: Genus 2 Curves That Admit a Degree 5 Map to an Elliptic Curve, Forum Math., 21 (2009), pg. 547-566
2004-2: Genus Two Curves Covering Elliptic Curves: A Computational Approach, Lecture Notes Ser. Comput., 13 (2005), pg. 206-231
2002-1: Genus 2 Curves with (3,3)-Split Jacobian and Large Automorphism Group, Lecture Notes in Comput. Sci., 2369, Springer (2002), pg. 205-218
2001-1: Genus 2 Fields with Degree 3 Elliptic Subfields, Forum Math., 16 (2004), pg. 263-280
2001-0: Curves of Genus Two Covering Elliptic Curves, Ph.D. Thesis, University of Florida (2001)
2000-2: Elliptic Subfields and Automorphisms of Genus 2 Function Fields, Springer (2004), pg. 703-723
2000-1: Curves of Genus 2 with (n,n)-Decomposable Jacobians, J. Symbolic Comput., 31 (2001), pg. 603-617
Mathematical physics and string dualities
2018-3: Six Line Configurations and String Dualities, with A. Clingher and A. Malmendier, Comm. Math. Phys., 371 (2019), pg. 159-196
2016-4: The Satake Sextic in F-Theory, J. Geom. Phys., 120 (2017), pg. 290-305
2. Artificial Intelligence and Machine Learning
Graded architectures
sh-130: Toward Reasoning
sh-126: A Linear-Logical Semantics of Graded Neural Networks, with V. de Paiva
sh-121: ReLU Networks via Tropical Geometry, with M. Siadat
sh-120: Graded Algebraic Neural Networks, with L. Carbone and E. Jurisich
sh-119: Graded Transformers with Sigma-Pi
sh-114: Morphological Hierarchies for Graded Transformers in Low-Resource NLP
sh-111: Internalizing Tools as Morphisms in Graded Transformers
sh-109: Hierarchical Grading in Large Language Models
sh-108: Topological Learning in Weighted Spaces
sh-97: Geometric Learning and Finsler Metrics in Weighted Projective Spaces, Advances in Pure and Applied Mathematics
sh-95: Graded Transformers: A Symbolic-Geometric Approach to Structured Learning, AI in Mathematics and Theoretical Physics (2026)
sh-89: Graded Neural Networks, Int. J. Data Sci. Math. Sci. (2025), no. 2, pg. 87-116
2024-02: Artificial Neural Networks on Graded Vector Spaces, Contemporary Math., Vol. 835 (2026), pg. 1-72
Neurosymbolic methods and applications
sh-99: Categorical Hypergraph Models for Distributed Data Fabrics, with I. Kostireas, Springer Optimization and Its Applications
sh-86: Neuro-Symbolic Learning for Irreducible Sextics: Unveiling Probabilistic Trends in Polynomials
sh-85: Galois Groups of Quintics: A Neurosymbolic Approach to Polynomial Classification
2024-06: A Neurosymbolic Framework for Geometric Reduction of Binary Forms, Contemporary Math., Vol. 835 (2026), pg. 173-194
2024-05: Polynomials, Galois Groups, and Database-Driven Arithmetic, Contemporary Math., Vol. 835 (2026), pg. 231-305
2024-03: Machine Learning for M_2 and an Application to Isogeny Based Cryptography, Jour. Alg. Comb., 61, 23 (2025)
3. Computational and Symbolic Algebra
sh-123: Elimination Theory in Graded Rings
2024-04: Rational Functions on the Projective Line from a Computational Viewpoint
2018-2: On the Discriminant of Certain Quadrinomials, Contemporary Math., 724 (2019), pg. 55-72
2017-3: Some Remarks on the Non-Real Roots of Polynomials, Cubo, 20 (2018), pg. 67-93
2017-1: Reduction of Binary Forms via the Hyperbolic Centroid, Lobachevskii J. Math., 42 (2021), pg. 84-95
2007-4: Some Open Problems in Computational Algebraic Geometry, Albanian J. Math., 1 (2007), pg. 297-319
2005-4: A Maple Package for Hyperelliptic Curves, with S. Zheng (2005), pg. 399-408
2004-3: Invariants of Binary Forms, with V. Krishnamoorthy, Dev. Math., 12, Springer (2005), pg. 101-122
2004-1: Galois Groups of Prime Degree Polynomials with Nonreal Roots, Lecture Notes Ser. Comput., 13 (2005), pg. 243-255
2003-4: Computational Algebra and Algebraic Curves, SIGSAM Bull., 37 (2003), pg. 117-124
2002-3: Determining the Automorphism Group of a Hyperelliptic Curve, ISSAC 2003 Proceedings, ACM, pg. 248-254
2002-2: Computational Aspects of Hyperelliptic Curves, Lecture Notes Ser. Comput., 10 (2003), pg. 248-257
4. Coding Theory and Cryptography
sh-118: Group Theoretic Approach to Binary Sequences and Correlations, with I. Kostireas
sh-110: Graded Noise and Weighted Projective Geometry in Fully Homomorphic Encryption
sh-107: Graded Quantum Codes, Master Thesis, Computer Science and Engineering, Oakland University (2026)
sh-102: Quantum Weighted Algebraic Codes, Designs, Codes, and Cryptography (2026)
2018-1: Curves, Jacobians, and Cryptography, Contemporary Math., 724 (2019), pg. 279-344
2017-4: Coding Theory, Handbook of Discrete and Combinatorial Mathematics
2016-2: Self-Inversive Polynomials, Curves, and Codes, Contemp. Math., 703 (2018), pg. 189-208
2015-3: Weight Distributions, Zeta Functions and Riemann Hypothesis for Linear and Algebraic Geometry Codes, Albanian J. Math., 41 (2015), pg. 328-359
2013-2: Theta Functions and Symmetric Weight Enumerators for Codes over Imaginary Quadratic Fields, Designs, Codes and Cryptography, 76 (2015), pg. 217-235
2011-1: Quantum Codes from Superelliptic Curves, Albanian J. Math., 5 (2011), pg. 175-191
2008-5: On Some Applications of Graphs to Cryptography and Turbocoding, with V. Ustimenko, Albanian J. Math., 2 (2008), pg. 249-255
2008-2: On the Homogeneous Algebraic Graphs of Large Girth and Their Applications, Linear Algebra Appl., 430 (2009), pg. 1826-1837
2007-5: Quantum Codes from Algebraic Curves with Automorphisms, Condensed Matter Physics, Vol. 11, No. 2 (2008), pg. 383-396
2007-2: Codes over Rings of Size p^2 and Lattices over Imaginary Quadratic Fields, Finite Fields Appl., 16 (2010), pg. 75-87
2006-3: Codes over F_{p^2} and F_p x F_p, Lattices, and Theta Functions, Ser. Coding Theory Cryptol., 3 (2007), pg. 70-80
2006-2: Codes over Rings of Size Four, Hermitian Lattices, and Corresponding Theta Functions, Proc. Amer. Math. Soc., 136 (2008), pg. 849-857
2006-1: On the Automorphism Groups of Some AG-Codes Based on C_{a,b} Curves, Serdica J. Comput., 1 (2007), pg. 193-206