RISAT - Papers

T. Shaska: a timeline of my mathematical journey.

Preprints, Papers, Notes

1. 1. 2025-8: Computing Weierstrass form of superelliptic curves
  2. 2025-7: Rational Points and Zeta Functions of Humbert Surfaces with Square Determinant over Finite Fields
  3. 2025-6: Weighted Heights and GIT Heights
  4. 2025-5: Graded Neural Networks (Neus 25)
  5. 2025-4: Optimization of Vector Functions Using the Max Norm (Notes)
  6. 2025-3: Rational points of weighted hypersurfaces over finite fields (in progress)
  7. 2025-2: Neuro-Symbolic Learning for Galois Groups: A Machine Learning Approach to Polynomial Solvability (submitted Neus)
  8. 2025-1: Galois groups of polynomials and neurosymbolic networks (submitted ISSAC)
  9. 2024-07: Irreducible sextics, invariants, and their Galois groups (Notes)
  10. 2024-06: A Neurosymbolic Framework for Geometric Reduction of Binary Forms, (submitted ISSAC)
  11. 2024-05: Polynomials, Galois groups, and Deep Learning, Contemporary Math. 2025
  12. 2024-04: Rational Functions on the Projective Line from a Computational Viewpoint, E. Badr, E. Shaska, T. Shaska
  13. 2024-03: Machine learning for moduli space of genus two curves and an application to isogeny based cryptography,
    Journal of Algebr Comb 61, 23 (2025).
  14. 2024-02: Artificial neural networks on graded vector spaces Contemporary Math. 2025
  15. 2024-01: Equations for generalized superelliptic Riemann surfaces
  16. 2023-01: Vojta's conjecture on weighted projective varieties,
    European Journal of Mathematics, 11, 12 (2025). https://doi.org/10.1007/s40879-024-00804-7
  17. 2022-1: Local and global heights on weighted projective varieties, S. Salami, T. Shaska;
    Houston J. Math. Vol. 49, #3, (2023), pg. 603-636
  18. 2021-2: Arithmetic inflection of superelliptic curves, E Cotterill, I Darago, C. G López, C Han, T Shaska,
    Michigan J. Math.
  19. 2021-1: Geometry of Prym varieties for certain bielliptic curves of genus three and five,
    Pure Appl. Math. Q. 17 1739--1784 (2021) https://doi.org/10.4310/PAMQ.2021.v17.n5.a5
  20. 2020-1: Reduction of superelliptic Riemann surfaces, Contemporary Math. 776 227--247 (2022) https://doi.org/10.1090/conm/776/15614
  21. 2020-i: Integrable systems: a celebration of Emma Previato's 65th birthday, Donagi/Shaska, 458,1--12 (2020)
  22. 2020-ii: Algebraic geometry: a celebration of Emma Previato's 65th birthday, Donagi/Shaska, 1--12 (2020)
  23. 2019-5: The addition on Jacobian varieties from a geometric viewpoint, Y. Kopeliovich, T. Shaska https://arxiv.org/abs/1907.11070
  24. 2019-4: From hyperelliptic to superelliptic curves, A. Malmendier and T. Shaska;
    Albanian J. Math. 13 107--200 (2019)
  25. 2019-3: Superelliptic curves with many automorphisms and CM Jacobians, A. Obus and T. Shaska
    Math. Comp. 90 2951--2975 (2021) https://doi.org/10.1090/mcom/3639
  26. 2019-2: On isogenies among certain abelian surfaces, A. Clingher, A. Malmendier, T. Shaska,
    Mich. Math. J. 71 227--269 (2022) https://doi.org/10.1307/mmj/20195790
  27. 2019-1: Weighted greatest common divisors and weighted heights,
    J. Number Theory 213 319--346 (2020) https://doi.org/10.1016/j.jnt.2019.12.012
  28. 2018-6: On automorphisms of algebraic curves, Contemporary Math. 724 175--212 (2019) https://doi.org/10.1090/conm/724/14590
  29. 2018-5: Kay Magaard (1962--2018), Gerhard Hiss and Tony Shaska
    Albanian J. Math. 12 33--35 (2018) https://albanian-j-math.com/archives/2018-05.pdf
  30. 2018-4: Computing heights on weighted projective spaces, J. Mandili, T. Shaska
    Contemporary Math. 724 149--160 (2019) https://doi.org/10.1090/conm/724/14588
  31. 2018-3: Six line configurations and string dualities, A.Clingher, A.Malmendier, T. Shaska,
    Comm. Math. Phys. 371 159--196 (2019) https://doi.org/10.1007/s00220-019-03372-0
  32. 2018-2: On the discriminant of certain quadrinomials, Sh. Otake, T. Shaska,
    Contemporary Math. 724 55--72 (2019) https://doi.org/10.1090/conm/724/14585
  33. 2018-1: Curves, Jacobians, and cryptography, G. Frey, T. Shaska
    Contemporary Math. 724 279--344 (2019) https://doi.org/10.1090/conm/724/14596
  34. 2017-4: Coing Theory, Alfred J. Menezes, Paul C. van Oorschot, David Joyner, Tony Shaska, Douglas R. Shier, Wayne Goddard,
    Chapter to Handbook of Discrete and Combinatorial Mathematics
  35. 2017-3: Some remarks on the non-real roots of polynomials, Sh. Otake, T. Shaska,
    Cubo 20 67--93 (2018)
  36. 2017-2: Isogenous components of Jacobian surfaces, L. Beshaj, A. Elezi, T. Shaska,
    Eur. J. Math. 6 1276--1302 (2020) https://doi.org/10.1007/s40879-019-00375-y
  37. 2017-1: Reduction of binary forms via the hyperbolic centroid, A. Elezi, T. Shaska,
    Lobachevskii J. Math. 42 84--95 (2021) https://doi.org/10.1134/s199508022101011x
  38. 2016-6: On generalized superelliptic Riemann surfaces, R. Hidalgo, S. Quispe, T. Shaska
    Transformation Groups (2025) https://arxiv.org/abs/1609.09576
  39. 2016-5: Rational points in the moduli space of genus two, Contemp. Math., 703, 83--115 (2018) https://doi.org/10.1090/conm/703/14132
  40. 2016-4: The Satake sextic in F-theory, A. Malmendier, T. Shaska,
    J. Geom. Phys. 120 290--305 (2017) https://doi.org/10.1016/j.geomphys.2017.06.010
  41. 2016-3: A universal genus-two curve from Siegel modular forms, A. Malmendier, T. Shaska;
    SIGMA Symmetry Integrability Geom. Methods Appl. 13 Paper No. 089, 17 (2017) https://doi.org/10.3842/SIGMA.2017.089
  42. 2016-2: Self-inversive polynomials, curves, and codes, D. Joyner, T. Shaska, Contemp. Math., 703, AMS, 2018, 189–208. https://doi.org/10.1090/conm/703/14138
  43. 2016-1: On the field of moduli of superelliptic curves, R. Hidalgo, T. Shaska, Contemp. Math., 703, AMS, 2018, 47–62. https://doi.org/10.1090/conm/703/14130
  44. 2015-4: Theta functions of superelliptic curves, NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., 41, IOS Press, Amsterdam, 2015, 47–69.
  45. 2015-3: Weight distributions, zeta functions and Riemann hypothesis for linear and algebraic geometry codes, A. Elezi, T. Shaska, 41 328--359 (2015)
  46. 2015-2: Weierstrass points of superelliptic curves, C. Shor, T. Shaska, NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., 41, IOS Press, Amsterdam, 2015, 15–46.
  47. 2015-1: The case for superelliptic curvesL. Beshaj, T. Shaska, E. Zhupa, NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., 41, IOS Press, Amsterdam, 2015, 1–14.
  48. 2014-2: Cyclic curves over the reals, M. Izquierdo, T. Shaska, NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., 41, IOS Press, Amsterdam, 2015, 70–83.
  49. 2014-1: Heights on algebraic curves, T. Shaska, L. Beshaj, NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., 41, IOS Press, Amsterdam, 2015, 137–175.
  50. 2013-7: Bielliptic curves of genus 3 in hyperelliptic moduli,
    Appl. Algebra Engrg. Comm. Comput. 24 387--412 (2013) https://doi.org/10.1007/s00200-013-0209-9
  51. 2013-4: 2-Weierstrass points of genus 3 hyperelliptic curves with extra involutions,
    Comm. Algebra, 45 1879--1892 (2017). https://doi.org/10.1080/00927872.2016.1226861
  52. 2013-2: Theta functions and symmetric weight enumerators for codes over imaginary quadratic fields, T. Shaska, C. Shor,
    Des. Codes Cryptogr. 76 217--235 (2015) https://doi.org/10.1007/s10623-014-9943-7
  53. 2013-1: On Jacobians of curves with superelliptic components, L. Beshaj, T. Shaska, C. Shor,
    Contemp. Math., 629, American Mathematical Society, Providence, RI, 2014, 1–14. https://doi.org/10.1090/conm/629/12557
  54. 2013-i: Computational algebraic geometry and its applications, T. Shaska,
    Appl. Algebra Engrg. Comm. Comput. 24 309--311 (2013) https://doi.org/10.1007/s00200-013-0204-1
  55. 2013-ii: Computational algebraic geometry, T. Shaska,
    J. Symbolic Comput. 57 1--2 (2013) https://doi.org/10.1016/j.jsc.2013.05.001
  56. 2012-2: Genus two curves with many elliptic subcovers, T. Shaska;
    Comm. Algebra, 44 4450--4466 (2016) https://doi.org/10.1080/00927872.2015.1027365
  57. 2012-1: Some remarks on the hyperelliptic moduli of genus 3, T. Shaska;
    Comm. Algebra, 42 4110--4130 (2014) https://doi.org/10.1080/00927872.2013.791305
  58. 2011-2: On superelliptic curves of level $n$ and their quotients, L. Beshaj, V. Hoxha, T. Shaska, Albanian J. Math. 5 115--137 (2011)
  59. 2011-1: Quantum codes from superelliptic curves, A. Elezi, T. Shaska, Albanian J. Math. 5 175--191 (2011)
  60. 2010-1: The arithmetic of genus two curves, T. Shaska, L. Beshaj, NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., 29, IOS Press, Amsterdam, 2011, 59–98.
  61. 2009-1: Theta functions and algebraic curves with automorphisms, T. Shaska, S. Wijesiri, NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., 24, IOS Press, Amsterdam, 2009, 193–237.
  62. 2008-5: On some applications of graphs to cryptography and turbocoding, T. Shaska, V. Ustimenko; Albanian J. Math. 2 249--255 (2008)
  63. 2008-4: Degree even coverings of elliptic curves by genus 2 curves, N. Pjero, M. Ramasaco, T. Shaska; Albanian J. Math. 2 241--248 (2008)
  64. 2008-3: Determining equations of families of cyclic curves, R. Sanjeewa, T. Shaska, Albanian J. Math. 2 199--213 (2008)
  65. 2008-2: On the homogeneous algebraic graphs of large girth and their applications, T. Shaska, V. Ustimenko;
    Linear Algebra Appl. 430 1826--1837 (2009) https://doi.org/10.1016/j.laa.2008.08.023
  66. 2008-1: Degree 4 coverings of elliptic curves by genus 2 curves, T. Shaska, S. Wijesiri, S. Wolf, L. Woodland, Albanian J. Math. 2 307--318 (2008)
  67. 2007-4: Some open problems in computational algebraic geometry, T. Shaska; Albanian J. Math. 1 297--319 (2007)
  68. 2007-3: Thetanulls of cyclic curves of small genus, E. Previato, T. Shaska, S. Wijesiri; Albanian J. Math. 1 253--270 (2007)
  69. 2007-2: Codes over rings of size {$p^2$} and lattices over imaginary quadratic fields, T. Shaska, C. Shor, S. Wijesiri,
    Finite Fields Appl. 16 75--87 (2010) https://doi.org/10.1016/j.ffa.2010.01.005
  70. 2006-4: Subvarieties of the hyperelliptic moduli determined by group actions,
    Serdica Math. J. 32 355--374 (2006)
  71. 2006-3: Codes over F_{p^2} and F_pxF_p, lattices, and theta functions, T. Shaska, C. Shor,
    Ser. Coding Theory Cryptol., 3, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2007, 70–80. https://doi.org/10.1142/9789812772022%5C_0005
  72. 2006-2: Codes over rings of size four, Hermitian lattices, and corresponding theta functions, T. Shaska, S. Wijesiri,
    Proc. Amer. Math. Soc. 136 849--857 (2008) https://doi.org/10.1090/S0002-9939-07-09152-6
  73. 2006-1: On the automorphism groups of some AG-codes based on $C_{a,b}$ curves, T. Shaska, Q. Wang,
    Serdica J. Comput. 1 193--206 (2007)
  74. 2005-4: A Maple package for hyperelliptic curves, T. Shaska, S. Zheng, 399--408 (2005)
  75. 2005-3: Hyperelliptic curves of genus 3 with prescribed automorphism group, J. Gutierrez, D. Sevilla, T. Shaska,
    Lecture Notes Ser. Comput., 13, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005, 109–123. https://doi.org/10.1142/9789812701640%5C_0009
  76. 2005-2: Hyperelliptic curves with reduced automorphism group $A_5$, D. Sevilla, T. Shaska,
    Appl. Algebra Engrg. Comm. Comput. 18 3--20 (2007) https://doi.org/10.1007/s00200-006-0030-9
  77. 2005-1: Genus 2 curves that admit a degree 5 map to an elliptic curve, K. Magaard, T. Shaska, H. Volklein,
    Forum Math. 21 547--566 (2009) https://doi.org/10.1515/FORUM.2009.027
  78. 2004-3: Invariants of binary forms, V. Krishnamoorthy, T. Shaska, H. Volklein,
    Dev. Math., 12, Springer, New York, 2005, 101–122.
  79. 2004-2: Genus two curves covering elliptic curves: a computational approach,
    Lecture Notes Ser. Comput., 13, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005, 206–231.
  80. 2004-1: Galois groups of prime degree polynomials with nonreal roots, A. Bialostocki, T. Shaska,
    Lecture Notes Ser. Comput., 13, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005, 243–255.
  81. 2003-4: Computational algebra and algebraic curves,
    SIGSAM Bull. 37, 117--124 (2003) https://doi.org/10.1145/968708.968713
  82. 2003-3: Hyperelliptic curves with extra involutions, J. Gutierrez, T. Shaska,
    LMS J. Comput. Math. 8 102--115 (2005) https://doi.org/10.1112/S1461157000000917
  83. 2003-2: Some special families of hyperelliptic curves, T. Shaska,
    J. Algebra Appl. 3 75--89 (2004) https://doi.org/10.1142/S0219498804000745
  84. 2003-1: On the generic curve of genus 3, T. Shaska, J. Thompson,
    Contemp. Math., Contemporary Math., 369, AMS, Providence, RI, 2005 https://doi.org/10.1090/conm/369/06814
  85. 2002-3: Determining the automorphism group of a hyperelliptic curve, (ISSAC 2003)
    Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation, 248–254. (ACM), 2003 https://doi.org/10.1145/860854.860904
  86. 2002-2: Computational aspects of hyperelliptic curves, Lecture Notes Ser. Comput., 10, World Scientific Publishing Co., Inc., River Edge, NJ, 2003, 248–257.
  87. 2002-1: Genus 2 curves with (3,3)-split Jacobian and large automorphism group, (ANTS 2003)
    Lecture Notes in Comput. Sci., 2369, Springer-Verlag, Berlin, 2002, 205–218. https://doi.org/10.1007/3-540-45455-1%5C_17 math/0201008
  88. 2001-2: The locus of curves with prescribed automorphism group, K. Magaard, T. Shaska, S. Shpectorov, H. Volklein,
    Sürikaisekikenkyüsho K\B{o}kyüroku 112--141 (2002) math/0205314
  89. 2001-1: Genus 2 fields with degree 3 elliptic subfields,
    Forum Math. 16 263--280 (2004) https://doi.org/10.1515/form.2004.013 math/0109155
  90. 2001-0: Curves of genus two covering elliptic curves,
    Thesis (Ph.D.)--University of Florida pg.72 (2001).
  91. 2000-2: Elliptic subfields and automorphisms of genus 2 function fields, T. Shaska, H. Volklein;
    Algebra, arithmetic and geometry with applications (Abhyankar's 70th birthday), West Lafayette, IN, 2000, 703–723, Springer-Verlag, Berlin, (2004) math/0107142
  92. 2000-1: Curves of genus 2 with (n,n)-decomposable Jacobians,
    J. Symbolic Comput. 31, 603--617, (2001). https://doi.org/10.1006/jsco.2001.0439 math/0312285