T. Shaska: a timeline of my mathematical journey.

Papers and preprints

In progress

1. Homomorphic encryption over graded rings

2025

2. 2025-06: Galois Groups and Machine Learning, J. Mezinaj, T. Shaska

3. 2025-05: Computing (n,n)-isogenies on Abelian surfaces

4. 2025-04: Weighted varieties defined over finite fields

5. 2025-03: Automorphisms of rational functions, E. Badr, T. Shaska

6. 2025-02: Geometry of Weighted Projective Space and Machine Learning

7. 2025-01: Isogeny based cryptography on Abelian surfaces

2024

8. 2024-06: Reduction of binary forms, Julia invariant, and machine learning, I Kotsireas, T. Shaska

9. 2024-05: Polynomials, Galois groups,  and Machine Learning

10. 2024-04: Exploring Rational Functions on the Projective Line through Machine Learning Techniques, E. Badr, E. Shaska, T. Shaska

11. 2024-03: Machine learning for moduli space of genus two curves and an application to isogeny based cryptography, E. Shaska and T. Shaska, 
    Journal of Algebraic Combinatorics (submitted),   https://arxiv.org/abs/2403.17250

12. 2024-02: Artificial neural networks on graded vector spaces,   https://arxiv.org/abs/2407.19031

13. 2024-01: Equations for generalized superelliptic Riemann surfaces, R. Hidalgo, S. Quispe, T. Shaska

2023

14. 2023-01: Vojta's conjecture on weighted projective varieties, S. Salami, T. Shaska,
    https://www.risat.org/pdf/2023-1.pdf

2022

15. 2022-1: Local and global heights on weighted projective varieties, S. Salami, T. Shaska, Houston J. Math. Vol. 49, #3, (2023), pg. 603-636
    https://www.risat.org/pdf/2022-1.pdf

2021

16. 2021-2: Arithmetic inflection of superelliptic curves,  E Cotterill, I Darago, C. G López, C Han, T Shaska,
    Michigan J. Math.  https://www.risat.org/pdf/2021-2.pdf

17. 2021-1: Geometry of Prym varieties for certain bielliptic curves of genus three and five,
    A.Clingher, A.Malmendier, T.Shaska,
    Pure Appl. Math. Q.  17  1739--1784  (2021)
    https://doi.org/10.4310/PAMQ.2021.v17.n5.a5  https://www.risat.org/pdf/2021-1.pdf

2020

18. 2020-1: Reduction of superelliptic Riemann surfaces, T. Shaska,776  227--247  (2022)
    https://doi.org/10.1090/conm/776/15614  https://www.risat.org/pdf/2020-1.pdf

19. 2020-i: Integrable systems: a celebration of Emma Previato's 65th birthday Donagi/Shaska, 458,1--12  (2020)
    https://www.risat.org/pdf/2020-i.pdf

20. 2020-ii: Algebraic geometry: a celebration of Emma Previato's 65th birthday, Donagi/Shaska,  1--12  (2020)
    https://www.risat.org/pdf/2020-ii.pdf

2019

21. 2019-5: The addition on Jacobian varieties from a geometric viewpoint,
    Y. Kopeliovich, T. Shaska 
    https://arxiv.org/abs/1907.11070

22. 2019-4: From hyperelliptic to superelliptic curves,
    A. Malmendier, T. Shaska, Albanian J. Math.  13  107--200  (2019)
    https://albanian-j-math.com/archives/2019-03.pdf

23. 2019-3:  Superelliptic curves with many automorphisms and CM Jacobians,
    Andrew Obus and Tanush Shaska,
    Math. Comp.  90  2951--2975  (2021)
    https://doi.org/10.1090/mcom/3639  https://www.risat.org/pdf/2019-3.pdf

24. 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  https://www.risat.org/pdf/2019-2.pdf

25. 2019-1:  Weighted greatest common divisors and weighted heights, Beshaj, L., Gutierrez, J., and Shaska, T.,
    J. Number Theory  213  319--346  (2020)
    https://doi.org/10.1016/j.jnt.2019.12.012  https://www.risat.org/pdf/2019-1.pdf

2018

26. 2018-6: On automorphisms of algebraic curves,
    A. Broughton, T. Shaska, A. Wootton, Contemporary Math. 724  175--212  (2019)
    https://doi.org/10.1090/conm/724/14590  https://www.risat.org/pdf/2018-6.pdf

27. 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

28. 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   https://www.risat.org/pdf/2018-4.pdf

29. 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   https://www.risat.org/pdf/2018-3.pdf

30. 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   https://www.risat.org/pdf/2018-2.pdf

31. 2018-1: Curves, Jacobians, and cryptography,
    G. Frey, T. Shaska, Contemporary Math. 724  279--344  (2019)
    https://doi.org/10.1090/conm/724/14596   https://www.risat.org/pdf/2018-1.pdf

2017

32. 2017-3: Some remarks on the non-real roots of polynomials,
    Sh. Otake, T. Shaska, Cubo  20  67--93  (2018)
    https://www.risat.org/pdf/2017-5.pdf

33. 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   https://www.risat.org/pdf/2017-3.pdf

34. 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   https://www.risat.org/pdf/2017-1.pdf

2016

35. 2016-6: On generalized superelliptic Riemann surfaces,
    R. Hidalgo, S. Quispe, T. Shaska
    https://arxiv.org/abs/1609.09576

36. 2016-5: Rational points in the moduli space of genus two,
    L. Beshaj, R. Hidalgo, S. Kruk, A. Malmendier, S. Quispe, T. Shaska, Contemp. Math., 703, 83--115  (2018)
    https://doi.org/10.1090/conm/703/14132   https://www.risat.org/pdf/2016-5.pdf

37. 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   https://www.risat.org/pdf/2016-4.pdf

38. 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   https://www.risat.org/pdf/2016-3.pdf

39. 2016-2: Self-inversive polynomials, curves, and codes,
    D. Joyner, T. Shaska, Contemp. Math., 703, American Mathematical Society, [Providence], RI, 2018, 189–208.
    https://doi.org/10.1090/conm/703/14138   https://www.risat.org/pdf/2016-2.pdf

40. 2016-1:  On the field of moduli of superelliptic curves,
    R. Hidalgo, T. Shaska, Contemp. Math., 703, American Mathematical Society, [Providence], RI, 2018, 47–62.
    https://doi.org/10.1090/conm/703/14130   https://www.risat.org/pdf/2016-1.pdf

2015

41. 2015-1: The case for superelliptic curves
    L. Beshaj, T. Shaska, E. Zhupa, NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., 41, IOS Press, Amsterdam, 2015, 1–14.
    https://www.risat.org/pdf/2015-1.pdf

42. 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.
    https://www.risat.org/pdf/2015-2.pdf

43. 2015-3: Weight distributions, zeta functions and Riemann hypothesis for linear and algebraic geometry codes,
    A. Elezi, T. Shaska, 41  328--359  (2015)
    https://www.risat.org/pdf/2015-3.pdf

44. 2015-4: Theta functions of superelliptic curves,
    L. Beshaj, A. Elezi, T. Shaska, NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., 41, IOS Press, Amsterdam, 2015, 47–69.
    https://www.risat.org/pdf/2015-4.pdf

2014

45. 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.
    https://www.risat.org/pdf/2014-3.pdf

46. 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.
    https://www.risat.org/pdf/2014-2.pdf

2013

47. 2013-7: Bielliptic curves of genus 3 in the hyperelliptic moduli
    T. Shaska, F. Thompson, Appl. Algebra Engrg. Comm. Comput.  24  387--412  (2013)
    https://doi.org/10.1007/s00200-013-0209-9   https://www.risat.org/pdf/2013-7.pdf

48. 2013-4: 2-{W}eierstrass points of genus 3 hyperelliptic curves with extra involutions,
    T. Shaska, C. Shor, Comm. Algebra  45  1879--1892  (2017).
    https://doi.org/10.1080/00927872.2016.1226861   https://www.risat.org/pdf/2013-4.pdf

49. 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   https://www.risat.org/pdf/2013-2.pdf

50. 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   https://www.risat.org/pdf/2013-1.pdf

51. 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

52. 2013-ii: Computational algebraic geometry,
    T. Shaska, J. Symbolic Comput.  57  1--2  (2013)
    https://doi.org/10.1016/j.jsc.2013.05.001

2012

53. 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

54. 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   https://www.risat.org/pdf/2012-1.pdf

2011

55. 2011-2: On superelliptic curves of level $n$ and their quotients,
    L. Beshaj, V. Hoxha, T. Shaska, Albanian J. Math.  5  115--137  (2011)
    https://albanian-j-math.com/archives/2011-12.pdf

56. 2011-1: Quantum codes from superelliptic curves,
    A. Elezi, T. Shaska, Albanian J. Math.  5  175--191  (2011)
    https://albanian-j-math.com/archives/2011-16.pdf

2010

57. 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.
    https://www.risat.org/pdf/2010-1.pdf

2009

58. 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.
    https://www.risat.org/pdf/2009-1.pdf

2008

59. 2008-5: On some applications of graphs to cryptography and turbocoding,
    T. Shaska, V. Ustimenko;  Albanian J. Math.  2  249--255  (2008)
    https://albanian-j-math.com/archives/2008-26.pdf

60. 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)
    https://albanian-j-math.com/archives/2008-25.pdf

61. 2008-3: Determining equations of families of cyclic curves,
    R. Sanjeewa, T. Shaska,  Albanian J. Math.  2  199--213  (2008)
    https://albanian-j-math.com/archives/2008-20.pdf

62. 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

63. 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)
    https://albanian-j-math.com/archives/2008-32.pdf

2007

64. 2007-4: Some open problems in computational algebraic geometry,
    T. Shaska, Albanian J. Math.  1  297--319  (2007)
    https://albanian-j-math.com/archives/2007-24.pdf

65. 2007-3: Thetanulls of cyclic curves of small genus,
    E. Previato, T. Shaska, S. Wijesiri, Albanian J. Math.  1  253--270  (2007)
    https://albanian-j-math.com/archives/2007-21.pdf

66. 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   https://www.risat.org/pdf/2007-2.pdf

2006

67. 2006-4: Subvarieties of the hyperelliptic moduli determined by group actions, Serdica Math. J.  32  355--374  (2006)
    https://www.risat.org/pdf/2006-4.pdf

68. 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   https://www.risat.org/pdf/2006-3.pdf

69. 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   https://www.risat.org/pdf/2006-2.pdf

70. 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)
    https://www.risat.org/pdf/2006-1.pdf

2005

71. 2005-4: A Maple package for hyperelliptic curves, T. Shaska, S. Zheng, 399--408  (2005)
    https://www.risat.org/pdf/2005-4.pdf

72. 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   https://www.risat.org/pdf/2005-3.pdf

73. 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   https://www.risat.org/pdf/2005-2.pdf

74. 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   https://www.risat.org/pdf/2005-1.pdf

75. 2005:  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.
    https://doi.org/10.1142/9789812701640%5C_0013   https://www.risat.org/pdf/2004-2.pdf

2004

76. 2004-3: Invariants of binary forms, V. Krishnamoorthy, T. Shaska, H. Volklein, Dev. Math., 12, Springer, New York, 2005, 101–122.
    https://doi.org/10.1007/0-387-23534-5%5C_6   https://www.risat.org/pdf/2004-3.pdf

77. 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.
    https://doi.org/10.1142/9789812701640%5C_0015   https://www.risat.org/pdf/2004-1.pdf

2003

78. 2003-4; Computational algebra and algebraic curves,
    SIGSAM Bull. 37, 117--124  (2003)
    https://doi.org/10.1145/968708.968713   https://www.risat.org/pdf/2003-4.pdf

79. 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  https://www.risat.org/pdf/2003-3.pdf

80. 2003-2: Some special families of hyperelliptic curves,
    T. Shaska, J. Algebra Appl.  3  75--89  (2004)
    https://doi.org/10.1142/S0219498804000745   https://www.risat.org/pdf/2003-2.pdf

81. 2003-1: On the generic curve of genus 3,
    T. Shaska, J. Thompson, Contemp. Math., Contemporary Math., 369, American Mathematical Society, Providence, RI, 2005
    https://doi.org/10.1090/conm/369/06814   https://www.risat.org/pdf/2003-1.pdf

2002

82. 2002-3: Determining the automorphism group of a hyperelliptic curve,
    Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation, 248–254. (ACM), 2003
    https://doi.org/10.1145/860854.860904   https://www.risat.org/pdf/2002-3.pdf

83. 2002-2: Computational aspects of hyperelliptic curves,
    Lecture Notes Ser. Comput., 10, World Scientific Publishing Co., Inc., River Edge, NJ, 2003, 248–257. https://www.risat.org/pdf/2002-2.pdf

84. 2002-1: Genus 2 curves with (3,3)-split Jacobian and large automorphism group,
    Lecture Notes in Comput. Sci., 2369, Springer-Verlag, Berlin, 2002, 205–218.
    https://doi.org/10.1007/3-540-45455-1%5C_17   https://www.risat.org/pdf/2002-1.pdf
    math/0201008

2001

85. 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)
    https://www.risat.org/pdf/2001-2.pdf  math/0205314

86. 2001-1: Genus 2 fields with degree 3 elliptic subfields, Forum Math. 16  263--280  (2004)
    https://doi.org/10.1515/form.2004.013     https://www.risat.org/pdf/2001-1.pdf   math/0109155

87. 2001-0: Curves of genus two covering elliptic curves,
    Thesis (Ph.D.)--University of Florida pg.72 (2001).
    https://www.risat.org/pdf/2001-0.pdf

2000

88. 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)
    https://www.risat.org/pdf/2000-2.pdf math/0107142 

89. 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     https://www.risat.org/pdf/2000-1.pdf  math/0312285