T. Shaska: a timeline of my mathematical journey.

Papers and preprints

• 2025-07:  Homomorphic encryption over graded rings

• 2025-06: Computing (n,n)-isogenies on Abelian surfaces

• 2025-05: Weighted varieties defined over finite fields

• 2025-04: Automorphisms of rational functions

• 2025-03: Geometry of Weighted Projective Space and Machine Learning

• 2025-02: Isogeny based cryptography on Abelian surfaces

• 2025-01:   Polynomials, Galois groups,  and Neurosymbolic AI,
  ISSAC 2025, (submitted)
  
  

• 2024-07: Irreducible sextics, invariants, and their Galois groups

• 2024-06: Reduction of binary forms, Julia invariant, and machine learning
  ISSAC 2025 (submitted)

• 2024-05: Polynomials, Galois groups,  and Deep Learning
  Contemporary Math.  AMS, 2025 

• 2024-04: Rational Functions on the Projective Line through Machine Learning Techniques

• 2024-03: Machine learning for moduli space of genus two curves and an application to isogeny based cryptography,  
  Journal of Algebraic Combinatorics,  (to appear)

• 2024-02: Artificial neural networks on graded vector spaces,
  Annals of Mathematics and Artificial Intelligence (submitted)  https://arxiv.org/abs/2407.19031

• 2024-01: Equations for generalized superelliptic Riemann surfaces
  
  

• 2023-01: Vojta's conjecture on weighted projective varieties, S. Salami, T. Shaska; 
  European Journal of Mathematics, (to appear)
  
  

• 2022-1: Local and global heights on weighted projective varieties, S. Salami, T. Shaska;
  Houston J. Math. Vol. 49, #3, (2023), pg. 603-636
  
  

• 2021-2: Arithmetic inflection of superelliptic curves,  E Cotterill, I Darago, C. G López, C Han, T Shaska, 
  Michigan J. Math. 

• 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
  
  

• 2020-1: Reduction of superelliptic Riemann surfaces, Contemporary Math. 776  227--247  (2022)    https://doi.org/10.1090/conm/776/15614   

• 2020-i: Integrable systems: a celebration of Emma Previato's 65th birthday,  Donagi/Shaska, 458,1--12  (2020) 

• 2020-ii: Algebraic geometry: a celebration of Emma Previato's 65th birthday, Donagi/Shaska,  1--12  (2020)
  
  

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

• 2019-4: From hyperelliptic to superelliptic curves, A. Malmendier and T. Shaska;
  Albanian J. Math.  13  107--200  (2019)

• 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 

• 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 

• 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 
  
  

• 2018-6: On automorphisms of algebraic curves, Contemporary Math. 724  175--212  (2019) https://doi.org/10.1090/conm/724/14590 

• 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

• 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   

• 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 

• 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   

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

• 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

• 2017-3: Some remarks on the non-real roots of polynomials, Sh. Otake, T. Shaska,
  Cubo  20  67--93  (2018)

• 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 

• 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
  
  

• 2016-6: On generalized superelliptic Riemann surfaces, R. Hidalgo, S. Quispe, T. Shaska
  Transformation Groups (accepted)       https://arxiv.org/abs/1609.09576

• 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 

• 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 

• 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 

• 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  

• 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  
  
  

• 2015-4: Theta functions of superelliptic curves, NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., 41, IOS Press, Amsterdam, 2015, 47–69.

• 2015-3: Weight distributions, zeta functions and Riemann hypothesis for linear and algebraic geometry codes, A. Elezi, T. Shaska, 41  328--359  (2015)

• 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.

• 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.
  
  

• 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.

• 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.
  
  

• 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 

• 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   

• 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 

• 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   

• 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

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

• 2012-2:  Genus two curves with many elliptic subcovers, T. Shaska;
  Comm. Algebra,  44  4450--4466  (2016)  https://doi.org/10.1080/00927872.2015.1027365

• 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  
  
  

• 2011-2: On superelliptic curves of level $n$ and their quotients, L. Beshaj, V. Hoxha, T. Shaska, Albanian J. Math.  5  115--137  (2011)

• 2011-1: Quantum codes from superelliptic curves, A. Elezi, T. Shaska, Albanian J. Math.  5  175--191  (2011)
  
  

• 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.
  
  

• 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.
  
  

• 2008-5: On some applications of graphs to cryptography and turbocoding, T. Shaska, V. Ustimenko;  Albanian J. Math.  2  249--255  (2008)

• 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)

• 2008-3: Determining equations of families of cyclic curves, R. Sanjeewa, T. Shaska,  Albanian J. Math.  2  199--213  (2008)

• 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

• 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)
  
  

• 2007-4: Some open problems in computational algebraic geometry, T. Shaska; Albanian J. Math.  1  297--319  (2007)

• 2007-3: Thetanulls of cyclic curves of small genus, E. Previato, T. Shaska, S. Wijesiri;  Albanian J. Math.  1  253--270  (2007)

• 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
  
  

• 2006-4: Subvarieties of the hyperelliptic moduli determined by group actions,
  Serdica Math. J.  32  355--374  (2006)

• 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 

• 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   

• 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)
  
  

• 2005-4: A Maple package for hyperelliptic curves, T. Shaska, S. Zheng, 399--408  (2005)

• 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 

• 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 

• 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  
  
  

• 2004-3: Invariants of binary forms, V. Krishnamoorthy, T. Shaska, H. Volklein,
  Dev. Math., 12, Springer, New York, 2005, 101–122. 

• 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. 

• 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.
  
  

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

• 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  

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

• 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
  
  

• 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 

• 2002-2: Computational aspects of hyperelliptic curves, Lecture Notes Ser. Comput., 10, World Scientific Publishing Co., Inc., River Edge, NJ, 2003, 248–257. 

• 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
  
  

• 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

• 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

• 2001-0: Curves of genus two covering elliptic curves, 
  Thesis (Ph.D.)--University of Florida pg.72 (2001).
  
  

• 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 

• 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