T. Shaska: a timeline of my mathematical journey.
Papers and preprints
2000
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 Â Â https://www.risat.org/pdf/2000-1.pdf
math/0312285Â2000-2: 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/0107142Â
2001
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.pdf2001-1: Genus 2 fields with degree 3 elliptic subfields, Forum Math. 16Â 263--280Â (2004)
https://doi.org/10.1515/form.2004.013 Â Â https://www.risat.org/pdf/2001-1.pdf
math/01091552001-2: 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
2002
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 Â https://www.risat.org/pdf/2002-1.pdf
math/02010082002-2: 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.pdf2002-3: Determining the automorphism group of a hyperelliptic curve, Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation, 248–254. Association for Computing Machinery (ACM), New York, 2003
https://doi.org/10.1145/860854.860904 Â https://www.risat.org/pdf/2002-3.pdf
2003
2003-1: On the generic curve of genus 3, T. Shaska, J. Thompson, Contemp. Math., 369, American Mathematical Society, Providence, RI, 2005
https://doi.org/10.1090/conm/369/06814 Â https://www.risat.org/pdf/2003-1.pdf2003-2: 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.pdf2003-3: Hyperelliptic curves with extra involutions, J. Gutierrez, T. Shaska, LMS J. Comput. Math. 8 102--115 (2005)
https://doi.org/10.1112/S1461157000000917Â https://www.risat.org/pdf/2003-3.pdf2003-4; Computational algebra and algebraic curves, SIGSAM Bull. 37, 117--124Â (2003)
https://doi.org/10.1145/968708.968713 Â https://www.risat.org/pdf/2003-4.pdf
2004
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.pdf2004-3: 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 Â https://www.risat.org/pdf/2004-3.pdf
2005
2005:Â 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 Â https://www.risat.org/pdf/2004-2.pdf2005-1: 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 Â https://www.risat.org/pdf/2005-1.pdf2005-2: 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 Â https://www.risat.org/pdf/2005-2.pdf2005-3: 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 Â https://www.risat.org/pdf/2005-3.pdf2005-4: A Maple package for hyperelliptic curves
T. Shaska, S. Zheng, 399--408Â (2005)
https://www.risat.org/pdf/2005-4.pdf
2006
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.pdf2006-2: 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 Â https://www.risat.org/pdf/2006-2.pdf2006-3: 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.pdf2006-4: Subvarieties of the hyperelliptic moduli determined by group actions, Serdica Math. J. 32 355--374 (2006)
https://www.risat.org/pdf/2006-4.pdf
2007
2007-1: Special issue on algebra and computational algebraic geometry
A. Elezi, T. Shaska, Albanian J. Math. 1 175--177 (2007)
https://albanian-j-math.com/archives/2007-14.pdf2007-2: 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 Â https://www.risat.org/pdf/2007-2.pdf2007-3: 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.pdf2007-4: 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
2008
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.pdf2008-2: 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.2008.08.0232008-3: Determining equations of families of cyclic curves
Sanjeewa, R. and Shaska, T., Albanian J. Math. 2 199--213 (2008)
https://albanian-j-math.com/archives/2008-20.pdf2008-4: Degree even coverings of elliptic curves by genus 2 curves
Pjero, N., Ramasaco, M., and Shaska, T., Albanian J. Math. 2 241--248 (2008)
https://albanian-j-math.com/archives/2008-25.pdf2008-5: On some applications of graphs to cryptography and turbocoding
Shaska, Tanush and Ustimenko, V., Albanian J. Math. 2 249--255 (2008)
https://albanian-j-math.com/archives/2008-26.pdf2008-i: Algebraic aspects of digital communications
T. Shaska, M. Qarri, Albanian J. Math. 2 141--144 (2008)
https://albanian-j-math.com/archives/2008-14.pdf
2009
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
2010
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
2011
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.pdf2011-2: 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
2012
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 Â https://www.risat.org/pdf/2012-1.pdf2012-2:Â Genus two curves with many elliptic subcovers
T. Shaska, Comm. Algebra 44 4450--4466 (2016)
https://doi.org/10.1080/00927872.2015.1027365
2013
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.pdf2013-2: 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 Â https://www.risat.org/pdf/2013-2.pdf2013-4: 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 Â https://www.risat.org/pdf/2013-4.pdf2013-7: 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 Â https://www.risat.org/pdf/2013-7.pdf2013-i: Computational algebraic geometry and its applications
T. Shaska, Appl. Algebra Engrg. Comm. Comput. 24 309--311 (2013)
https://doi.org/10.1007/s00200-013-0204-12013-ii: Computational algebraic geometry, J. Symbolic Comput. 57 1--2 (2013)
https://doi.org/10.1016/j.jsc.2013.05.001
2014
2014-2: 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.pdf2014-3: 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
2015
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.pdf2015-2: 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.pdf2015-3: Weight distributions, zeta functions and Riemann hypothesis for linear and algebraic geometry codes, A. Elezi, T. Shaska, 41Â 328--359Â (2015)
https://www.risat.org/pdf/2015-3.pdf2015-4: 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
2016
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 Â https://www.risat.org/pdf/2016-1.pdf2016-2: 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.pdf2016-3: 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.pdf2016-4: 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 Â https://www.risat.org/pdf/2016-4.pdf2016-5: Rational points in the moduli space of genus two, L. Beshaj, R. Hidalgo, S. Kruk, A. Malmendier, S. Quispe, T. Shaska, 703Â 83--115Â (2018)
https://doi.org/10.1090/conm/703/14132 Â https://www.risat.org/pdf/2016-5.pdf2016-6: On generalized superelliptic Riemann surfaces
R. Hidalgo, S. Quispe, T. Shaska
https://arxiv.org/abs/1609.09576
2017
2017-1:Â 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.pdf2017-3: 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.pdf2017-5: 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
2018
2018-1: Curves, {J}acobians, and cryptography
G. Frey, T. Shaska, 724Â 279--344Â (2019)
https://doi.org/10.1090/conm/724/14596 Â https://www.risat.org/pdf/2018-1.pdf2018-2: On the discriminant of certain quadrinomials
Sh. Otake, T. Shaska, 724Â 55--72Â (2019)
https://doi.org/10.1090/conm/724/14585 Â https://www.risat.org/pdf/2018-2.pdf2018-3:Â 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 Â https://www.risat.org/pdf/2018-3.pdf2018-4: Computing heights on weighted projective spaces
J. Mandili, T. Shaska, 724Â 149--160Â (2019)
https://doi.org/10.1090/conm/724/14588 Â https://www.risat.org/pdf/2018-4.pdf2018-5: Kay Magaard (1962--2018)
Gerhard Hiss and Tony Shaska, Albanian J. Math. 12 33--35 (2018)
https://albanian-j-math.com/archives/2018-05.pdf2018-6: On automorphisms of algebraic curves
A. Broughton, T. Shaska, A. Wootton, 724Â 175--212Â (2019)
https://doi.org/10.1090/conm/724/14590Â https://www.risat.org/pdf/2018-6.pdf
2019
2019-1:Â 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.2019.12.012Â https://www.risat.org/pdf/2019-1.pdf2019-2: 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/20195790Â https://www.risat.org/pdf/2019-2.pdf2019-3:Â 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/3639Â https://www.risat.org/pdf/2019-3.pdf2019-4: From hyperelliptic to superelliptic curves
A. Malmendier, T. Shaska, Albanian J. Math. 13 107--200 (2019)
https://albanian-j-math.com/archives/2019-03.pdf2019-5: The addition on Jacobian varieties from a geometric viewpoint
Y. Kopeliovich, T. Shaska https://arxiv.org/abs/1907.11070
2020
2020-1: Reduction of superelliptic Riemann surfaces
T. Shaska,776Â 227--247Â (2022)
https://doi.org/10.1090/conm/776/15614Â https://www.risat.org/pdf/2020-1.pdf2020-i: Integrable systems: a celebration of Emma Previato's 65th birthday
R. Donagi, T. Shaska, 458,1--12Â (2020) https://www.risat.org/pdf/2020-i.pdf2020-ii: Algebraic geometry: a celebration of Emma Previato's 65th birthday
Donagi, Ron and Shaska, Tony, 1--12 (2020)
https://www.risat.org/pdf/2020-ii.pdf
2021
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.a5Â https://www.risat.org/pdf/2021-1.pdf2021-2: Arithmetic inflection of superelliptic curves
https://www.risat.org/pdf/2021-2.pdf
2022
2022-1: Local and global heights on weighted projective varieties, S. Salami, T. Shaska, Houston J. Math. Vol. 49, #3, (2023)
https://www.risat.org/pdf/2022-1.pdf
2023
2023-01 Vojta's conjecture on weighted projective varieties, S. Salami, T. Shaska,
https://www.risat.org/pdf/2023-1.pdf
2024
Automorphism groups of rational functions (to be posted soon)
Machine learning and Julia reduction (to be posted soon)
Isogenies of Jacobian surfaces and post-quantum cryptography, NATO Series (late 2024)
Group actions and deep learning, Contemporary Math, 2024 (late 2024)
Weighted homomorphic encryption (in progress)
Weighted varieties defined over finite fields (in progress)