Dr. Beshaj

Dr. Lubjana Beshaj

Associate Professor

Lubjana.Beshaj@westpoint.edu

Biography


Currently teaching: MA464 Applied Algebra with Cryptography

Dr. Beshaj is a Cyber Fellow of Mathematics at the Army Cyber Institute and an Assistant Professor in the department of Mathematical Sciences at West Point.

For more information please refer to the following webpage: https://cyber.army.mil/Research/Research-Team/Beshaj/

Ongoing Research Projects


Kummer surfaces with (3, 3)-split Jacobian and aplications to isogeny based cryptography (work in progress)

Isogenous elliptic subcovers of genus 2 curves (with A. Elezi and T. Shaska, submitted),

Weighted greatest common divisors and weighted heights, (with J. Gutierrez, and T. Shaska, submitted)

Solving machine learning optimization problems using quantum computers, (with Venkat R. Dasari and Mee Seong Im, submitted)

Publications & Presentations


Books

Algebraic curves and their applications, edited by L. Beshaj and T. Shaska, Contemporary Math. American Math. Soc. volume 724, 2019

Advances on Superelliptic Curves and Their Applications edited by T.Shaska, E.Zhupa, L.Beshaj, NATO Science for Peace and Security Series D: Information and Communication Security, IOS Press, Amsterdam 2015

Articles

Absolute reduction of binary forms, Special issue in honor of Kay Magaard, Albanian J. Math. 2019,(to appear).

On the weighted projective space of binary octavics, Contemp. Math., 724, Amer. Math. Soc., Providence, RI, 2019, pg. 161-175, (with M. Polak).

The weighted moduli space of sextics, Contemp. Math., 724, Amer. Math. Soc., Providence, RI, 2019, pg. 33-45, (with S. Guest).

 Optimization problems with low SWaP tactical Computing, Proc. SPIE (2018), (to appear) (with M. S. Im, V. Dasari, and D. Shires).

On Prym varieties for the coverings of some singular plane curves, Manuscripta Mathematica, , 2018, pg. 1-18, (with T. Yamauchi).

 Minimal integral equations for genus 2 curves, Contemp. Math., 703, Amer. Math. Soc., Providence, RI, 2018, pg. 63-82, (2018).

Rational points in the moduli space of genus two, Contemp. Math., 703, Amer. Math. Soc., Providence, RI, 2018, pg. 83-115, (2018), (with R. Hidalgo, S. Kruk, A. Malmendier, S. Quispe, and T. Shaska).

Reduction of binary forms, Sci. Peace Secur. Ser. D Inf. Commun. Secur., 41, IOS Press, Amsterdam, 2015, pg. 84-116.

Heights on algebraic curves, NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., 41, IOS Press, Amsterdam, 2015, pg. 137-175, (with T. Shaska).

The case for superelliptic curves, Sci. Peace Secur. Ser. D Inf. Commun. Secur., 41, IOS Press, Amsterdam, 2015, pg. 1-14, (with T. Shaska and E. Zhupa).

Theta functions of superelliptic curves, Sci. Peace Secur. Ser. D Inf. Commun. Secur., 41, IOS Press, Amsterdam, 2015, pg. 47-69, (with A. Elezi and T. Shaska).

Decomposition of some Abelian varieties of dimension 3, Conference on Artificial Intelligence and Symbolic Computation, LNCS vol. 8884, (2014), 193-204, (with T. Shaska).

On Jacobians of curves with superelliptic components, Contemporary Math., vol. 229, (2014), pg: 3-21, (with T. Shaska, and C. Shor).

Equations for superelliptic curves over their minimal field of definition, Albanian J. Math., Vol. 8 (2014), no. 1, 3-8, (with F. Thompson).

The arithmetic of genus two curves, NATO Advanced Study Institute, Croatia, NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., 29, IOS, Amsterdam, 2011, 59–98, (with T. Shaska).

On superelliptic curves of level n and their quotients, Albanian J. Math., Vol 5, Nr. 3, (2011), pg. 115-137, (with V. Hoxha, T. Shaska).

The singular locus of the space of genus 2 curves with decomposable Jacobians, Albanian J. Math., Vol. 4, Nr. 4, (2010), pg, 375-390.

Presentations

Jan. 2019, Isogenous components of 2-dimensional reducible Jacobians, AMS Joint Meetings, Baltimore, MD

Nov. 2018, Isogenous elliptic subcovers of genus 2 curves, Santander Cryptography Day, Universidad de Cantabria, Santander, Cantabria, Spain.

Oct. 2018, On Prym varieties for the coverings of some singular plane curves, AMS Special Session on Algebraic Curves, University of Michigan, Ann Arbor, MI

Apr. 2018, Minimal Models for Superellipic Riemann Surfaces with Extra Automorphism, AMS Special Session on Automorphisms of Riemann Surfaces and Related Topics, Portland, Portland State University, OR

Mar. 2018, Isogenous elliptic subcovers of genus 2 curves, AMS Special Session on Algebraic Curves and Their Applications, Ohio State University, OH

Nov. 2017, Isogeny based cryptography in the post-quantum world, Department of Mathematics and Statistics, Oakland University, MI

Sep. 2017, Elliptic and hyperelliptic curve cryptography, Department of Electrical Engineering and Computer Science, The United States Military Academy, West Point, NY

Mar. 2017, From Elliptic to superelliptic curves, Army Cyber Institute, The United States Military Academy, West Point, NY

Jan. 2017, The number of binary forms of bounded moduli height, AMS Special Session on Minimal integral models of algebraic curves, Joint Mathematics Meetings in Atlanta, Georgia.

Nov. 2016, Minimal models for superelliptic curves with extra automorphisms, AMS Special Session on Varieties, Their Fibrations and Automorphisms in Mathematical Physics and Arithmetic Geometry, Raleigh, North Carolina.

May. 2016, Hyperelliptic curve cryptography, General Motors Research and Development, GMC, Detroit, MI

May 2016, Special lecture: Elliptic curve cryptography in automotive industry, Mathematics in Automotive Security, Oakland University, Rochester, Michigan

January 2016, Integral minimal models for binary forms, AMS Special Session on Higher Genus Curves and Fibrations of Higher Genus Curves in Mathematical Physics and Arithmetic Geometry, Seattle, Washington.

Nov. 2015, Superelliptic curves with minimal height, Department of Mathematics Colloquium, Georgia Southern University, Georgia.

March 2015, Reduction of binary forms, AMS Special Session on Arithmetic of Hyperelliptic Curves, East Lansing, Michigan.

March 2015, Binary forms of minimal height, Department of Mathematics Colloquium, University of Akron, Ohio.

August 2014, Decomposition of Jacobians in superelliptic components, NATO ASI, Arithmetic of hyperelliptic curves, Ohrid, Macedonia.

July 2014, Curves with minimal height, Applications of Computer Algebra Conference, Special Session on Arithmetic Geometry, New York.

July 2014, Decomposition of Jacobians in superelliptic components, Applications of Computer Algebra Conference, Special Session on Algorithms and applications in the geometry of algebraic curves and surfaces, New York.

July 2013, On superelliptic curves and their Jacobians, Applications of Computer Algebra, Malaga, Spain.

May 2013, Genus 3 algebraic curves, Michigan Computational Algebraic Geometry, Western Michigan University, Michigan.

October 2011, Theta functions of genus 3 curves, Special Session on Computational and Algorithmic Algebraic Geometry, II, Salt Lake City, Utah.

January 2011, Some remarks on the arithmetic of genus 2 curves, AMS Special Session on Computational Algebraic and Analytic Geometry for Low-Dimensional Varieties, I, New Orleans.