I have graduated with a PhD in Mathematics in 2016 under the direction of Tony Shaska . My areas of research are arithmetic and algebraic geometry. More specifically I am interested in minimal models of curves, arithmetic of superelliptic curves, elliptic and hyperelliptic curve cryptography, and moduli space of curves.

I am part of a project on algebraic curves, which is about creating a computational package written in Sagemath and computes with superelliptic curves. See algcurves.org for more details about this project. Some of my hobbies outside mathematics include learning foreign languages, reading(primarly science, history, and mystery), and hiking. My native language is Albanian. Other than that I can speak English, Spanish, Italian and have basic knowledge in several other languages.## Editorial

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.

## Papers

On Prym varieties for the coverings of some singular plane curves, submited (with T. Yamauchi)

Minimal integral Weierstrass equations for genus 2 curves, Contemporary math, 2016, (to appear).

Some arithmetic statistics of the moduli space of genus two curves, Contemporary Math, 2016, (with S. Kruk, A. Malmendier, and T. Shaska) (to appear).

Reduction of binary forms, NATO Advanced Study Institute, Macedonia, NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., 41, IOS, Amsterdam, 2015, pp. 84-117

Heights on algebraic curves, NATO Advanced Study Institute, Macedonia, NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., 41, IOS, Amsterdam, 2015, pp. 137-176 (with T. Shaska)

The case of superelliptic curves , NATO Advanced Study Institute, Macedonia, NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., 41, IOS, Amsterdam, 2015, pp. 1-15, (with T. Shaska and E. Zhupa)

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

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

On Jacobians of curves with superelliptic components, L. Beshaj, T. Shaska, and C. Shor, Contemporary Math, vol 229, pg 3-21.

On superelliptic curves of level n and their quotients I. , L. Beshaj, V. Hoxha, T. Shaska, Albanian J. Math. Vol 5, Nr. 3. pg. 115--140.

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

The arithmetic of genus two curves , (with T. Shaska), NATO Advanced Study Institute, Croatia, 2010. ISO Press, 2010, pg. 59--98.

## Work in Progres

On binary forms with minimal height.

Counting algebraic curves with bounded moduli height. (with T. Shaska)

## Talks

The number of binary forms of bounded moduli height, JMM Special Session Minimal integral models of algebraic curves, Joint Mathematics Meetings in Atlanta, GA, January 2017

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, November 2016.

Integral minimal models of binary forms, Joint Mathematics Meetings in Seattle, January 2016

Superelliptic curves with minimal height, Georgia Southern University, Georgia, November 2015

Reduction of binary forms, AMS sectional meeting, East Lansing, March 2015

Binary forms with minimal height, University of Akron, Akron, March 2015

On Jacobians of curves with superelliptic components, NATO-ACI, Macedonia, August 2014

Heights on Algebraic curves, ACA 2014, Fordham Univ., July 2014

On Jacobians of curves with superelliptic components, ACA 2014, Fordham Univ., July 2014

Theta functions of curves, Algebra Seminar, Oakland University, September 2011.

Theta functions of genus 3 curves, AMS Sectional meeting, October 2011, Salt Lake City.

Theta-nulls and Jacobians of algebraic curves (with T. Shaska), Special session on Number Theory, AMMCS-2011,

Some remarks on the arithmetic of genus 2 curves, AMS National Meeting, New Orleans, 2011.

## Visiting Institutions

Princeton University, New Jersey, USA, Jan- Jun 2015

MSRI (Mathematical Sciences Research Institute), Berkeley, CA, USA

CRM (Centre de Recerca Matematica), Barcelona, Spain

UMCS(Uniwersytet Marri Curie Sklodowskiej), Lublin, Poland.