## 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 hyperelliptic and superelliptic curves, elliptic and hyperelliptic curve cryptography, post-quantum 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. ## ResearchAreas: Algebraic geometry, arithmetic geometry Topics: Hyperelliptic and superelliptic curves, Elliptic and hyperelliptic curve cryptography, post quantum cryptography, minimal models of curves ## Papers and PreprintsEditorialContemporary Math. American Math. Soc. (to appear)## Algebraic curves and their applications, edited by L. Beshaj and T. Shaska,## 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.
**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, R,. Hidalgo, S. Quispe, 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,**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,****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.
Posters## Professional Services and Memberships- Organizer: Algebraic Curves and their applications, AMS Special Session "Algebraic curves and their applications", Orlando, September, 2017
- Organizer:
*Special Session on Arithmetic of Algebraic Curves (with**A. Malmendier and C. Shor**), Knoxville, March 2014* - Organizer:
*Special Session on Computational Advances on Special Functions and Tropical Geometry (with Emma Previato)* - Co-organizer: MCAG 2012, Michigan Computational Algebraic Geometry
- Co-organizer: ACA 2010, Applications of Computer Algebra,
## Conferences and VisitingTalks*The number of binary forms of bounded moduli height*,**Minimal integral models of algebraic curves**, Joint Mathematics Meetings in Atlanta, GA, Jan, 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, AMS annual meeting, 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.
Other conferences- Sage Days 69: Women in Sage 6, La Jolla, California, September 2015.
- Bootcamp for
**the 2015 Algebraic Geometry Summer Research Institute,**University of Utah, Salt Lake City, July 2015 - Aspects of Algebraic Geometry, IAS and Princeton University, Princeton, May 2015
- Arizona Winter School 2015, Arithmetic and Higher-Dimensional Varieties, University of Arizona in Tucson, AZ, March 2015
- NATO ASI 2014, Arithmetic of Hyperelliptic Curves and Cryptography, Ohrid,
*the former Yugoslav Republic of Macedonia*, August 2014 - Arizona Winter School 2014, Arithmetic Statistics, University of Arizona in Tucson, AZ, March 2014,
- Clay Summer School 2012 "Resolution of Singularities", Obergurgl June 2012
- MSRI, Hybrid Methods in Computation, November 2010
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.
## Grants and Awards- Algebraic Geometry- Bootcamp, Salt Lake City, July 2015
- Institute of Advanced Study, Princeton, May 2015
- Arizona Winter School, University of Arizona, March 2015
- AMS Travel Award, March 2015
- NATO Advanced Study Institute, August 2014
- Arizona Winter School, University of Arizona, March 2014
- Dep. of Math. and Stat., Oakland University, March 2014
- University Research Office, Oakland University, March 2014
- Association for Women in Mathematics Travel Award, January 2014
- Dep. of Math. and Stat., Oakland University, April 2013
- Office of Research, Oakland University, March 2013
- Clay Mathematical Institute Fellowship, June 2012
- Dep. of Math. and Stat., Oakland University, June 2012
- AMS Travel Award, March 2012
- Office of Research, Oakland University, October 2011
- AMS Travel Award, October 2011
- MSRI Travel Award, November 2010
| ## EditorialAlgebraic Curves and their ApplicationsContemporary Math. (AMS) Eds: L. Beshaj, T. Shaska Deadline for submission: October 2017 ## Computational Algebraic Geometry## Photo gallery |