Lubjana Beshaj


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.




Research


Areas: Algebraic geometry, arithmetic geometry
Topics: Hyperelliptic and superelliptic curves, Elliptic and hyperelliptic curve cryptography, post quantum cryptography, minimal models of curves

Papers and Preprints

Editorial
  • Algebraic curves and their applications, edited by L. Beshaj and T. Shaska,  

    Contemporary Math. American Math. Soc. (to appear)
  • 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

  1. On Prym varieties for the coverings of some singular plane curves submited (with  T. Yamauchi)
  2. Minimal integral Weierstrass equations for genus 2 curves, Contemporary math, 2016, (to appear).
  3. 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).
  4. 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
  5. 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) 
  6. The case of superelliptic curvesNATO 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) 
  7. Decomposition of some Abelian varieties of dimension 3, L. Beshaj, T. Shaska, Conference on Artificial Intelligence and Symbolic Computation,  LNCS vol. 8884, 193-204.
  8. Equations for superelliptic curves over their minimal field of definition, L. Beshaj, F. Thompson; Albanian J. Math., Vol. 8 (2014), no. 1, 3-8.
  9. On Jacobians of curves with superelliptic components, L. Beshaj, T. Shaska, and C. Shor,  Contemporary Math, vol 229, pg 3-21.
  10. 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.
  11. The singular locus of the space of genus 2 curves with decomposable Jacobians, Albanian J. Math, Vol. 4, Nr. 4, pg, 375-390. 
  12. 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


Conferences and Visiting

Talks

Other conferences
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






Editorial

Algebraic Curves and their Applications
Contemporary Math. (AMS)
Eds: L. Beshaj, T. Shaska

Deadline for submission: 
October 2017





Nato Advanced Study Institute


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Lubjana Beshaj,
Sep 28, 2017, 7:53 PM
Ċ
Lubjana Beshaj,
Jan 21, 2014, 10:31 AM