# Research

## Fields of interest

I am currently most interested in numerical semigroups. I have also done some work in algebraic geometry, number theory, and coding theory.

## Publications

- (with T. A. Gassert) “Characterizations of numerical semigroup complements via Apéry sets.” Submitted May 2017.
- (with T. A. Gassert) “On Sylvester sums of compound sequence semigroup complements,”
*Journal of Number Theory*, in press. - “Higher-order Weierstrass weights of branch points on superelliptic curves.” To appear in
*Contemporary Mathematics*. - (with T. Shaska) “2-Weierstrass points of genus 3 hyperelliptic curves with extra involutions,”
*Communications in Algebra*, vol. 45, no. 5, 2017, pp. 1879–1892. - (with T. Shaska) “Theta functions and symmetric weight enumerators for codes over imaginary quadratic fields,”
*Designs, Codes and Cryptography*, vol. 76, issue 2, 2015, pp. 217–235. - (with T. Shaska) “Weierstrass points of superelliptic curves,”
*Advances on superelliptic curves and their applications*, NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., vol. 41, IOS, Amsterdam, 2015, pp. 15–46. - (with L. Beshaj, T. Shaska) “On Jacobians of curves with superelliptic components,”
*Contemporary Mathematics*, vol. 629, 2014, pp. 1–14. - “Genus calculations for towers of function fields arising from equations of $C_{ab}$ curves,”
*Albanian Journal of Mathematics*, vol. 5, no. 1, 2011, pp. 31–40. - (with T. Shaska, S. Wijesiri) “Codes over rings of size p^2 and lattices over imaginary quadratic fields,”
*Finite Fields and Their Applications*, no. 2, 2010, pp. 75–87. - “On the construction of codes from an asymptotically good tower over $F_8$,"
*Serdica J. Computing*, no. 2, 2007, pp. 171–184. - (with T. Shaska) “Codes over $F_{p^2}$ and $F_p\times F_p$ , lattices, and theta functions,”
*Advances in Coding Theory and Cryptography*, vol 3, 2007, pp. 70–80. - "On towers of function fields and the construction of the corresponding Goppa codes," Ph.D. Dissertation, Boston University, 2005.

## My research profiles

Here are my various research profiles.