Department of Mathematics

# Mentors

## Dr. Morgan Rodgers

I received my PhD from the University of Colorado Denver in 2012, and have done postdoctoral work at Ghent University in Belgium, and at the University of Padova in Italy. I just joined the Department of Mathematics at Fresno State in Fall 2017. My research is mainly focused on finite incidence structures, including finite geometries, polar spaces, combinatorial designs, etc. The nature of these objects puts this work at the intersection of geometry, combinatorics, and algebra. I especially enjoy applying computational tools to find substructures of these geometries having nice properties. Below is a list of my publications.

- M. Lavrauw and M. Rodgers, Classification of 8-dimensional rank two commutative semifields.
To appear in
*Advanced in Geometry*. - M. Rodgers, L. Storme and A. Vansweenelt, Cameron-Liebler k-classes in PG(2k+1,q). To appear in Combinatorica.
- J. De Beule, J. Demeyer, K. Metsch and M. Rodgers, A new family of tight sets in Q+(5,q).
*Designs, Codes and Cryptography,*(2016), Vol. 78, (3), pp. 655-678. - S. Payne and M. Rodgers, Double k-sets in symplectic generalized quadrangles.
*Designs, Codes and Cryptography,*(2014), Vol. 72, (2), pp. 265-271. - M. Rodgers, Cameron-Liebler line classes,
*Designs, Codes and Cryptography,*(2013), Vol. 68, (1-3), pp. 33-37.

## Dr. Khang Tran

I graduated from University of Illinois at Urbana-Champaign and joined the Department of Mathematics at California State University, Fresno in 2015. My research interest lie in analytic number theory and analysis, with a special focus on the zero distribution of sequences of polynomials. I enjoy working and publishing research papers with students. Below are my papers and those of students (marked with an *) working under my supervision.

- T. Forgacs, K. Tran, Zeros of polynomials generated by a rational function with a
hyperbolic-type denominator. To appear in
*Constructive Approximation*. - K. Tran, A. Zumba*, Zeros of polynomials with four-term recurrence. To appear in
*Involve-A Journal of Mathematics*. - A. Mai*, Exceptional zeros of polynomials satisfying a three-term recurrence,
*Journal of Pure and Applied Algebra*222 (2018), 534-545. - T. Forgacs, K. Tran, Polynomials with rational generating functions and real zeros,
*J. Math. Anal. Appl.*443 (2016), 631–651. - K. Tran, The root distribution of polynomials with a three-term recurrence,
*J. Math. Anal. Appl*. 421 (2015), 878–892. - K. Tran, Connections between discriminants and the root distribution of polynomials
with rational generating function,
*J. Math. Anal. Appl.*410 (2014), 330–340. - K. Tran, A. Zaharescu, Pair correlation of roots of rational functions with rational
generating functions and quadratic denominators,
*Ramanujan J.*31 (2013), no. 1, 129–145. - K. Tran, Discriminants of Polynomials Related to Chebyshev Polynomials: The "Mutt
and Jeff" Syndrome,
*J. Math. Anal. Appl.*383 (2011), 120–129. - A. Bostan, B. Salvy, K. Tran, Generating functions of Chebyshev-like polynomials,
*Int. J. Number Theory*6 (2010), no. 7, 1659–1667. - M. Erickson, S. Fernando, K. Tran, Enumerating rook and queen paths,
*Bull. Inst. Combin. Appl.*60 (2010), 37–48. - K. Tran, Discriminants of Chebyshev-like polynomials and their generating functions,
*Proc. Amer. Math. Soc.*137 (2009), no. 10, 3259–3269.