Department of Mathematics University of Kansas 1460 Jayhawk Blvd Lawrence, Kansas 66045-7567

I am currently pursuing my PhD in mathematics at the University of Kansas. My advisor is Hailong Dao.

Office: 560 Snow Hall Fax: (785) 864-5255 E-mail: brentholmes@ku.edu

Wednesday 2 PM - 3PM or by appointment.

Rainbow colorings of some geometrically defined uniform hypergraphs in the plane. Geombinatorics 23 (2014), no. 4, 158–169.. Two kinds of Frobenius problems in Z[√m]. Int. J. Math. Comput. Sci. 7 (2012), no. 2, 93–100.

On the Diameter of Dual Graphs of Stanley-Reisner Rings with Serre (S_2) Property and Hirsch Type Bounds on Abstractions of Polytopes..

Proof of Proposition 3.6 .

Examining Hochster-Huneke graphs and their diameters. Examining bounds of projective dimension. Cohen-Macaulay rings and conditions which imply Cohen-Macaulyness of a ring. Serre condition and generalizations of Serre condition.

You can see my CV here