In this thesis, we describe a geometric method for computing diagonal Cartier algebras of toric rings arising from two-dimensional cones. Evan's Thesis can be found here.

This thesis explores several demand-aware network design problems through the lens of the skip graph. We describe and implement two heuristics to find the optimal skip graph for a given communication demand, with empirical evidence that suggest they outperform random sampling. Hrishee's Thesis can be found here.

We are investigating which toric varieties are diagonally F-regular. Dylan prepared a poster for the University of Utah undergraduate research symposium and slides for a talk he gave at the JMM in 2019.

We are attempting to generalize the work with Dylan Johnson and Daniel Smolkin to show that all Hibi rings are diagonally F-regular.

We are developing and implementing an improved algorithm with multithreading capabilities for computing the ideal of minors in Macaulay2. The current version of the code can be found here. Boyana presented a poster on her work at the University of Utah ACCESS Symposium 2019.