Graduate Research Seminar
For Spring 2014, I will be posting my assignment from FGCU's Graduate Research Seminar on this page, along with other related materials.
Summary of Project: A while ago I notice a peculiar behavior of the graphs associated with a well studied class of algebraic varieties, Schubert varieties. It appears to be the case that when a Schubert variety is rationally smooth, it's associated graph is an integral graph. As a start to verifying this observation, I will be computing the eigenvalues of the Schubert varieties in exceptional Lie types, as well as learning about the techniques involved in proving classes of graphs are integral.
Assignment 1 :
Copy of First Page of Research Paper
First Three Entries of Bibliography
Assignment 2 :
Assignment 3 :
Assignment 4 :
Assignment 5 :
Assignment 6 :
Presentation of research paper : Constructing fifteen infinite classes of nonregular bipartite integral graphs
Assignment 7:
Assignment 8:
Presentation of research paper : Graphs with integral spectrum
Assignment 9:
Rough draft of research day poster.
Assignment 10:
Rough draft of research paper.
Assignment 11:
Another Draft of research day poster.