Department of Mathematics

# Research Topics

Students will conduct research in one of the following two areas:

## Survival Analysis

Survival analysis involves the modeling of time to event data. It is a rapidly growing field due to innovative technology, our knowledge of biological and mechanical systems and problems, and the impact of computation on data storage and analysis. Students in this research group will apply different parametric models to fit simulated as well as real data. They will learn to use nonparametric techniques to analyze lifetime data when the common distribution functions are not known, and will also use different censoring models to fit censored data. This project can serve as a steppingstone to graduate programs in statistics, biostatistics, biometrics, and other related disciplines.

## Embeddings of Graphs

Students in this group will study embeddings of graphs in (finite) affine and projective spaces. The origins of this problem can be traced back to Erdös, or to the study of Levi graphs admitting certain subgraphs. Particular topics we will investigate include: (i) studying conditions for graphs to be embedded in given spaces (a `planarity' problem), (ii) the number of ways an embedding can be made (yielding study of the orbits of an embedding under the space's automorphism group), (iii) on how the automorphism groups (of the graph and the space) connect/relate, and (iv) on how this study could yield results that may further the understanding of graphs and/or projective spaces.