By sequencing the genome or transcriptome of a tumor, scientists and doctors can gain detailed insights into the tumor's genetic history. For example, how many mutations drove the tumor's progression, and what specific mutations were most important? Doctors can use this information to determine the best courses of treatment and the frequency of surveillance tests. In recent years, scientists have developed novel sequencing technologies -- including single-cell sequencing, multi-region sequencing, and sequencing of circulating tumor DNA (ctDNA). In this project, the investigators will develop new mathematical and statistical tools to analyze the large amounts of data generated by these new sequencing technologies. Their methods will leverage the latest knowledge of biological mechanisms driving cancer progression to develop constrained statistical models that maximize insights from cancer sequencing data. The investigators will incorporate real-world limitations of cancer sequencing data availability, e.g. limited time points and samples. This project will support the training of graduate students in inter-disciplinary science that combines mathematics, statistics, and bioinformatics. The mathematical tools will be built upon the underlying principles of population genetics which govern tumor progression. Due to the rapid expansion of tumor cell populations, work will primarily be done with branching process models; however, variants of the branching process model th