Topological data analysis (TDA) is a new area of study focusing on obtaining qualitative rather than quantitative information about data. A central idea of TDA is to capture the "shape" of the data using topological summaries, which are typically computed using a specific data dependent function called filter. In this talk I will discuss why the approach of TDA is particularly well suited for biological data. I will describe several topological summaries: persistence trees, Reeb graphs, and persistence diagrams, and present important stability results showing that the latter objects are highly robust. I will then focus on the question of performing inference using topological summaries and discuss existing results and remaining challenges.
Throughout the talk I will use two biological problems to motivate the topological techniques as well as illustrate their application: the problem of discovering regions of the genome which underlie the structure of plant root systems and the problem of detecting genes involved in regulation of periodic processes, such as somitogenesis and the cell cycle.
The speaker is a candidate for a tenure-track position in the Mathematics Department. The talk will be preceded by tea in Kidder 368 at 3:30. All are welcome.