Mathematics Colloquia and Seminars

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The recent onslaught of data has brought about profound changes in understanding a range of phenomena as dynamic, high complexity processes. New technology has provided an unprecedented wealth of information, but it has generated data that are hard to analyze mathematically, thereby making an interpretation difficult. These challenges have given rise to myriad novel exciting mathematical problems and have provided an impetus to modify and adapt traditional mathematics tools, as well as develop novel techniques to tackle the data analysis problems.

I will discuss a general approach to address some of these computational challenges by way of a combination of geometric data transformations and topological methods. In essence geometric transformations deform the data to focus intensity on relevant questions, and topological methods identify statistically significant shape characteristics of the data. These methods have been applied in a range of settings, in particular for the study of the biology of disease. I will discuss some concrete applications of these methods, including their use to discover a new type of breast cancer, identify differences in recovery from surgery, and highlight the driving mechanisms in acute myeloid leukemia.

While the specifics of the work are focused on biological data analysis, the general approach addresses computational challenges in the analysis of any type of large data.