iFEM is a MATLAB software package containing robust, efficient, and easy-following codes for the main building blocks of adaptive finite element methods on unstructured simplicial grids in both two and three dimensions. Besides the simplicity and readability, sparse matrixlization, an innovative programming style for MATLAB, is introduced to improve the efficiency. In this novel coding style, the sparse matrix and its operations are used extensively in the data structure and algorithms.

In 2009, US National Research Council of the National Academies published a report, called “A New Biology for the 21st Century”.  One of the major emphases in the New Biology is the integration between biology and mathematics. As explosion of biological measurements takes place in biology due to rapid technology development in recent years, the challenge lies in how to connect and make sense of the massive experimental data collected in various forms at different spatial and temporal scales. Mathematical modeling is becoming an increasingly important tool that enables better understanding of the complex data in biology.  In this talk, I will use research carried out in my group as examples to illustrate how mathematics can help discover new knowledge in biology as well as how biological models introduce new challenges and opportunities in mathematics.