Abstract: Cells make fate decisions in response to different and dynamic environmental and pathological stimuli. Recent technological breakthroughs have enabled biologists to gather data in previously unthinkable quantities at single cell level. However, synthesizing and analyzing such data require new mathematical and computational tools, and in particular, understanding multiscale cellular dynamics emerging from molecular and genomic scale details demands new multiscale modeling. In this talk, I will present our recent works on analyzing single-cell molecular data, and their connections with cellular and spatial tissue dynamics. Our mathematical approaches bring together optimization, statistical physics, ODEs/PDEs, and stochastic simulations along with machine learning techniques. By utilizing our novel mathematical methods and their integration with new datasets from our collaborators, we are able to investigate several complex systems during development and regeneration to uncover new mechanisms, such as novel beneficial roles of noise and intermediate cellular states, in cell fate determination.
Abstract: One of the most closely watched Supreme Court cases this year is also one of the most mathematical â Gill v. Whitford, a case about whether the state legislative districts in Wisconsin were drawn to favor Republicans so greatly that the right of Wisconsin Democrats to representation in the legislature was unconstitutionally diminished. The court will also hear a companion case, Benisek v. Lamone, concerning congressional districts in Maryland, which are drawn to favor Democrats. As a native of Maryland, a current resident of Wisconsin, and a mathematician, Iâm naturally following this closely. How can we use mathematics to test whether district boundaries are drawn to favor one party or the other? How much unfairness is too much? And how can people with mathematical, statistical, and computational training participate in the process and help us get to a point where the legal status quo has good mathematical grounding?
Abstract: I will present a survey of micro, meso and macroscopic models where repulsion and attraction effects are included through pairwise potentials. I will discuss their interesting mathematical features and applications in mathematical biology and engineering. Qualitative properties of local minimizers of the interaction energies are crucial in order to understand these complex behaviors. I will showcase the breadth of possible applications with three different phenomena in applications: segregation, phase transitions and consensus.