Introductory presentations for DOmath 2022.

Mathematics is being used in many ways to improve the analysis and interpretation of DNA and other molecules that can affect our health. I will describe how math was used to identify genes associated with tumor progression, and to develop methods to identify and quantify genetic variations without expensive and time-consuming sequencing. resulting in a rapid, economical test for transplant compatibility, a cancer therapy, and numerous clinical diagnostic assays. I will also discuss some surprising mathematical connections discovered in the course of this work.

We will discuss the proof of the conjecture due to M. Khovanov relating the algebraic and topological categorification of the chromatic polynomial. We show that there exists a spectral sequence relating the chromatic graph homology and the homology of a graph configuration space and discuss higher differentials.

TBD

Schedule (approximate times): 1:00-2:00: An, Deng, McPhail-Snyder research groups 2:00-2:20: break 2:20-3:00: Robles, Stokols research groups