Explore the fascinating intersection of tropical geometry and shallow water waves in this captivating lecture delivered at the Virtual Joint Mathematics Meetings. Delve into the insights presented by Harvard University's Lauren Kiyomi Williams as she delivers the prestigious AMS-MAA-SIAM Gerald and Judith Porter Public Lecture. Introduced by Jennifer Quinn, President of the Mathematical Association of America, this hour-long talk offers a unique perspective on the application of tropical geometry to understanding the behavior of shallow water waves. Gain valuable knowledge about this cutting-edge research area and its potential implications for both mathematics and physics.