Aparna Higgins, University of Dayton
Title: Demonic Graphs and Undergraduate Research
Abstract: Working with undergraduates on mathematical research has been one of the most satisfying aspects of my professional life. This talk will highlight some of the beautiful and interesting research done by my former undergraduate students on line graphs and pebbling on graphs. We will consider line graphs, some pioneering results in pebbling graphs, and pebbling numbers of line graphs. This work has inspired other students to investigate questions in these areas, and it has contributed to my research as well.
Frank Morgan, Williams College
Title: From Soap Bubbles to the Poincaré Conjecture
Abstract: A single round soap bubble provides the least-area way to enclose a given volume. How does the solution change if space is given some density like r^2 or e^-r^2 that weights both area and volume? There has been much recent progress by undergraduates. Such densities appear prominently in Perelman’s paper proving the Poincaré Conjecture.