Title: From airlines to healthcare: scheduling services with high variability
Abstract: What do the airline and healthcare industries have in common when it comes to managing their capacity? What makes scheduling surgeries so much more difficult than an airline’s management of its seat inventory? How can hospitals improve their surgical scheduling system? While most optimization models suffer from the curse of dimensionality, simulation-based optimization is often a better choice when dealing with demand that is highly variable. Drawing from revenue management techniques developed by the airline industry, I will show how simulation modeling can help hospitals to more efficiently schedule surgical procedures, in order to better address and balance over- and under-utilization of their resources.
Title: Mock and quantum modular forms
Abstract: Mock modular forms were first formally defined in the literature by Zagier in 2007, though their roots trace back to the mock theta functions, curious power series described by Ramanujan in his last letter to Hardy in 1920. As the overarching theory of harmonic Maass forms has progressed over the last 15 years, we have seen applications of mock modular forms in number theory, combinatorics, representation theory, and more. Zagier also defined quantum modular forms in 2010, which like mock modular forms feign modularity in some way, but unlike mock modular forms are only defined on sets of rational numbers. In this talk, we will give an introduction to and brief history of these subjects. We will also discuss an application in joint work with Ken Ono (Emory) and Rob Rhoades (CCR Princeton), in which we revisit Ramanujan’s last letter and prove one of his remaining claims as a special case of a more general result.
Title: A McNemar’s-like Odds Ratio and Test for Multivariate Paired Binary Data.
Title: “Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk.” – L. Kronecker. Translation: “God made the integers. All else is the work of Man.”
Abstract: We were taught about the number line and its properties in middle school. Only in college do we learn that the number line is created by taking the rationals and “filling in the holes”. (It took mathematicians 200+ years to understand all this, so the 8 or so years it’s taking you is fast.) In this talk we’ll explore other ways of “filling in the Holes” and why these other number systems are both natural and powerful things.