MathAcrossCampus is a quarterly colloquium series at the University of Washington to showcase applications of mathematics, with a special emphasis on the growing role of discrete methods in math applications. The goal of this seminar is to expose theoreticians to applied work, to create a community of mathematicians and users of mathematics at UW, and to serve as a guide to students and researchers looking for projects and jobs in math-related areas by offering exposure to ongoing math applications in the Seattle area.
The sharing economy has helped to transform many aspects of our day-to-day lives, leveraging the IT revolution in increasingly novel ways. At the same time, the sharing economy presents new computational challenges to provide tools to support the operations of these emerging industries. Although perhaps not quite as visible in impact as Uber and Airbnb (and their competitors), bike-sharing systems have fundamentally changed the urban landscape as well. Even in a city as notoriously inhospitable to cycling as New York, Citibike has emerged as a significant player in the cityís transportation network, supporting more than 1.5 million rides per month for a subscriber base of roughly 100,000 individuals. We have been working with Citibike to develop analytics and optimization models and algorithms to help manage this system. The key challenge is to cope with huge rush-hour usage that simultaneously creates stark shortages of bikes in some neighborhoods, and surpluses of bikes (and consequently, shortages of parking docks) elsewhere. We will explain how mathematical models can be used to answer questions such as, how should we position the fleet of bikes at the start of a rush hour, and how should we mitigate the imbalances that develop? Since a fundamental aspect of the behavior of these systems is the fluctuation in traffic patterns that vary over time, the resulting mathematical questions fall in the domain of stochastic optimization, where we develop a probabilistic model of the demand, and then optimize the expected performance of the system over a planning horizon. We will also describe some of the algorithmic challenges that these models pose, and highlight the computational tools developed to address them.
Sometimes you just don't have enough time to read an entire proof, a brief scan is all you can afford. Probabilistically checkable proofs (PCPs), discovered 25 years ago, guarantee that even a brief scan will find an error if there is one. A PCP proof is created by taking a regular proof and splitting it cleverly into fragments. The key is a theorem asserting that locally consistent fragments must be coming from a globally correct proof. We will describe this surprising local-to-global phenomenon and show a variety of implications from computational optimization all the way to secure cloud computing.
MathAcrossCampus is also made possible by the efforts of UW Mathematics graduate students Clayton Barnes, Gerandy Brito Montes de Oca, Christopher Fowler, Avi Levy, Siddharth Mathur, Andrew Pryhuber, Harishchandra Ramadas, Jacob Richey, Amy Wiebe, and Yizhe Zhu.
The MathAcrossCampus website was designed and created by Nathaniel Blair-Stahn.
Additional support has been provided by: The NSF VIGRE grant at UW; the departments of Applied Mathematics and Economics; the Milliman Fund; and the NSF Research Training Group in Inverse Problems and PDEs.