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 two subjects of math and music are connected in myriad ways, from the rhythm of notes to the frequencies of the pitches. At the advanced level, both mathematical theories and music theories help us understand the other subject. In this talk, we first explore what mathematics tells us about musical instruments, the basic tools of musical practice. In the second half, we flip sides, looking at music theory and how the structure of chords gives us another way to understand topological structures (circles, Möbius strips and higher dimensional tori), some of the basic tools of mathematical practice. Thus the first "movement" connects mathematical theory to musical practice, and the second "movement" connects musical theory to mathematical practice. Throughout, examples played on the violin will illustrate all of these beautiful and surprising connections.
We will show how physical metaphors can help us understand the structure of a graph. The graphs arising in different disciplines can have very different characteristics: social networks, protein-protein interactions networks, road networks, and scientific meshes are all graphs. But, they can look very different from each other. This diversity makes it difficult to understand arbitrary graphs.
We will explore an approach to understanding graphs that has been unreasonably successful: imagining that a graph represents a phyisical object. For example, we may pretend that the edges of a graph are springs, rubber bands, or resistors. Linear algebraic techniques for understanding these physical systems naturally lead to the development of spectral and algebraic graph theory. We will survey some of the fundamental ideas from these fields.
MathAcrossCampus is also made possible by the efforts of UW Mathematics graduate students Clayton Barnes, Gerandy Brito Montes de Oca, Christopher Fowler, Matthew Junge, Hon Leung Lee, Harishchandra Ramadas, and Richard Robinson.
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.