Fall 2017 Projects
Title: Music and Geometry
Project Mentor: Arindam Roy
Graduate Mentor: Yikai Chen
Description: People spent hundreds of years to build the western music system based on tonality. The complicated structure and variations fascinate some mathematicians as well as musicians. One can use Fourier analysis to explain and recreate the sound of musical instruments by vibration of strings. But it takes more than making sound to create music. In 2011, Dr. Dmitri Tymoczko published A Geometry of Music, brought the possibility of understanding what was going on in those great composers’ mind mathematically. In this project, we will explore the structure of western music by using mathematical ideas like distance, symmetries, and finally embedding into a specific geometric structure.
Title: Understanding the works by Nash on isometric embeddings
Project Mentor: Siran Li
Graduate Mentor: Xian Dai
Description: In the project let us study the works by the legendary mathematician, J. F. Nash Jr., on the existence of isometric embeddings/immersions of Riemannian manifolds into Euclidean spaces. His work on $C^1$ isometric immersions has later been developed into the $h$-principle by M. Gromov, and in his work on $C^\infty$ isometric immersions, the now-standard technique known as the Nash-Moser (hard) Inverse Function Theorem has been developed..
Rice Geometry Lab Fall 2017 Poster Presentation
Please join us for the Rice Geometry Lab poster session.
December 1, 4:30 PM
Herman Brown Hall 438
Refreshments will be served!
Office: 456 Herman Brown Hall