## Rice Geometry Laboratory

Rice Geometry Laborary (RGL) In the Department of Mathematics is designed to encourage and support undergraduate research through computational projects. Each project will have a faculty and graduate student mentor.

Fall 2017 Projects

Title: Music and Geometry
Project Mentor: Arindam Roy

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

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..

Fall 2017 News

## Rice Geometry Laboratory Information Session September 15, 5:30 - 6:30 PM Herman Brown Hall 227

Pizza will be served!

The Rice geometry lab is a unique research opportunity for undergraduates. In this lab, undergraduate students will work closely with graduate students on visualization projects set forth by a faculty member or a postdoc.

Other labs around the country: http://geometrylabs.net

If you cannot come to the info session and want more information please send an email to Arindam.Roy@rice.edu.

Hope to see you there!

Organizers

 Arindam RoyOffice: 456 Herman Brown HallEmail: Arindam.Roy@rice.edu Tony Várilly-Alvarado