Division of Applied Mathematics
I am a fifth year graduate student in the Division of Applied Math here at Brown. My thesis advsior is Walter Strauss. My undergraduate degree is a B.S. in Mathematical Sciences from Carnegie Mellon University. I also spent a year as an exchange student at Keio University.
My research centers on the study of steady water waves, particularly those that are periodic, and exhibit a heterogeneous density distribution. These waves are ubiquitous in nature and a classical object of interest. Nonetheless, significant progress in describing them mathematically has only been made quite recently, and a number of fundamental questions remain largely open. My main contribution has been to establish the existence of global continua of solutions with variable density, both with or without surface tension.
For an overview of my work to date, as well as some future projects, please see my research statement [pdf]. A summary of my teaching and research experience can be found in my CV [pdf].
Nonlinear partial differential equations, elliptic equations, bifurcation theory, water waves, stratification, capillary-gravity waves, geophysical fluid dynamics.
1. Stratified steady periodic water waves, SIAM J. Math. Anal., 41 (2009), pp. 1054--1105 [preprint].
2. Steady periodic gravity waves with surface tension, submitted (2009). [preprint].
3. Some criteria for the symmetry of stratified water waves, Wave Motion, 46 (2009), pp. 350--362. [preprint].
AMS Joint Mathematics Meeting, January 2010.
Contributed talk for session on Differential and Difference Equations (I).
SIAM Conference on Analysis of PDE, December 2009.
Invited talk for session on Mathematical Topics of Surface Water Waves (MS37).
Wave Motion Workshop (Mathematisches Forschungsinstitut Oberwolfach)
Talk: Stratified steady water waves [pdf]. (Many thanks to Andreas Klöckner for his beamer theme)
2008 Center for Nonlinear Analysis Summer School (Carnegie Mellon University)
Nonlinear Waves Conference in Honor of Walter Strauss (Brown University)
11th Riviere-Fabes Symposium on Analysis and PDE (University of Minnesota)
I am not currently teaching any courses.
Instructor for MATH 0200: Intermediate Calculus (Physics/Engineering), Fall 2009.
TA for APMA 0650: Essential Statistics, Spring 2009, Brown.
Instructor: Stuart Geman.
TA for APMA 0330: Methods of Applied Mathematics I, Fall 2007, Brown.
Instructors: Bo Dong, Vladimir A. Dobrushkin.
TA for APMA 0340: Methods of Applied Mathematics II, Spring 2007, Brown.
Instructor: Suzanne Sindi.
TA for APMA 0330: Methods of Applied Mathematics I, Fall 2006, Brown.
Instructors: Suzanne Sindi, Natalie Kleinfelter Domelle.
TA for 21-127: Concepts of Mathematics, Spring 2005, CMU.
Instructor: John Mackey.
TA for 21-122: Integration, Differential Equations, and Approximation, Fall 2004, CMU.
Instructor: Katherine Thompson.