Your Name

About Me

Welcome! I am a PhD candidate in the Department of Mathematics at Your University, advised by Prof. Advisor's Name. My research lies at the intersection of Geometric Analysis and Partial Differential Equations, with a focus on the long-time behavior of nonlinear dispersive systems.

Email: your.name@university.edu
Office: Room 123, Math Building

Research Interests

I am broadly interested in analytical aspects of mathematical physics. My current work involves:

• Strichartz estimates and scattering theory for the inhomogeneous nonlinear Schrödinger equation: $$ i\partial_t u + \Delta u = |x|^{-b} |u|^{p-1}u. $$
• Stability of soliton solutions in non-integrable models.
• Microlocal analysis and propagation of singularities.

Here is an example of an inline formula: The energy \( E(u) = \frac{1}{2} \int_{\mathbb{R}^d} |\nabla u|^2 dx - \frac{\lambda}{p+1} \int_{\mathbb{R}^d} |u|^{p+1} dx \) is conserved.

Recent Preprints & Publications

Teaching

• Spring 2024: Teaching Assistant for MATH 301 - Real Analysis I.
• Fall 2023: Instructor for MATH 101 - Calculus with Applications.