Geometry and analysis
Geometric analysis, differential geometry, minimal surfaces, and partial differential equations.
Research overview →Mathematics · University of Washington
Shaoda Ji
PhD student in mathematics
I work in geometric analysis, differential geometry, and partial differential equations. I am especially interested in geometry on manifolds, geometric visualization, and teaching mathematics both in person and online.
About
I am pursuing a PhD in the Department of Mathematics at the University of Washington, with an expected completion in 2030. My advisers are Jonathan Zhu and Yu Yuan.
Ideas made visible
Teaching experience in UW Math 124 and Math 125, together with a large online mathematics archive.
Teaching and outreach →Mathematical notes
Expository calculations and visual explanations developed from study, research, and teaching.
Read the notes →Featured work
A direct calculation of the Gaussian curvature formula for a graph in Euclidean three-space.
Expository note · July 2026
The Gaussian Curvature Formula for Graphs of Functions on R²
The note computes the curvature of the graph of a twice continuously differentiable function by differentiating the global unit normal and representing the resulting linear map in a tangent basis. At a critical point, the formula reduces to the determinant of the Hessian.
Selected updates
Recent academic and expository work.
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Gaussian curvature note added
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PhD studies at the University of Washington
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Teaching and mathematics outreach