Description：

The four lectures start with the definition of calibrations, introduce area-minimizing currents and singularities, and end with my results on fractal and persistent singularities and the limits of calibrations. Examples and proof sketches guide the course.

Prerequisite：

Basic analysis and linear algebra. Necessary geometric notions will be introduced.

Reference：

R. Harvey and H. B. Lawson, Jr., “Calibrated geometries,” Acta Mathematica 148 (1982).

L. Simon, Lectures on Geometric Measure Theory, ANU (1983).

Target Audience：Undergraduate and graduate students.

Teaching Language：English and Chinese, depending on the audience.

Bio: Visiting Researcher at Duke University. Ph.D. in mathematics, Princeton University, January 2026.

Fields of Research: Geometric measure theory; calibrations.

Registration: https://www.wjx.top/vm/QN5phd6.aspx#