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Research Interest
Research Interest
My research focuses on low-dimensional topology, intersecting with discrete geometry, statistical mechanics, and differential geometry. By leveraging insights from classical smooth theories, I develop analogous tools and results in the discrete setting. This offers new perspectives for addressing interdisciplinary problems and has immediate applications in computational geometry. This approach aligns with the broader framework of discrete differential geometry, understood as the study of structure-preserving discretizations.
A recurring theme in my research is the use of circle packings as discrete conformal maps.
What is Discrete Differential Geometry?
What is Discrete Differential Geometry?
For an introduction, I recommend the lecture notes from TU Berlin, which begin with polygonal curves in space. If you are familiar with parameterized surfaces (which is not usually covered in an introductory differential geometry course), you might find Bobenko and Suris's book valuable, as it approaches the topic from the perspective of discrete integrable systems. For those interested in practical applications, Keenan Crane's notes provide an excellent resource.
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