#### Research Interests

My general interests are in graph theory and theoretical computer science. Recently, I have been focusing on *topological graph theory*, in particular embeddings of dense graphs in surfaces and problems related to the Map Color Theorem, and *randomized algorithms*, in particular property testing and sublinear algorithms. In the past I did some work in computer graphics and discrete geometry.

#### Recent Papers

- Settling the genus of the
*n*-prism
- T. Sun,
*manuscript*
- Jungerman ladders and index 2 constructions for genus embeddings of dense regular graphs
- T. Sun,
*in preparation*
- A Lower Bound on Cycle-Finding in Sparse Digraphs
- X. Chen, T. Randolph, R. Servedio, T. Sun,
*SODA 2020*, invited to special issue of ACM Trans. Algs.
- Simultaneous constructions for minimum triangulations and complete graph embeddings
- T. Sun,
*Ars Mathematica Contemporanea 18(20) (2020) 309-337*
- A simple construction for orientable triangular embeddings of the complete graphs on 12s vertices
- T. Sun,
*Discrete Mathematics 342(4) (2019) 1147-1151* [preprint]
- Face distributions of embeddings of complete graphs
- T. Sun,
*Journal of Graph Theory, available online* [preprint]
- Sample-based high-dimensional convexity testing
- X. Chen, A. Freilich, R. Servedio, T. Sun,
*RANDOM 2017* [full version]

#### Tools

- Heffter-Edmonds Face Tracer
- For computing the genus of a rotation system of a simple graph.

#### Older Work

- Deployable 3D Linkages With Collision Avoidance
- C. Zheng,
**T. Sun**, X. Chen, *ACM/EG SCA 2016 (Best Paper Award)*
- Computational Design of Twisty Joints and Puzzles
**T. Sun**, C. Zheng, *ACM SIGGRAPH (Proc. Trans. on Graphics) 2015*
- Fast Multipole Representation of Diffusion Curves and Points
**T. Sun**, P. Thamjaroenporn, C. Zheng, *ACM SIGGRAPH (Proc. Trans. on Graphics) 2014*
- Genus distributions of cubic series-parallel graphs
- J. L. Gross, M. Kotrbčik, T. Sun,
*Discrete Math. and Theoretical Comp. Sci. 16(3) (2014)*
- On Milgram's construction and the Duke embedding conjectures
- T. Sun,
*senior thesis, Columbia University (advisor: Jonathan L. Gross)*
- Drawing some 4-regular planar graphs with integer edge lengths
- T. Sun,
*25th Canadian Conference on Computational Geometry (2013)*
- Rigidity-theoretic constructions of integral Fary embeddings
- T. Sun,
*23rd Canadian Conference on Computational Geometry (2011)*