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.

- Index 3 biembeddings of the complete graphs
- J. F. Barajas, T. Sun,
*submitted* - AAnim: an Animation Engine on Visualizing Algorithms and Data Structures for Educators
- Z. J. Liu, T. Sun,
*to appear in SIGCSE TS 2023 Posters*[abstract] - Commutators in the Rubik's Cube group
- T. Sun,
*to appear in the American Mathematical Monthly*[preprint] - On the bigenus of the complete graphs
- T. Sun,
*Australasian Journal of Combinatorics 84(1) (2022) 212-219* - Settling the genus of the
*n*-prism - T. Sun,
*European Journal of Combinatorics 110 (2023) 103667* - 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,
*ACM Trans. Algs. 18(4) (2022) #31 (SODA 2020)*[conference version] - 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 97(2) (2021) 281-304*[preprint] - Sample-based high-dimensional convexity testing
- X. Chen, A. Freilich, R. Servedio, T. Sun,
*RANDOM 2017*[full version]

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

- 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)*