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.
PREPRINTS
- Jungerman ladders and index 2 constructions for genus embeddings of dense regular graphs
- T. Sun, accepted to the European Journal of Combinatorics
- Face-simple minimal quadrangulations of surfaces
- S. Abusaif, W. Singh, T. Sun, submitted
RECENT PUBLICATIONS
- Commutators in the Rubik's Cube group
- T. Sun, American Mathematical Monthly, 131(1) (2024) 3-19 [online supplement]
- Index 3 biembeddings of the complete graphs
- J. F. Barajas, T. Sun, Discrete Mathematics 347(1) (2024) 113688
- Settling the nonorientable genus of the nearly complete bipartite graphs
- W. Singh, T. Sun, Graphs and Combinatorics 39 (2023) 96 [preprint]
- Settling the genus of the n-prism
- T. Sun, European Journal of Combinatorics 110 (2023) 103667
- AAnim: an Animation Engine for Visualizing Algorithms and Data Structures for Educators
- Z. J. Liu, T. Sun, SIGCSE TS 2023 Posters [abstract]
- 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]
- On the bigenus of the complete graphs
- T. Sun, Australasian Journal of Combinatorics 84(1) (2022) 212-219
- Face distributions of embeddings of complete graphs
- T. Sun, Journal of Graph Theory 97(2) (2021) 281-304 [preprint]
- 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]
- Sample-based high-dimensional convexity testing
- X. Chen, A. Freilich, R. Servedio, T. Sun, RANDOM 2017 [full version]
MATHEMATICAL ARTWORK
- Neighborly Nine
- T. Sun, Bridges 2023 Art Exhibition
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)