My current research deals with combinatorics, commutative algebra, and artificial intelligence.

Primary interests:

Particular interests:

A common theme in my research is the understanding of numerical or algebraic data via some underlying combinatorial structure, and I find it useful to draw ideas from other fields such as discrete geometry, algebraic geometry and algebraic topology.

Research grants and projects

Publications and preprints

  1. K. F. E. Chong, E. Nevo, "Flag complexes and homology," 14 pages. (preprint)
  2. K. F. E. Chong, T. S. Tay, "The face numbers of homology spheres," 31 pages. (preprint)
  3. K. F. E. Chong, "Generalized Macaulay representations and the flag f-vectors of generalized colored complexes," 28 pages. (preprint)
  4. K. F. E. Chong, "A closer look at the approximation capabilities of neural networks," Eighth International Conference on Learning Representations (ICLR), 2020, to appear.
  5. K. F. E. Chong, "An application of liaison theory to the Eisenbud–Green–Harris conjecture," J. Algebra, vol. 445, pp. 221--231, 2016. (preprint)
  6. K. F. E. Chong, "Hilbert functions of colored quotient rings and a generalization of the Clements–Lindström theorem," J. Algebraic Combinatorics, vol. 42, no. 1, pp. 1--23, 2015. (preprint)
  7. E. Kurniawan, K. F. E. Chong, S. Sun, K. Yen, "Application of FASTAR Code in Multimedia Broadcast Multicast Service," Proceedings of IEEE 73rd Vehicular Technology Conference (VTC) Spring 2011, pp. 1--5, May 2011.
  8. E. Kurniawan, K. F. E. Chong, S. Sun, K. Yen, "Outage analysis of Joint Channel-Network Coding and its dependence on the interleaver pattern," Proceedings of the IEEE Wireless Communications and Networking Conference (WCNC), 2011, pp. 2000--2005, Mar 2011.
  9. E. Kurniawan, S. Sun, K. Yen, and K. F. E. Chong, "Application of Network Coding in Rateless Transmission over Wireless Relay Networks," IEEE Transactions on Communications, vol. 59, no. 2, pp. 507--517, Feb 2011.
  10. E. Kurniawan, S. Sun, K. Yen, and K. F. E. Chong, "Improving error performance of Joint Channel and Network Coding in Multiple Access Relay Channel," Proceedings of the International Symposium on Information Theory and its Applications (ISITA), 2010, pp. 145--150, Oct 2010.
  11. K. F. E. Chong, E. Kurniawan, S. Sun, and K. Yen, "Fountain codes with varying probability distributions," Proceedings of the 6th International Symposium on Turbo Codes and Iterative Information Processing (ISTC), 2010, pp. 176--180, Sep 2010. (preprint)
  12. E. Kurniawan, S. Sun, K. Yen, and K. F. E. Chong, "Network Coded Transmission of Fountain Codes over Cooperative Relay Networks," Proceedings of the IEEE Wireless Communications and Networking Conference (WCNC), 2010, pp. 1--6, Apr 2010.

Other Research Papers

  1. K. F. E. Chong, and K. S. R. Poh, "On Riemann Zeta Function and Twin Prime Conjecture," Proceedings of the 15th Science Research Congress, organized by Faculty of Science, National University of Singapore and Gifted Education Branch, Ministry of Education, Singapore, March 18--19, 2003.
    This is the winning research paper (grand prize) at the Singapore National Science Talent Search in 2003, and I wrote it as a high school student. The National Science Talent Search is a research-based science competition in areas including Physics, Chemistry, Biology, Computer Science, and Mathematics, and I was the first grand winner in Singapore's history to win with a math research project. The grand prize includes $10,000 cash, and a scholarship that fully funds both my undergraduate and PhD studies. The main highlight of this paper is a new characterization of when p and p+2k are simultaneously prime numbers, where k is any fixed positive integer. Note however that it does not imply the twin prime conjecture (or the more general Polignac's conjecture).
  2. K. F. E. Chong, "The Weak Order of Coxeter Systems and the Combinatorial Properties of Descent Sets," Senior Thesis, May 2009, Cornell University, Department of Mathematics, Thesis Advisor: Edward Swartz.
    This is my senior thesis that I wrote as an undergraduate student. It deals with the combinatorial properties of descent sets in relation to the weak Bruhat order of finite Coxeter systems. The main results include a generalization of a proposition in Nyman-Swartz's paper ["Inequalities for the h-vectors and flag h-vectors of geometric lattices," Discrete Comput. Geom. 32 (2004) 533-548], and a partial answer to a problem posed in Swartz's paper ["g-elements, finite buildings and higher Cohen-Macaulay connectivity," J. Combin. Theory Ser. A 113 (2006) 1305-1320].