Kai Fong Ernest Chong

My current research deals with **combinatorics**, **commutative algebra**, and **machine learning**.

*Primary interests:*

- algebraic, geometric, topological, and enumerative combinatorics
- combinatorial and computational commutative algebra
- theoretical and computational aspects of deep learning

*Particular interests:*

*f*-vectors and flag*f*-vectors of various classes of simplicial complexes, posets, polytopes, and triangulated manifolds- Hilbert functions and graded Betti numbers of various classes of graded rings and modules
- unsupervised and semi-supervised learning, architecture hyperparameters of neural networks

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.

- K. F. E. Chong, T. S. Tay, "The face numbers of homology spheres," 31 pages. (preprint)
- K. F. E. Chong, "Generalized Macaulay representations and the flag
*f*-vectors of generalized colored complexes," 28 pages. (preprint) - K. F. E. Chong, "An application of liaison theory to the Eisenbud–Green–Harris conjecture,"
*J. Algebra*, vol. 445, pp. 221--231, 2016. (preprint) - 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) - 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. - 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. - 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. - 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. - 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) - 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.

- 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). - 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].