CHAN Song Heng
His research interests lie primarily in Number Theory, Combinatorics and Special functions, in particular, sums of squares formula, the partition function and various related functions, and q-series which includes modular forms, theta functions, and basic hypergeometric series.
ROBINS, Sinai
His research areas include Discrete and computational geometry, the combinatorial geometry of polytopes, analytic number theory and modular forms, and secure communications / cryptography.
His current research interests include the growing interplay between the continuous volume of a polytope and its discrete volume, the latter defined by the number of integer points that are contained in the polytope. Many branches of combinatorics, discrete geometry, and number theory can be unified using this interplay. Indeed, one of the main problems in encryption is to find the number of integer points that are contained inside a given parallelepiped whose vertices have rational coordinates.
Some of his recent research deals with extensions of angles to higher dimensions, where generalized angles – called solid angles – play a role in defining new discrete volumes of polytopes. Some of the Number Theory that comes into the general analysis consists of Dedekind Sums and their many higher dimensional generalizations.
Among the applications of the theory of discrete volumes of polytopes are the Frobenius coin exchange problem, the enumeration of doubly-stochastic matrices, new volume formulas for the Birkhoff polytopes and related transportation polytopes, and algorithms for integer flow networks.
Wang Huaxiong
His research areas are in cryptography, information security,
coding theory and combinatorics. His current research interests
include authentication codes, public-key cryptosystems,
digital signature schemes, hash functions, provable security,
broadcast encryption, secret sharing, secure multiparty computation,
key distributions, Private Information Retrieval, stream authentication,
cover-free families, perfect hash families etc.
YEO Sze Ling
Her research interests include counting the number of closed points on algebraic curves over finite fields as well as their applications, notably in coding theory and cryptography. In addition, she is keen to work on some of the fundamental number theoretic problems underlying the main public-key cryptosystems, such as the integer factorization and the discrete logarithm problems. .
ZHAO Liangyi
He studies analytic number theory. More specifically, he is interested in the theory of large sieve, mean-value type theorems, exponential and character sums, sieve methods, automorphic forms and elliptic curves. Some of his recent research deals with primes represented by polynomials, traces of Frobenius morphism for elliptic curves and analytic ranks of elliptic curves.