Wai Kiu Chan

Email: wkchan [at] wesleyan.edu
Office: Exley Science Tower 617

Research

I am a Professor of Mathematics at Wesleyan University. My research interests are the arithmetic theory of quadratic forms and other related areas such as algebraic groups, lattices in Euclidean spaces, and modular forms.

Publications

[30] (with M. Icaza and E. Lauret) On a generalized Hermite constant for imaginary quadratic number fields, submitted.

[29] (with Anna Haensch) Almost universal ternary sums of squares and triangular numbers, to appear in ``Quadratic and Higher Degree Forms", Developments in Mathematics, Springer Verlag.

[28] (with L. Fukshansky) Small zeros of hermitian forms over a quaternion algebra, Acta Arith., 142 (2010), 251-266.

[27] (Edited with R. Baeza, D. Hoffmann, and R. Schulze-Pillot) Quadratic forms: algebra, arithmetic, and geometry, Contemporary Math. AMS, 493 (2009).

[26] (with B.-K. Oh) Almost universal ternary sums of triangular numbers, Proc. of AMS, 137 (2009), 3553-3562.

[25] (with M. Icaza) Positive definite almost regular ternary quadratic forms over totally real number fields, Bull. London Math. Soc., 40 (2008), 1025-1037.

[24] (with B.-M. Kim, M.-H. Kim and B.-K. Oh) Extensions of representations of integral quadratic forms, The Ramanujan Journal, 17 (2008), 145-153.

[23] (with C. Beli) Strong approximation for quadrics and representation of quadratic forms, J. Number Theory, 128 (2008), 2091-2096.

[22] (with A. G. Earnest, M. Icaza and J.-Y. Kim) Finiteness results for regular definite ternary quadratic forms over $\mathbb Q(\sqrt{5})$, Int. J. Number Theory, Vol 3, Issue 4 (2007), 541-556.

[21] (with A. Rokicki) Positive definite binary hermitian forms with finitely many exceptions, J. Number Theory, 124 (2007), 167-180.

[20] (with R. Dan Mauldin) Steinhaus tiling problem and integral quadratic forms, Proc. of AMS, 135 (2007), 337-342.

[19] (with J. Daniels) Definite regular quadratic forms over $\mathbb F_q[T]$, Proc. of AMS, 133 (2005), no. 11, 3121-3131.

[18] (with A. G. Earnest) Discriminant bounds for spinor regular ternary quadratic lattices, Journal London Math. Soc. (2) 69 (2004), 545-561.

[17] On almost strong approximation for some exceptional groups, J. Algebra, 277 (2004), no.1, 27-35.

[16] (with M. Peters) Quaternary quadratic forms and Hilbert modular surfaces, Contemporary Math. AMS, 344 (2004), 85-97.

[15] (with M. Icaza) Effective results on representations of quadratic forms, Contemporary Math. AMS, 344 (2004), 73-83.

[14] (with A. G. Earnest and B.-K. Oh) Regularity properties of positive definite integral quadratic forms, Contemporary Math. AMS, 344 (2004), 59-71.

[13] (with F. Xu) On representations of spinor genera, Compositio Math., 140 (2004), no.2, 287-300.

[12] (with B.-K. Oh) Positive ternary quadratic forms with finitely many exceptions, Proc. of AMS, 132 (2004), no.6, 1567-1573.

[11] (with B.-K. Oh) Finiteness theorems for positive definite $n$-regular quadratic forms, Trans. of AMS, 355 (2003), no.6, 2385-2396.

[10] (with J. S. Hsia) On almost strong approximation for algebraic groups, J. Algebra, 254 (2002), no.2, 441-461.

[9] Class numbers of quaternary quadratic forms of discriminant $4p$, Contemporary Math. AMS, 249 (1999), 29-41.

[8] Quaternary even positive definite quadratic forms of discriminant $4p$, J. Number Theory, 76 (1999), no.2, 265-280.

[7] Spinor genera under ${\mathbb Z}_p$-extension, Pacific J. Math., 185 (1998), no.2, 237-267.

[6] (with D. R. Estes and M. J\"{o}chner) Representations of codimension $\geq 3$ by definite quadratic forms, J. Number Theory, 71 (1998), 81-85.

[5] (with Y. C. Chan and M. K. Siu) Minimal rank of abelian group matrices, Linear and Multilinear Alg., 44 (1998), no.3, 277-285.

[4] (with M.-H. Kim and S. Raghavan) Ternary universal integral quadratic forms over real quadratic fields, Japanese J. Math., 22 (1996), no.2, 263-273.

[3] (with S. L. Ma and M. K. Siu) Nonexistence of certain perfect arrays, Disc. Math., 125 (1994), no.1-3, 107-113.

[2] Necessary conditions for Menon difference sets, Designs, Codes and Crypt., 3 (1993), no.2, 147-154.

[1] (with M. K. Siu) A summary of perfect $s\times t$ arrays, $1\leq s\leq t \leq 100$, Electron. Lett., 27 (1991), 709-710.

Joshua Daniels (MA 2004) , On definite regular ternary quadratic forms over F_q[T].

Anna Rokicki (PhD 2005), Finiteness results for definite n-regular and almost n-regular Hermitian forms.

Daniel Greengard (MA 2008), Representations of definite quadratic forms over F_q[T].

Anna Radlowski (MA 2009), Small zeros of quadratic forms over function fields.

Glenn Henshaw (PhD 2012), Search bounds for points in linear and quadratic spaces.

Anna Haensch , current PhD student.

James Ricci, current PhD student.

Jingbo Liu, current PhD student.