Wee Teck Gan

Wee Teck Gan

How to reach me

Mathematics Department
National University of Singapore
Block S17, 10 Lower Kent Ridge Road
Singapore 119076

E-mail: matgwt(AT)nus(\cdot)edu.sg
Phone: +65-6516-2739 (office)
Fax: +65-67795452

Teaching

Fall 2003: Math109: Mathematical Reasoning
Winter 2004: Math20C: Calculus and Analytic Geometry
Fall 2004: Math103A: Applied Modern Algebra
Winter 2005: Math207B: Elliptic Curves and Modular Forms
Spring 2006: Math104A: Number Theory and Math200C: (Graduate) Algebra
Fall 2006: Math104A: Number Theory and Math251A: Lie Groups
Winter 2007: Math251B: Lie Groups
Spring 2007: Math205: L-functions and Modular Forms
Fall 2007: Math20D: Ordinary Differential Equations and Math 204: Algebraic Number Theory
Winter and Spring 2008: Math203: Algebraic Geometry
Fall 2008: Math140A: Foundations of Analysis, and Math204: Analytic Number Theory
Winter 2010: Math20F: Linear Algebra, and Math202B: Applied Algebra (aka Representation theory of finite groups)
2010-2011: Semester 1: MA3265: Introduction to Number Theory; Semester 2: MA6292 : Topics in Mathematics II (Trace formula for GL(2))
2011-2012: Semester 1: MA2202S: Algebra I S; Semester 2: MA 5204: Graduate Algebra II
2012-2013: Semester 1: MA 4203: Galois theory; Semester 2: MA 5204: Graduate algebra II

Papers and Preprints

The metaplectic tensor product as an instance of Langlands functoriality, pdf
Local theta correspondence of tempered representations and Langlands parameters (with H. Atobe), pdf
On the local Langlands correspondence and Arthur conjecture for even orthogonal groups (with H. Atobe), pdf
The Langlands-Weissman program for Brylinski-Deligne extensions (with F. Gao), pdf
Globalization of supercuspidal representations over function fields and applications (with L. Lomeli), to appear in Journal of European Math Soc. pdf
The Gross-Prasad conjecture and local theta correspondence (with A. Ichino), to appear in Inventiones Math. pdf
The Howe duality conjecture: quaternionic case (with B.Y. Sun), to appear in Contemporary Math (volume in honor of R. Howe's 70th birthday). pdf
A proof of the Howe duality conjecture (with S. Takeda), J. of American Math. Society 29 (2016), no. 2, 473-493. pdf
On the Howe duality conjecture in classical theta correspondence (with S. Takeda), to appear in Contemporary Math. (volume in honor of J. Cogdell's 60th birthday). pdf
Theta correspondence: recent progress and applications, Procedings of ICM (2014) Vol. 2, 343-366. pdf
Twisted Bhargava cubes (with G. Savin), Algebra and Number Theory 8 (2014), no 8, 1913-1957. pdf
Recent progress on the Gross-Prasad conjecture (a survey talk given at the annual meeting of VIASM, July 2013), Acta Math Vietnam 39 (2014), no. 1, 11-33. pdf
A Langlands program for covering groups? (a talk given at the Sixth International Congress of Chinese Mathematicians, July 2013), pdf
The regularized Siegel-Weil formula (the second term identity) and the Rallis inner product formula (with Y. Qiu and S. Takeda), Inventiones Math. 198 (2014), 739-831. pdf
The local Langlands conjecture for GSp(4) II: the case of inner forms (with W. Tantono), American J. of Math 136 (2014), no. 3, 761-805. pdf
The local Langlands conjecture for GSp(4) III: stability and twisted endoscopy (with P. S. Chan), J. of Number Theory 146 (2015) (memorial issue for Steve Rallis), 69-133. pdf
Arithmeticity for periods of automorphic forms (with A. Raghuram), in ``Automorphic Representations and L-functions", Tata Inst. Fundam. Res. Stud. Math. 22 (2013), 187-229. pdf
On a conjecture of Sakellaridis-Venkatesh on the unitary spectrum of spherical vareities (with R. Gomez), in "Symmetry: representation theory and its applications", Progress in Math 257 (2014), Birkhauser/Springer, 185-226. pdf
Formal degrees and local theta correspondence (with A. Ichino), Inventiones Math 195 (2014), 509-672. pdf
The Shimura correspondence a la Waldspurger (Notes of a short course given at the Postech Theta Festival) pdf
Representation of metaplectic groups, Fifth International Congress of Chinese Mathematicians. Part 1, 2, 155-170, AMS/IP Stud. Adv. Math., 51, pt. 1, 2, Amer. Math. Soc., Providence, RI, 2012 pdf
Doubling zeta integrals and local factors for metaplectic groups, Nagoya Math. Journal 208 (2012), 67-95 (a volume in memory of Hiroshi Saito) pdf
Representations of metaplectic groups II: Hecke algebra correspondences (with G. Savin), Represent. Theory 16 (2012), 513-539 pdf
Representations of metaplectic groups I: epsilon dichotomy and local Langlands correspondence (with G. Savin), Compositio Mathematica, volume 148, issue 06, pp. 1655-1694 pdf
Restriction of representations of classical groups: examples (with B. H. Gross and D. Prasad), Asterisque 346, 111-170. pdf
Symplectic local root numbers, central critical L-values and restriction problems in the representation theory of classical groups (with B. H. Gross and D. Prasad), Asterisque 346, 1-110. pdf
Bessel and Fourier-Jacobi Models of the Weil Representation, in preparation.
A regularized Siegel-Weil formula for exceptional groups, in Arithmetic geometry and automorphic forms, 155-185 (a volume in honor of Steve Kudla),2, Adv. Lect. Math. (ALM), 19, Int. Press, Somerville, MA, 2011 pdf
On endoscopy and the refined Gross-Prasad conjecture for (SO_5,,SO_4) (with A. Ichino), J. Inst. Math. Jussieu 10 (2011), no. 2, 235-324 pdf
The regularized Siegel-Weil formula: second term identity and non-vanishiing of theta lifts from orthogonal groups (with S. Takeda), J. Reine Angew. Math. 659 (2011), 175-244. pdf
Theta Correspondences for GSp(4) (with S. Takeda), Represent. Theory 15 (2011), 670–718. pdf
The local Langlands conjecture for GSp(4) (with S. Takeda), Ann. of Math. (2) 173 (2011), no. 3, 1841-1882 pdf
The local Langlands conjecture for Sp(4) (with S. Takeda), Int. Math. Res. Not. IMRN 2010, no. 15, 2987-3038. pdf
On Shalika periods and a theorem of Jacquet-Martin (with S. Takeda), American J. of Math. 132 (2010), 475-528, pdf
Trilinear forms and triple product epsilon factor, International Mathematics Research Notices 2008 2008: rnn058-15, pdf
Restrictions of Saito-Kurokawa representations (with N. Gurevich), With an appendix by Gordan Savin. Contemp. Math., 488, Automorphic forms and L-functions I. Global aspects, 95–124, Amer. Math. Soc., Providence, RI, 2009. pdf
CAP representations of G_2 and the Spin L-function of PGSp_6 (with N. Gurevich), Israel J. Math. 170 (2009), 1–52. pdf
A Siegel-Weil formula for automorphic characters: cubic variation of a theme of Snitz, J. Reine Angew. Math. 625 (2008), 155-185. pdf
The Spin L-function of quasi-split D_4 (with J. Hundley), in International Math Research Papers Vol. 2006 (Article ID 68213), 1-74.. pdf
The Saito-Kurokawa space of $PGSp_4$ and its transfer to inner forms, in Eisenstein series and applications, 87–123, Progr. Math., 258, Birkhäuser Boston, Boston, MA, 2008. pdf
Non-tempered Arthur packets of $G_2$: liftings from $\tilde{SL}_2$ (with N. Gurevich), American Journal of Math 128, No. 5 (2006), 1105-1185. pdf
The Rallis-Schiffmann lifting and Arthur packets of $G_2$ (with N. Gurevich, an announcement of the results of the above long paper), Quarterly Journal of Pure and Applied Math Vol 1, No 1 (2005), 109-126. pdf
Multiplicity formula for cubic unipotent Arthur packets, Duke Math Journal 130, no. 2 (2005), 297-320. pdf
The mass of unimodular lattices (with M. Belolipetsky), J. of Number Theory 114 (2005),221-237. pdf
Non-tempered Arthur packets of $G_2$ (with N. Gurevich), in proceedings of Rallis' 60th birthday conference: "Automorphic Representations, L-functions and Applications:Progress and Prospects", 129-155. pdf
Uniqueness of Joseph ideal (with G. Savin), Math. Research Letters 11 (2004), No. 5-6, 589-598. pdf
On minimal representations: definitions and properties (with Gordan Savin), Representation Theory Vol 9 (2005), 46-93. pdf
Real and global lifts from $PGL_3$ to $G_2$ (with G. Savin), IMRN 2003, Vol. 50 (2003). pdf
Endoscopic lifts from $PGL_3$ to $G_2$ (with Gordan Savin), Compositio Math 140, No. 3 (2004), 793-808. pdf
Cubic unipotent Arthur parameters and multiplicities of square-integrable automorphic forms (with N. Gurevich and D.H. Jiang), Invent. Math. 149 (2002), 225-265. pdf
Schemas en groupes et immeubles des groupes exceptionels sur un corp locale. Deuxieme partie: les groupes $F_4$ et $E_6$ (with J.-K. Yu), Bulletin Math. Soc. France 133 (2005), no. 2, 159--197. ps
pdf
Schemas en groupes et immeubles des groupes exceptionels sur un corp locale. Premiere partie: le groupe $G_2$ (with J.-K. Yu), Bull. Math. Soc. France 131 (2003), 307-358. ps
Equidistribution of integer points on a family of homogeeneous varieties: a problem of Linnik (with H. Oh), Compositio Math. 323 (2003), 323-352. pdf
Fourier coefficients of modular forms on $G_2$ (with B. H. Gross and G. Savin), Duke Math. Journal 115 (2002), 105-169. pdf
On an exact mass formula of Shimura, (with J. Hanke and J.-K. Yu), Duke Math. J. 107 (2001), 101-131. pdf
A Siegel-Weil formula for exceptional groups, Crelle 528 (2000), 149-181. pdf
Group schemes and local densities (with J.-K. Yu), Duke Math. J. 105 (2000), 497-524. pdf
Integral embeddings of cubic norm structures (with B. H. Gross), J. Algebra 233 (2000), no. 1, 363--397. pdf
Commutative subrings of certain non-associative rings (with B. H. Gross), Math. Ann. 314 (1999), no. 2, 265--283. pdf
An automorphic theta module for quaternionic exceptional groups. Canad. J. Math. 52 (2000), no. 4, 737--756. pdf
The dual pair $G\sb 2\times {\rm PU}\sb 3(D)$ ($p$-adic case) (with G. Savin), Canad. J. Math. 51 (1999), no. 1, 130--146. pdf
Exceptional Howe correspondences over finite fields. Compositio Math. 118 (1999), no. 3, 323--344. pdf
Haar measure and the Artin conductor (with B. H. Gross), Trans. Amer. Math. Soc. 351 (1999), no. 4, 1691--1704. pdf
A note on Kottwitz's invariant $e(G)$. J. Algebra 208 (1998), no. 1, 372--377. pdf
Modular forms of level $p$ on the exceptional tube domain (with H. Y. Loke), J. Ramanujan Math. Soc. 12 (1997), no. 2, 161--202. pdf

Talks and Course Notes

Slides of a short course on automorphic forms given in Hangzhou, China (Summer 2004). They may contain some minor inaccuracies which I'm too lazy to correct right now.

Classical Modular Forms
Automorphic Forms on Real Groups
Automorphic Forms on Adele Groups
Eisenstein Series
Multiplicity One for GL(n)

Slides of two lectures on Tate's thesis and Automorphic L-functions given in Seville (Oct 2009)

Tate's Thesis
Automorphic L-functions

Slides of a colloquium talk on the local Langlands correspondence given at Univ. of Michigan (Dec 2009)

Local Langlands Correspondence

Slides of a talk on the Gross-Prasad conjecture given at Chinese University of Hong Kong (Sept 2010)

Restriction of representations of classical groups

Slides of talk at the ICM satellite conference (Goa, Aug 2010) and the ICCM

Representations and automorphic forms of metaplectic groups

Notes of a representation theory course given in Princeton (not completed. I'll work on it if I get to teach a similar course again)

Weeks 1 and 2: Haar measure and Peter-Weyl theorem
Week 3: Basic Lie theory
Week 4.1: Linear algebraicity and Complexification
Week 4.2: Maximal Tori
Week 5.1: Abstract Root Systems
Week 5.2: Root Systems of Compact Lie Groups