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

- 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

- 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

Classical Modular Forms

Automorphic Forms on Real Groups

Automorphic Forms on Adele Groups

Eisenstein Series

Multiplicity One for GL(n)

Tate's Thesis

Automorphic L-functions

Local Langlands Correspondence

Restriction of representations of classical groups

Representations and automorphic forms of metaplectic groups

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