Mathematics Department
University of California, San Diego
9500 Gilman Drive
La Jolla, CA 92093-0112
USA
E-mail: wganAATTmath.ucsd.edu
Phone: (858) 534-0997 (office)
Fax: (858) 534-5273
Teaching
Representation Theory Seminar
Recent Papers and Preprints
- Trilinear forms and triple product epsilon factor, pdf , International Mathematics Research
Notices 2008 2008: rnn058-15
- Formal degrees and local theta correspondence (with W. Tantono), in
preparation
- The local Langlands conjecture for GSp(4) II: the case of inner forms
(with W. Tantono), in preparation
- The regularized Siegel-Weil formula: second term identity and
non-vanishiing of theta lifts from orthogonal groups (with S. Takeda),
- The local Langlands conjecture for GSp(4) (with S. Takeda),
pdf
- The local Langlands conjecture for Sp(4) (with S. Takeda),
pdf
- On Shalika periods and a conjecture of Jacquet-Martin (with S.
Takeda),
pdf
- Restrictions of Saito-Kurokawa representations (with N. Gurevich),
to appear in proceedings of Gelbart's 60th birthday conference. pdf
- CAP representations of G_2 and the Spin L-function of PGSp_6 (with
N. Gurevich), to appear in Israel J. of Math. pdf
- A regularized Siegel-Weil formula for exceptional groups, in
preparation.
- A Siegel-Weil formula for automorphic characters: cubic variation of
a theme of Snitz, to appear in Crelle.
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, to appear in the proceedings of the AIM workshop "Eisenstein Series
and Applications" (Palo Alto, Aug 2005). 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.
ps
- 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
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)
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