**Some of my papers/preprints**

**Expository Notes**

The cocenter-representation duality.

Note on affine Deligne-Lusztig varieties.

Notes on partial conjugation (with C. Fang), Fifth International Congress of Chinese Mathematicians, 171-181, AMS/IP Stud. Adv. Math., 51, 2012.

**Papers on Algebraic Geometry**

Families of rationally simply connected varieties over surfaces and torsors for semisimple groups (with J. de Jong and J. Starr), Publ. IHES 114 (2011), 1--85.

Frobenius splitting and geometry of $G$-Schubert varieties (with J. F. Thomsen), Adv. Math. 219 (2008) 1469--1512.

Geometry of $B \times B$-orbit closures in equivariant embeddings (with J. F. Thomsen), Adv. Math, 216 (2007), 626--646.

**Papers on Arithmetic Geometry**

Kottwitz-Rapoport conjecture on unions of affine Deligne-Lusztig varieties.

Basic loci in Shimura varieties of Coxeter type (with U. Goertz), Cambridge Journal of Mathematics 3 (2015), 323--353.

$P$-alcoves and nonemptiness of affine Deligne-Lusztig varieties (with U. Goertz and S. Nie), Ann. Sci. Ecole Norm. Sup. 48 (2015), 647--665.

Geometric and homological properties of affine Deligne-Lusztig varieties, Ann. Math. 179 (2014), 367--404.

Normality and Cohen-Macaulayness of local models of Shimura varieties, Duke Math. J., 162 (2013), 2509-2523.

**Papers on Combinatorics of Weyl groups**

Minimal length elements of extended affine Weyl group (with S. Nie), Compos. Math. 150 (2014), 1903--1927.

Minimal length elements of finite Coxeter group (with S. Nie), Duke Math. J., 161 (2012), 2945-2967.

Minimal length elements in some double cosets of Coxeter groups, Adv. Math. 215 (2007), 469--503.

**Papers On Representation theory**

Cocenters and representations of affine Hecke algebras (with D. Ciubotaru), to appear in JEMS.

Green polynomials of Weyl groups, elliptic pairings, and the extended Dirac index (with D. Ciubotaru), Adv. Math. 283 (2015), 1--50.

A generalization of Steinberg's cross-section (with G. Lusztig), J. Amer. Math. Soc. 25 (2012), 739-757.

Character sheaves on the semi-stable locus of a group compactification, Adv. Math. 225 (2010), 3258--3290.

Singular supports for character sheaves on a group compactification (with G. Lusztig), Geom. Funct. Anal. 17 (2008), no. 6, 1915--1923.

Character sheaves on certain spherical varieties, Adv. Math. 217 (2008), 1154--1191.

The $G$-stable pieces of the wonderful compactification, Trans. Amer. Math. Soc. 359 (2007), 3005--3024.

The character sheaves on the group compactification, Adv. Math. 207 (2006), 805--827.

Unipotent variety in the group compactification, Adv. Math. 203 (2006), 109--131.

**Some other papers**

Projected Richardson varieties and affine Schubert varieties (with T. Lam).

Parametrization of orbits on double flag variety of finite type (with K. Nishiyama, H. Ochiai and Y. Oshima), Transformation Groups 18 (2013), 1091-1136.

Semi-stable locus of a group compactification (with J. Starr), Represent. Theory 15 (2011), 574--583.

On intersections of certain partitions of a group compactificaiton (with J.-H. Lu), Int. Math. Res. Notices 11 (2011), 2534--2564.

On the closure of Steinberg fibers in the wonderful compactification (with J. F. Thomsen), Transformation Groups, 11 (2006), no. 3, 427--438.