**Some of my papers/preprints**

**Expository Notes**

Some results on affine Deligne-Lusztig varieties, to appear in the proceeding of ICM 2018.

Hecke algebras and $p$-adic groups, Current developments in mathematics 2015, 73--135, Int. Press, Somerville, MA, 2016.

**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**

Good and semi-stable reductions of Shimura varieties (with G. Pappas and M. Rapoport).

Fully Hodge-Newton decomoposable Shimura varieties (with U. Goertz and S. Nie).

On the connected components of affine Deligne-Lusztig varieties (with R. Zhou).

On the $\mu$-ordinary locus of a Shimura variety (with S. Nie), Adv. Math. 321 (2017), 513--528.

Stratifications in the reduction of Shimura varieties (with M. Rapoport), Manuscripta Math. 152 (2017), 317--343.

Kottwitz-Rapoport conjecture on unions of affine Deligne-Lusztig varieties, Ann. Sci. Ecole Norm. Sup. 49 (2016), 1125--1141.

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 of $p$-adic groups, II: Induction map.

Cocenters of $p$-adic groups, III: Elliptic cocenter and rigid cocenter (with D. Ciubotaru).

Jordan Decompositions of cocenters of reductive p-adic groups (with. J.-L. Kim).

Soergel calculus and Schubert calculus (with G. Williamson), to appear in the proceedings of Lusztig's birthday conference, a special issue of the Bulletin of the Institute of Mathematics Academia Sinica.

Cocenters of $p$-adic groups, I: Newton decomposition, Forum Math. Pi 6 (2018), e2, 27 pp.

Cocenters and representations of affine Hecke algebras (with D. Ciubotaru), J. Eur. Math. Soc. 19 (2017), 3143--3177.

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), Ann. Inst. Fourier (Grenoble) 65 (2015), 2385--2412.

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.