Selected Publications

Expository Notes

• “Some results on affine Deligne-Lusztig varieties”, Proceedings of the International Congress of Mathematicians, Rio de Janeiro 2018.
• “Hecke algebras and p-adic groups”, Current developments in mathematics 2015, 73–135, Int. Press, Somerville, MA, 2016.

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×B‑orbit closures in equivariant embeddings” (with J. F. Thomsen), Adv. Math, 216 (2007), 626–646.

AI for Math

• “Machine learning assisted exploration for affine Deligne-Lusztig varieties” (with B. Dong, P. Jin, F. Schremmer, Q. Yu), Peking Math. J. 9 (2026), no. 1, 55–104.

Arithmetic Geometry

• “Cohen-Macaulayness of Local Models via Shellability of the Admissible Set” (with F. Schremmer and Q. Yu), arXiv:2603.05875.
• “Stabilizers of irreducible components of affine Deligne–Lusztig varieties” (with R. Zhou and Y. Zhu), J. Eur. Math. Soc. 27 (2025), no. 6, pp. 2387–2441.
• “Cordial elements and dimensions of affine Deligne-Lusztig varieties”, Forum Math. Pi 9 (2021), e9.
• “On the connected components of affine Deligne-Lusztig varieties” (with R. Zhou), Duke Math. J. 169 (2020), no. 14, 2697–2765.
• “Fine Deligne-Lusztig varieties and arithmetic fundamental lemmas” (with C. Li and Y. Zhu), Forum Math. Sigma 7 (2019), e47.
• “Fully Hodge-Newton decomposable Shimura varieties” (with U. Görtz and S. Nie), Peking Math. J. 2 (2019), no. 2, 99–154.
• “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. École Norm. Sup. 49 (2016), 1125–1141.
• “Basic loci of Coxeter type in Shimura varieties” (with U. Görtz), Camb. J. Math. 3 (2015), 323–353.
• “P‑alcoves and nonemptiness of affine Deligne-Lusztig varieties” (with U. Görtz and S. Nie), Ann. Sci. École Norm. Sup. 48 (2015), 647–665.
• “Geometric and homological properties of affine Deligne-Lusztig varieties”, Ann. of Math. (2) 179 (2014), 367–404.
• “Normality and Cohen-Macaulayness of local models of Shimura varieties”, Duke Math. J. 162 (2013), 2509–2523.

Canonical Basis

• “Positivity properties of canonical bases” (with J. Fang), arXiv:2510.12154.

Combinatorics

• “Vertexwise criteria for admissibility of alcoves” (with T. Haines), Amer. J. Math. 139 (2017), 769–784.
• “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.

Hecke algebras

• “Jordan Decompositions of cocenters of reductive p‑adic groups” (with J‑L. Kim), Represent. Theory 23 (2019), 294–324.
• “Cocenters of p‑adic groups, III: Elliptic cocenter and rigid cocenter” (with D. Ciubotaru), Peking Math J 4 (2021), 159–186.
• “Cocenters of p‑adic groups, II: Induction map”, Adv. Math. 345 (2019), 972–997.
• “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.

Total positivity

• “Total positivity in twisted flag varieties” (with K. Xie), arXiv:2602.09350.
• “Total positivity in twisted product of flag varieties” (with H. Bao), arXiv:2211.11168.
• “Product structure and regularity theorem for totally nonnegative flag varieties” (with H. Bao), Invent. Math. 237 (2024), no. 1, 1–47.
• “Flag manifolds over semifields” (with H. Bao), Algebra and Number theory 15 (2021), No. 8, 2037–2069.

Other topics in Representation theory

• “Irreducible components of affine Lusztig varieties”, arXiv:2502.16441.
• “On affine Lusztig varieties”, Ann. Sci. Ecole Norm. Sup (4) 58 (2025), no. 3, 749–776.
• “Soergel calculus and Schubert calculus” (with G. Williamson), Bull. Inst. Math. Acad. Sin. (N.S.) 13 (2018), no. 3, 317–350.
• “A generalization of Steinberg's cross‑section” (with G. Lusztig), J. Amer. Math. Soc. 25 (2012), 739–757.
• “Character sheaves on certain spherical varieties”, Adv. Math. 217 (2008), 1154–1191.
• “Singular supports for character sheaves on a group compactification” (with G. Lusztig), Geom. Funct. Anal. 17 (2008), 1915–1923.
• “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.

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