多様体の収束・崩壊理論の立場からリーマン多様体およびもっと特異な空間とリッチ曲率の関係を調べている．

1. (With Yuanlin Peng) A note on the topological stability theorem from RCD spaces to Riemannian manifolds, Manuscripta Math. 172 (2023),no. 3-4, 971-1007.
2. (With Xianzhe Dai, Jiayin Pan, Guofang Wei) Singular Weyl's law with Ricci curvature bounded below, Trans. Amer. Math. Soc. Ser. B 10(2023), 1212-1253.
3. (With Camillo Brena, Nicola Gigli, Xingyu Zhu) Weakly non-collapsed RCD spaces are strongly non-collapsed, J. Reine Angew. Math. 794(2023), 215-252.
4. (With Yannick Sire) Sobolev mappings between RCD spaces and applications to harmonic maps: a heat kernel approach, J. Geom. Anal.33 (2023), no. 9, Paper No. 272, 87 pp.
5. Isometric immersions of RCD spaces, Comment. Math. Helv. 96 (2021),no. 3, 515-559.
6. (With Ilaria Mondello) Sphere theorems for RCD and stratified spaces, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 22 (2021), no. 2, 903-923.
7. (With Luciano Mari, Michele Rimoldi, Giona Veronelli) Density and non-density of $C^{\infty}_0 \hookrightarrow W^{k, p}$ on complete manifolds with curvature bounds, Nonlinear Anal. 211 (2021), Paper No.112429, 26 pp.
8. (With Luigi Ambrosio, Jacobus W. Portegies, David Tewodrose) Embedding of $\mathrm{RCD}^*(K,N)$ spaces in $L^2$ via eigenfunctions,J. Funct. Anal. 280 (2021), no. 10, Paper No. 108968, 72 pp.
9. New differential operator and noncollapsed RCD spaces, Geom. Topol.24 (2020), no. 4, 2127-2148.
10. (With Song Sun, Ruobing Zhang) A note on the collapsing geometry of hyperkähler four manifolds, Sci. China Math. 62 (2019), no. 11,2195-2210.
11. (With Luigi Ambrosio) Local spectral convergence in $RCD^*(K,N)$spaces, Nonlinear Anal. 177 (2018), 1-23.
12. Elliptic PDEs on compact Ricci limit spaces and applications, Mem.Amer. Math. Soc. 253 (2018), no. 1211, v+92 pp.
13. (With Luigi Ambrosio, Jacobus W. Portegies) Continuity of nonlinear eigenvalues in $\mathrm{CD}(K,\infty)$ spaces with respect to measured Gromov-Hausdorff convergence, Calc. Var. Partial Differential Equations 57 (2018), no. 2, Paper No. 34, 23 pp.
14. (With Luigi Ambrosio, David Tewodrose) Short-time behavior of the heat kernel and Weyl's law on $\mathrm{RCD}^*(K,N)$ spaces, Ann.Global Anal. Geom. 53 (2018), no. 1, 97-119.
15. (With Luigi Ambrosio) New stability results for sequences of metric measure spaces with uniform Ricci bounds from below, Partial Differ.Equ. Meas. Theory De Gruyter Open, Warsaw, 2017, 1-51.
16. Spectral convergence under bounded Ricci curvature, J. Funct. Anal.273 (2017), no. 5, 1577-1662.
17. (With Akito Futaki, Shunsuke Saito) Fano-Ricci limit spaces and spectral convergence, Asian J. Math. 21 (2017), no. 6, 1015-1062.
18. Ricci curvature and $L^p$-convergence, J. Reine Angew. Math. 705(2015), 85-154.
19. A weakly second-order differential structure on rectifiable metric measure spaces, Geom. Topol. 18 (2014), no. 2, 633-668.
20. Ricci curvature and convergence of Lipschitz functions, Comm. Anal.Geom. 19 (2011), no. 1, 79-158.

2018年度日本数学会幾何学賞

平成29年度科学技術分野の文部科学大臣表彰若手科学者賞

2015年度建部賢弘特別賞