期刊： ANNALS OF MATHEMATICS, 2021; 194 (2)
We introduce a new technique for isolating components on the spectral side of the trace formula. By applying it to the Jacquet-Rallis relative trace f......
期刊： ANNALS OF MATHEMATICS, 2021; 194 (1)
In this paper we analyze the local and global boundary rigidity problem for general Riemannian manifolds with boundary (M,g). We show that the boundar......
期刊： ANNALS OF MATHEMATICS, 2021; 193 (2)
This paper is concerned with the structure of Gromov-Hausdorff limit d spaces (M-i(n), gi, pi) ->(dGH )(X-n ,d,p) of Riemannian manifolds satisfyin......
期刊： ANNALS OF MATHEMATICS, 2021; 193 (1)
Consider a Riemannian manifold with bounded Ricci curvature vertical bar Ric vertical bar <= n - 1 and the noncollapsing lower volume bound Vol ver......
期刊： ANNALS OF MATHEMATICS, 2020; 192 (3)
In this paper, we consider the CM line bundle on the K-moduli space, i.e., the moduli space parametrizing K-polystable Fano varieties. We prove it is ......
期刊： ANNALS OF MATHEMATICS, 2019; 189 (3)
We prove the Ax-Schanuel theorem for a general (pure) Shimura variety. A basic version of the theorem concerns the transcendence of the uniformization......
期刊： ANNALS OF MATHEMATICS, 2019; 189 (3)
We show that, for n >= 3, limt(t -> 0) e(it Delta) f (x) = f (x) holds almost everywhere for all f is an element of H-s (R-n) provided that s &g......
期刊： ANNALS OF MATHEMATICS, 2019; 190 (2)
We prove that K-polystable degenerations of Q-Fano varieties are unique. Furthermore, we show that the moduli stack of K-stable Q-Fano varieties is se......
期刊： ANNALS OF MATHEMATICS, 2017; 185 (3)
We generalize classical theorems due to Lichnerowicz and Hitchin on the existence of Riemannian metrics of positive scalar curvature on spin manifolds......
期刊： ANNALS OF MATHEMATICS, 2017; 186 (2)
We prove that the 2-primary pi(61) is zero. As a consequence, the Kervaire invariant element theta(5) is contained in the strictly defined 4-fold Toda......
