Calabi flow, geodesic rays, and uniqueness of constant scalar curvature...
We prove that constant scalar curvature Kähler metric “adjacent” to a fixed Kähler class is unique up to isomorphism. The proof is based on the study of a fourth order evolution equation, namely, the...
View ArticleStable logarithmic maps to Deligne–Faltings pairs I
We introduce a new compactification of the space of relative stable maps. This approach uses logarithmic geoemetry in the sense of Kato-Fontaine-Illusie without taking expansions of the target. The...
View ArticleACC for log canonical thresholds
We show that log canonical thresholds satisfy the \rm ACC.
View ArticleMicrodifferential systems and the codimension-three conjecture
In this paper we give a proof of a fundamental conjecture, the codimension-three conjecture, for microdifferential holonomic systems. The conjecture states that any (regular) holonomic module extends...
View ArticleSets of integers with no large sum-free subset
Answering a question of P. Erdős from 1965, we show that for every $\varepsilon> 0$ there is a set $A$ of $n$ integers with the following property: every set $A’ \subset A$ with at least...
View ArticleEuler systems for Rankin–Selberg convolutions of modular forms
We construct a Euler system in the cohomology of the tensor product of the Galois representations attached to two modular forms, using elements in the higher Chow groups of products of modular curves....
View ArticleOn self-similar sets with overlaps and inverse theorems for entropy
We study the dimension of self-similar sets and measures on the line. We show that if the dimension is less than the generic bound of $\mathrm{min}\{1,s\}$, where $s$ is the similarity dimension, then...
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