Entropies of commuting transformations on Hilbert spaces

Banach空间上交换变换的测度熵的次可加性

Sub-additivity of measure-theoretic entropies of commuting transformations on Banach space

该研究将有限维空间交换微分同胚测度熵的相关结论推广到无限维Banach空间，证明了空间上两交换光滑变换测度熵的次可加性，并给出熵等式成立的附加条件。

希尔伯特点面的范畴熵与超kähler流形的范畴熵

Categorical Entropies of Hilbert Schemes of Points on Surfaces and Hyperkähler Manifolds

本文研究了希尔伯特点面和超kähler流形的导出范畴自同构的范畴熵，证明了当表面不满足GY性质时，其希尔伯特方案也不满足，并通过构造实例证明超kähler和恩里ques流形不满足该性质。

Entropies of compact strictly convex projective manifolds

Let M be a compact manifold of dimension n with a strictly convex projective structure. We consider the geodesic flow of the Hilbert metric on it, which is known to be Anosov. We prove that its topological entropy is less than n-1, with equality if and only if the structure is Riemannian, that is hyperbolic. As a corollary, we get that the volume entropy of a divisible strictly convex set is less than n-1, with equality if and only if it is an ellipsoid.

Norm-variation of ergodic averages with respect to two commuting transformations

We study double ergodic averages with respect to two general commuting transformations and establish a sharp quantitative result on their convergence in the norm. We approach the problem via real harmonic analysis, using recently developed methods for bounding multilinear singular integrals with certain entangled structure. A byproduct of our proof is a bound for a two-dimensional bilinear square function related to the so-called triangular Hilbert transform.