4 papers
Monotonicity of the deficit in the local log-Brunn-Minkowski inequality
Shouda Wang
We establish a monotonicity property of the deficit associated with the local log-Brunn-Minkowski inequality (LLBM) under addition of line segments. As a corollary, if the LLBM hol…
On Minkowski's monotonicity problem
Ramon van Handel, Shouda Wang
We address an old open question in convex geometry that dates back to the work of Minkowski: what are the equality cases of the monotonicity of mixed volumes? The problem is equiva…
Realizations of homology classes and projection areas
Daoji Huang, June Huh, Mateusz Michałek +2
The relationship between convex geometry and algebraic geometry has deep historical roots, tracing back to classical works in enumerative geometry. In this paper, we continue this…
Renyi Differential Privacy of Propose-Test-Release and Applications to Private and Robust Machine Learning
Jiachen T. Wang, Saeed Mahloujifar, Shouda Wang +2
Propose-Test-Release (PTR) is a differential privacy framework that works with local sensitivity of functions, instead of their global sensitivity. This framework is typically used…