11 citations · 11 across the 10 of their papers we have counts for
12 papers
Higher-order Godbersen inequality and a characterization of simplices via the face lattice
Filip Fryš, Jan Kotrbatý, Mohamed A. Mouamine +1
We settle the long-standing Godbersen conjecture that the mixed volume of a convex body of fixed positive volume with its reflection about the origin is maximized precisely by simp…
The Bézout inequality for mixed volumes characterizes simplices
Dylan Langharst, Shouda Wang
We prove that the Bézout inequality for mixed volumes characterizes simplices among full dimensional convex bodies in every dimension, resolving a conjecture of Soprunov and Zvavit…
Volume and Projection Inequalities I: Zonoids and Courtade's Conjecture
Matthieu Fradelizi, Alfredo Hubard, Auttawich Manui +3
We study volume and projection inequalities for zonoids through the multiaffine determinant polynomials that encode their volumes. We show that a log-submodularity conjecture for t…
Matroid flat counts can have many peaks
Alexander Divoux, Matt Larson, Chayim Lowen +1
We disprove Rota's conjecture that the counts of flats in a matroid according to rank form a unimodal sequence. Furthermore, we show that this sequence can have arbitrarily many pe…
A complete solution to the Grünbaum--Loewner centroid problems
Wang Shouda, Xiong Ge, Yang Kaiwen
In the 1960s, Grünbaum and Loewner raised problems concerning the minimum possible number of hyperplane sections of a convex body in whose centroids coincide with the centroi…
Matroid flat counts are not unimodal
Alexander Divoux, Chayim Lowen, Shouda Wang
We give counterexamples to Rota's 1970 conjecture that the sequence counting flats of varying rank in a matroid is unimodal. More specifically, inspired by Larson's recent disproof…
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…
Choosing the Right Algorithm With Hints From Complexity Theory
Shouda Wang, Weijie Zheng, Benjamin Doerr
Choosing a suitable algorithm from the myriads of different search heuristics is difficult when faced with a novel optimization problem. In this work, we argue that the purely acad…
An identity in distribution between full-space and half-space log-gamma polymers
Guillaume Barraquand, Shouda Wang
We prove an identity in distribution between two kinds of partition functions for the log-gamma directed polymer model: (1) the point-to-point partition function in a quadrant, (2)…