On the Unique Games Conjecture Page 1 On the Unique Games Conjecture Subhash Khot
Courant Institute of Mathematical Sciences, NYU ∗ Abstract This article surveys recently …

In this article, we disprove a conjecture of Goemans and Linial; namely, that every negative
type metric embeds into ℓ1 with constant distortion. We show that for an arbitrarily small …

Current societies must make the necessary plans for effective responses and to reduce the
destructive effects of disasters. For this reason, this research has developed a mathematical …

Segmentation is an important step in medical imaging to acquire qualitative measurements
such as the location of the desired objects and also for quantitative measurements such as …

Given k∊ ℕ, the k'th discrete Heisenberg group, denoted ℍ ℤ 2 k+ 1, is the group generated
by the elements a 1, b 1,…, ak, bk, c, subject to the commutator relations a 1, b 1=···= ak, bk …

We study graph partitioning problems from a min-max perspective, in which an input graph
on n vertices should be partitioned into k parts, and the objective is to minimize the …

This chapter focuses on approximation algorithms, which are algorithms of the second kind
with a provably good worst‐case ratio between the value of the solution found by the …

Proceedings of the International Congress of Mathematicians (ICM 2018) : METRIC
DIMENSION REDUCTION: A SNAPSHOT OF THE RIBE PROG Page 1 PRoc. INT. CoNG …

This is one of a series of papers examining the interplay between differentiation theory for
Lipschitz maps X→ V and bi-Lipschitz nonembeddability, where X is a metric measure …

We improve upon recent lower bounds on the minimum distortion of embedding certain finite
metric spaces into L_1. In particular, we show that for every n\ge1, there is an n-point metric …