We study the computational complexity of two related problems: recovering a planted q-
coloring in G (n, 1/2), and finding efficiently verifiable witnesses of non-q-colorability (aka …

Suppose we are given an n-dimensional order-3 symmetric tensor T∈(ℝ n)⊗ 3 that is the
sum of r random rank-1 terms. The problem of recovering the rank-1 components is possible …

Given independent standard Gaussian points $ v_1,\ldots, v_n $ in dimension $ d $, for what
values of $(n, d) $ does there exist with high probability an origin-symmetric ellipsoid that …

We prove a SOS degree lower bound for the planted clique problem on the Erdös-Rényi
random graph G (n, 1/2). The bound we get is degree d= Ω (ε²log n/log log n) for clique size …

We prove that for every D∈ N, and large enough constant d∈ N, with high probability over
the choice of G∼ G (n, d/n), the Erdos-Renyi random graph distribution, the canonical …

Nonlinear random matrices and applications to the Sum of Squares hierarchy Page 1 THE
UNIVERSITY OF CHICAGO NONLINEAR RANDOM MATRICES AND APPLICATIONS TO THE …

We prove that polynomial calculus (and hence also Nullstellensatz) over any field requires
linear degree to refute that sparse random regular graphs, as well as sparse Erdős-Rényi …

The goal of this thesis to contribute towards a computational complexity theory of statistical
inference problems. In recent years, researchers have built evidence in favor of an emerging …

Some Results in Proof Complexity and Sat-Solving Page 1 THE UNIVERSITY OF CHICAGO
SOME RESULTS IN PROOF COMPLEXITY AND SAT-SOLVING A DISSERTATION SUBMITTED …