Seminars Sorted by Series

A 2-server Private Information Retrieval (PIR) scheme allows a user to retrieve the $i$'th bit of an $n$-bit database replicated among two servers (which do not communicate) while not revealing any information about $i$ to either server. The privacy...

We prove an $\omega(\log n)$ lower bound on the conondeterministic communication complexity of the Clique vs. Independent Set problem introduced by Yannakakis (STOC 1988, JCSS 1991). As a corollary, this implies superpolynomial lower bounds for the...

Given a $k$-edge-connected graph $G = (V,E)$, a spanning tree $T$ is $\alpha$-thin w.r.t. $G$, if for any $S \subset V$, $|T(S,V - S)| \leq \alpha.|E(S,V - S)|$. The thin tree conjecture asserts that for a sufficiently large $k$ (independent of size...

Various motivations recently led Mendel and Naor, Hatami and Kalai to study functions in tail spaces - i.e. function all of whose low level Fourier coefficients vanish. I will discuss the questions and conjectures that they posed and our recent work...

We prove that for any $\epsilon > 0$ it is NP-hard to approximate the non-commutative Grothendieck problem to within a factor $1/2 + \epsilon$, which matches the approximation ratio of the algorithm of Naor, Regev, and Vidick (STOC'13). Our proof...

At the heart of every local search algorithm is a directed graph on candidate solutions (states) such that every unsatisfactory state has at least one outgoing arc. In stochastic local search the hope is that a random walk will reach a satisfactory...

During last fifty years a strong machine learning theory has been developed. This theory includes: 1. The necessary and sufficient conditions for consistency of learning processes. 2. The bounds on the rate of convergence which in general cannot be...

In the last few years, there has been a significant interest in the computational abilities of Physarum Polycephalum (a slime mold). This drew from a remarkable experiment which showed that this organism can compute shortest paths in a maze...

The sensitivity conjecture is a major outstanding foundational problems about boolean functions is the sensitivity conjecture. In one of its many forms, it asserts that the degree of a boolean function (i.e. the minimum degree of a real polynomial...

We explicitly construct an extractor for two independent sources on $n$ bits, each with min-entropy at least $\log^C n$ for a large enough constant $C$. Our extractor outputs one bit and has error $n^{-\Omega(1)}$. The best previous extractor, by...

The Ramsey number of a graph $G$ is the minimum integer $n$ for which every edge-coloring of the complete graph on $n$ vertices with two colors contains a monochromatic copy of $G$. A graph is $d$-degenerate if all its subgraphs have a vertex of...

Vapnik's fundamental theorem of statistical learning establishes a computational equivalence between optimization (empirical risk minimization) and learning in the statistical setting. Is the same true for learning in games? We give a precise answer...

In [kal89], Kaltofen proved the remarkable fact that multivariate polynomial factorization can be done efficiently, in randomized polynomial time. Still, more than twenty years after Kaltofen's work, many questions remain unanswered regarding the...

Suppose you have access to iid samples from an unknown probability distribution $p = (p_1, \ldots, p_d)$ on $[d]$, and you want to learn or test something about it. For example, if one wants to estimate $p$ itself, then the empirical distribution...

In his 1947 paper that inaugurated the probabilistic method, Erdős proved the existence of $2 \log(n)$-Ramsey graphs on $n$ vertices. Matching Erdős' result with a constructive proof is a central problem in combinatorics that has gained a...

Many polynomial-time solvable (combinatorial) optimization problems can be reduced to the feasibility problem and the intersection problem. In this talk, I will present the first nearly cubic time algorithm for both problems using a new cutting...

Solving the following problem is crucial when compiling for a quantum computer: given a finite set $G$ of elements of $SU(2)$, target element $U$ from $SU(2)$ and real number $\epsilon$ find $g_1,\dotsc, g_N$ from $G$ such that $\| g_1 \dotsm g_N -...

Ramsey theory refers to a large body of deep results in mathematics whose underlying philosophy is captured succinctly by the statement that "Every very large system contains a large well-organized subsystem." Ramsey numbers capture how very large...

We introduce a method for proving lower bounds on the efficacy of semidefinite programming (SDP) relaxations for combinatorial problems. In particular, we show that the cut, TSP, and stable set polytopes on $n$-vertex graphs are not the linear image...

Let $f$ be a polynomial of degree $d$ in $n$ variables over a finite field $\mathbb{F}$. The polynomial is said to be unbiased if the distribution of $f(x)$ for a uniform input $x \in \mathbb{F}^n$ is close to the uniform distribution over $\mathbb...

One of the major challenges of the research in circuit complexity is proving super-polynomial lower bounds for de-Morgan formulas. Karchmer, Raz, and Wigderson suggested to approach this problem by proving that formula complexity behaves "as...

Interactive proofs have had a dramatic impact on Complexity Theory and Cryptography. In particular, the celebrated IP=PSPACE Theorem [LFKN92,Shamir92] allows an all-powerful but untrusted prover to convince a polynomial-time verifier of the validity...

We show that the bipartite perfect matching problem is in $\textrm{quasi-}\textsf{NC}^2$. That is, it has uniform circuits of quasi-polynomial size and $O(\log^2 n)$ depth. Previously, only an exponential upper bound was known on the size of such...

We study the two-party communication complexity of the geometric problem of finding an approximate Brouwer fixed-point of a composition of two Lipschitz functions $g \circ f$, where Alice knows $f$ and Bob knows $g$. We prove an essentially tight...

The algorithm indicated in the title builds on Luks's classical framework and introduces new group theoretic and combinatorial tools. In the first talk we outline the algorithm and state the core group theoretic and algorithmic ingredients. Some of...

Finding cliques in random graphs and the related planted variant where one wants to recover an added clique of size $k$ added to a random $G(n, 1/2)$ graph, have been extensively studied questions in algorithm design. Despite intense effort, state...

The last few years have seen substantial progress on the question of proving lower bounds for homogeneous depth-4 arithmetic circuits. Even though these results seem to come close to resolving the VP vs VNP question, it seems likely that the...

Tensor decompositions have been the key algorithmic components in provable learning of a wide range of hidden variable models such as topic models, Gaussian mixture models, independent component analysis, dictionary learning. Despite its success...

What is the distribution of the number of triangles in the random graph $G(n, 1/2)$? It was known for a long time that this distribution obeys a central limit theorem: from the point of view of large intervals (~ standard-deviation length), the...

We prove an average-case depth hierarchy theorem for Boolean circuits over the standard basis of AND, OR, and NOT gates. Our hierarchy theorem says that for every $d \\geq 2$, there is an explicit $n$-variable Boolean function $f$, computed by a...

Random constraint satisfaction problems encode many interesting questions in random graphs such as the chromatic and independence numbers. Ideas from statistical physics provide a detailed description of phase transitions and properties of these...

The determinant of an $n\times n$ matrix is an invariant polynomial of degree $n$ that is invariant under left and right multiplication with matrices in ${\rm SL}_n$. It generates in the sense that every other invariant polynomial is a polynomial...

Monotonicity testing has been a touchstone problem in property testing for more than fifteen years, with many exciting recent developments in just the past few years. When specialized to Boolean-valued functions over $\{0,1\}^n$, we are interested...

For a constant $\epsilon$, we prove a $\mathrm{poly}(N)$ lower bound on the communication complexity of $\epsilon$-Nash equilibrium in two-player $N \times N$ games. For $n$-player binary-action games we prove an $\exp(n)$ lower bound for the...

Let $G$ be a compact group and let $f_{ij}\in L_2(G)$ be bandlimited functions. We define the Non-Unique Games (NUG) problem as finding $g_1\ldots,g_n\in G$ to minimize $\sum_{i,j=1}^n f_{ij}(g_i g_j^{-1})$. We devise a relaxation of the NUG problem...

I will review some of the recent techniques we've used in our study of natural algorithms. These include Dirichlet series for matrix products, mean-field approximations in opinion dynamics, graph sequence grammars, and tools for renormalizing...

The random planted 3-coloring model generates a 3-colorable graph $G$ by first generating a random host graph $H$ of average degree $d$, and then planting in it a random 3-coloring (by giving each vertex a random color and dropping the monochromatic...

The stochastic block model (SBM) is a random graph model with planted clusters. It has been popular to model unsupervised learning problems, inhomogeneous random graphs and to study statistical versus computational tradeoffs. This talk overviews the...

Consider a set of $n$ points in $\mathbb R^d$. The classical theorem of Sylvester-Gallai says that, if the points are not all collinear then there must be a line through exactly two of the points. Let us call such a line an "ordinary line". In a...

The motivating question for this talk is: What does a sparse Erdős–Rényi random graph, conditioned to have twice the number of triangles than the expected number, typically look like? Motivated by this question, In 2014, Chatterjee and Dembo...

The "cap set problem" asks for the size of the largest subset $S$ of the vector space $\mathbb F_3^n$ containing no three elements summing to 0. Progress on this problem was slow for many years, until the spring of 2016, when a very short argument...

An active learning algorithm for a classification problem has access to many unlabelled samples. The algorithm asks for the labels of a small number of samples, carefully chosen, such that that it can leverage this information to correctly label...

In this talk, I will discuss our recent efforts to formalize a particular notion of “fairness” in online decision making problems, and study its costs on the achievable learning rate of the algorithm. Our focus for most of the talk will be on the...

Random constraint satisfaction problems (CSPs) are known to exhibit threshold phenomena: given a uniformly random instance of a CSP with $n$ variables and $m$ clauses, there is a value of $m = \Omega(n)$ beyond which the CSP will be unsatisfiable...

I will show a new efficient approximate nearest neighbor search (ANN) algorithm over an arbitrary high-dimensional *symmetric* norm. Traditionally, the ANN problem in high dimensions has been studied over the $\ell_1$ and $\ell_2$ distances with a...

The Minimum Circuit Size Problem (MCSP) and a related problem (MKTP) that deals with time-bounded Kolmogorov complexity are prominent candidates for NP-intermediate status. We present new results relating the complexity of various approximation...

The problem of constructing error-resilient interactive protocols was introduced in the seminal works of Schulman (FOCS 1992, STOC 1993). These works show how to convert any two-party interactive protocol into one that is resilient to constant...

The computational complexity of finding Nash Equilibria in games has received much attention over the past two decades due to its theoretical and philosophical significance. This talk will be centered around the connection between this problem and...