Seminars

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...

In this talk I will review some of the classical (and fundamental) results in the theory of graph rigidity.

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...

In this talk I will show how to derive the fastest coordinate descent method [1] and the fastest stochastic gradient descent method [2], both from the linear-coupling framework [3]. I will relate them to linear system solving, conjugate gradient...

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...

Seeded and seedless non-malleable extractors are non-trivial generalizations of the more commonly studied seeded and seedless extractors. The original motivation for constructing such non-malleable extractors are from applications to cryptography...

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...

In the matrix completion problem, we have a matrix $M$ where we are only given a small number of its entries and our goal is to fill in the rest of the entries. While this problem is impossible to solve for general matrices, it can be solved if $M$...

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...

We prove that there exists a constant $\epsilon > 0$ such that, assuming the Exponential Time Hypothesis for PPAD, computing an $\epsilon$-approximate Nash equilibrium in a two-player ($n \times n$) game requires quasi-polynomial time, $n^{\log^{1-o...