2011-2012 Seminars

A long-standing line of work in economic theory has studied models by which a group of people in a social network, each holding a numerical opinion, can arrive at a shared opinion through repeated averaging with their neighbors in the network...

For a graph $G$, let $t(G)$ (resp. $b(G)$) denote the maximum size of a triangle-free (resp. bipartite) subgraph of $G$. Of course $t(G) \geq b(G)$ for any $G$, and a classic result of Mantel from 1907 (the first case of Turan’s Theorem) says $t(K_n...

We prove that a uniformly chosen proper coloring of Z_{2n}^d with 3 colors has a very rigid structure when the dimension d is sufficiently high. The coloring takes one color on almost all of either the even or the odd sub-lattice. In particular, one...

A pseudo-random graph is a graph G resembling a typical random graph of the same edge density. Pseudo-random graphs are expected naturally to share many properties of their random counterparts. In particular, many of their enumerative properties...

We present a unified approach to various topics in mathematics including: Ergodic theory, graph limit theory, hypergraph regularity, and Higher order Fourier analysis. The main theme is that very large complicated structures can be treated as...

Proving superpolylogarithmic lower bounds for dynamic data structures has remained an open problem despite years of research. Recently, Patrascu proposed an exciting new approach for breaking this barrier via a two player communication model in...

We present a unified approach to various topics in mathematics including: Ergodic theory, graph limit theory, hypergraph regularity, and Higher order Fourier analysis. The main theme is that very large complicated structures can be treated as...