Characteristic Polynomials of the Hermitian Wigner and Sample Covariance Matrices

Tatyana Shcherbina
Institute for Low Temperature Physics, Kharkov
November 1, 2011

We consider asymptotics of the correlation functions of characteristic polynomials of the hermitian Wigner matrices $H_n=n^{-1/2}W_n$ and the hermitian sample covariance matrices $X_n=n^{-1}A_{m,n}^*A_{m,n}$. We use the integration over the Grassmann variables to obtain a convenient integral representation.

How Bad is Forming Your Own Opinion

Sigal Oren
Cornell University
November 7, 2011

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. Motivated by the observation that consensus is rarely reached in real opinion dynamics, we study a related sociological model in which individuals’ intrinsic beliefs counterbalance the averaging process and yield a diversity of opinions.

Strong and Weak Epsilon Nets and Their Applications

Noga Alon
Tel Aviv University; Institute for Advanced Study
November 7, 2011

I will describe the notions of strong and weak epsilon nets in range spaces, and explain briefly some of their many applications in Discrete Geometry and Combinatorics, focusing on several recent results in the investigation of the extremal questions that arise in the area, and mentioning some of the remaining open problems.

Writers Talk - A Conversation with Stephen Sondheim

Stephen Sondheim
November 8, 2011

American composer and lyricist Stephen Sondheim talks about his life and work in a conversation with Derek Bermel, the Institute’s Artist-in-Residence. Sondheim, whose works for Broadway include A Funny Thing Happened on the Way to the Forum, Company, Follies, A Little Night Music, Sweeney Todd, Pacific Overtures, Into the Woods, and Assassins, received the Pulitzer Prize for Drama for Sunday in the Park with George in 1985. He also wrote the lyrics for West Side Story and Gypsy. He is the author of Finishing the Hat (Knopf, 2010) and Look, I Made a Hat (Knopf, 2011). Sondheim has received seven Tony Awards, an Academy Award, and seven Grammy Awards. He also was among the recipients of the Kennedy Center Honors in 1993.