The early work of Condorcet in the eighteenth century, and that of Arrow and others in the twentieth century, revealed the complex and interesting mathematical problems that arise in the theory of social choice. In this lecture, Noga Alon, Visiting Professor in the School of Mathematics, explains how the simple process of voting leads to strikingly counter-intuitive paradoxes, focusing on several recent intriguing examples.
Finding the longest increasing subsequence (LIS) is a classic algorithmic problem. Simple $O(n log n)$ algorithms, based on dynamic programming, are known for solving this problem exactly on arrays of length $n$.
Given a Hamiltonian on $T^n\times R^n$, we shall explain how the sequence of suitably rescaled (i.e. homogenized) Hamiltonians, converges, for a suitably defined symplectic metric. We shall then explain some applications, in particular to symplectic topology and invariant measures of dynamical systems.
I will talk about the computational complexity of computing the noncommutative determinant. In contrast to the case of commutative algebras, we know of (virtually) no efficient algorithms to compute the determinant over non-commutative domains. Our results show that the determinant in noncommutative settings can be as hard as the permanent.
The 2010–11 season of Writers Conversations, curated by Institute Artist-in-Residence Derek Bermel, began with a reading and discussion with a younger generation of groundbreaking poets.
Tracy K. Smith, the host of the panel, is Assistant Professor of Creative Writing at the Lewis Center for the Arts at Princeton University. Her second collection of poems, Duende (Graywolf Press), received the 2006 James Laughlin Award from the Academy of American Poets.
Thomas Sayers Ellis is Assistant Professor of CreativeWriting at Sarah Lawrence College and a core faculty member of the Lesley University Low Residency MFA Program. He won the John C. Zacharis First Book Award from Ploughshares for his first full-length collection, The Maverick Room (Graywolf Press).
Suji Kwock Kim’s first book, Notes from the Divided Country (Louisiana State University Press, 2003), won the Addison Metcalf Award from the American Academy of Arts and Letters, the Walt Whitman Award from the Academy of American Poets, the Whiting Writers’ Award, and The Nation/Discovery Award.
Wendy S.Walters’s work resides at the intersection of the poem, essay, and lyric drama. She is the author of Longer I Wait, More You Love Me (Palm Press, 2009) and a chapbook, Birds of Los Angeles (Palm Press, 2005).