(This page is currently under construction-- papers are being added. Let me know if there are particular papers you'd like me to add.)

If a paper has figures, these figures will not be visible with the "dvi" version of the paper.

• Linear Algebra and the Hanna Neumann Conjecture, July 28, 2011.
• Sheaves on Graphs, Their Homological Invariants, and a Proof of the Hanna Neumann Conjecture, May 30, 2011. Note: this paper is a merged version (with redundancies eliminated) of the two papers listed just below.
• Sheaves on Graphs and a Proof of the Hanna Neumann Conjecture, April 30, 2011.
• Sheaves on Graphs and Their Homological Invariants, April 13, 2011.
• The non-backtracking spectrum of the universal cover of a graph, with Omer Angel and Shlomo Hoory, last modified November 20, 2007.
• Cohomology in Grothendieck Topologies and Lower Bounds in Boolean Complexity II: A Simple Example (8 pages), last modified March 30, 2006.
• Cohomology in Grothendieck Topologies and Lower Bounds in Boolean Complexity (70 pages), last modified December 2, 2005.
• A Proof of Alon's Second Eigenvalue Conjecture (118 pages), last modified (third revision) May 3, 2004. Accepted to the Memoirs of the A.M.S.
• Generalized Alon-Boppana Theorems and Error-Correcting Codes, with Jean-Pierre Tillich, last modified May 27, 2002.
• Wave Equations for Graphs and The Edge-based Laplacian, with Jean-Pierre Tillich, last modified May 24, 2002, accepted to the Pacific Journal of Mathematics.
• Relative Expanders or Weakly Relatively Ramanujan Graphs, last modified April 8, 2002, Duke Mathematical Journal
• Recognizing more unsatisfiable random 3-SAT instances efficiently, with Andreas Goerdt, last modified January 26, 2001.
• Laplacian Eigenvalues and Distances Between Subsets of a Manifold, with Jean-Pierre Tillich, last modified November 22, 2000.
• On Cayley Graphs on the Symmetric Group Generated by Tranpositions, last modified March 27, 2000.
• The Action of a Few Permutations on r-tuples is Quickly Transitive, with Antoine Joux, Yuval Roichman, Jacques Stern, and Jean-Pierre Tillich, last modified January 23, 1998.
• Computing Betti Numbers via Combinatorial Laplacians, last modified June 4, 1997.
• On the Betti Numbers of Chessboard Complexes, with Phil Hanlon, last modified May 14, 1997.
• Relative Expansion and an Extremal Degree Two Cover of the Boolean Cube, last modified 1993--5.
• Some Geometric Aspects of Graphs and their Eigenfunctions, last modified October 26, 1992 (or earlier?).
• On the Bit Extraction Problem, last modified August 12, 1992.
• A Note on Matrix Rigidity, last modified October 25, 1991.
• The Spectra of Infinite Hypertrees, last modified September 13, 1990.
• On the Second Eigenvalue of Hypergraphs, last modified November 11, 1989.
• Some Graphs with Small Second Eigenvalue, last modified October 12, 1989.
• A Deterministic View of Random Sampling and its Use in Geometry, with Bernard Chazelle, last modified ???
• On the Second Eigenvalue and Random Walks in Random d-Regular Graphs, last modified May 22, 1989.
• On the Roadmap Coloring Problem, last modified January 1989.
• A Density Theorem for Purely Iterative Zero Finding Methods, last modified January 1989.
• On the Convergence of Newton's Method, last modified September 1988.
• Random Polynomials and Approximate Zeros of Newton's Method, last modified November 1987.