Browsing FAS Scholarly Articles by FAS Department "Mathematics"
Now showing items 2140 of 421

The Arrow Impossibility Theorem: Where Do We go from Here?
(Columbia University Press, 20141231) 
Asymptotic dynamics of nonlinear Schrödinger equations: Resonancedominated and dispersiondominated solutions
(WileyBlackwell, 2001)We consider a linear Schrödinger equation with a nonlinear perturbation in ℝ3. Assume that the linear Hamiltonian has exactly two bound states and its eigenvalues satisfy some resonance condition. We prove that if the ... 
Automorphisms of Even Unimodular Lattices and Unramified Salem Numbers
(Elsevier, 2002)In this paper we study the characteristic polynomials \(S(x)=\det(xI−F II_{p,q})\) of automorphisms of even unimodular lattices with signature \((p,q)\). In particular, we show that any Salem polynomial of degree \(2n\) ... 
Automorphisms of projective K3 surfaces with minimum entropy
(Springer Science + Business Media, 2015) 
Automorphisms of Rational Maps
(Springer, 1988) 
Automorphy for Some \(l\)Adic Lifts of Automorphic Mod \(l\) Galois Representations
(Springer Berlin / Heidelberg, 2008)We extend the methods of Wiles and of Taylor and Wiles from \(GL_2\) to higher rank unitary groups and establish the automorphy of suitable conjugate selfdual, regular (de Rham with distinct HodgeTate numbers), minimally ... 
Average Ranks of Elliptic Curves: Tension between Data and Conjecture
(American Mathematical Society, 2007)Rational points on elliptic curves are the gems of arithmetic: they are, to diophantine geometry, what units in rings of integers are to algebraic number theory, what algebraic cycles are to algebraic geometry. A rational ... 
The Basic Reproductive Ratio of Life
(Elsevier, 2010)Templatedirected polymerization of nucleotides is believed to be a pathway for the replication of genetic material in the earliest cells. We assume that activated monomers are produced by prebiotic chemistry. These monomers ... 
A Bayesian Treatment of the Stereo Correspondence Problem Using HalfOccluded Regions
(IEEE Computer Society Press, 1992)A halfoccluded region in a stereo pair is a set of pixels in one image representing points in space visible to that camera or eye only, and not to the other. These occur typically as parts of the background immediately ... 
Behavioral correlates of cheating: Environmental specificity and reward expectation
(Public Library of Science (PLoS), 2017)Academic dishonesty has been and continues to be a major problem in America’s schools and universities. Such dishonesty is especially important in high schools, where grades earned directly impact the academic careers of ... 
Billiards and Hilbert Modular Surfaces
(MaxPlanck Institut, 2003) 
Billiards and Teichmüller Curves on Hilbert Modular Surfaces
(American Mathematical Society, 2003)This paper exhibits an infinite collection of algebraic curves isometrically embedded in the moduli space of Riemann surfaces of genus two. These Teichmüller curves lie on Hilbert modular surfaces parameterizing Abelian ... 
Braid Groups and Hodge theory
(Springer, 2012)This paper gives an account of the unitary representations of the braid group that arise via the Hodge theory of cyclic branched coverings of \(\mathbb{P}^1\) , highlighting their connections with ergodic theory, complex ... 
Braiding of the Attractor and the Failure of Iterative Algorithms
(Springer Verlag, 1988) 
Breaking the Symmetry Between Interaction and Replacement in Evolutionary Dynamics on Graphs
(American Physical Society, 2007)We study the evolution of cooperation modeled as symmetric 2×2 games in a population whose structure is split into an interaction graph defining who plays with whom and a replacement graph specifying evolutionary competition. ... 
Bulk diffusivity of lattice gases close to criticality
(Springer Nature, 1995)We consider lattice gases where particles jump at random times constrained by hardcore exclusion (simple exclusion process with speed change). The conventional theory of critical slowing down predicts that close to a ... 
Bulk universality for deformed Wigner matrices
(Institute of Mathematical Statistics, 2016)We consider N×N random matrices of the form H=W+V where W is a real symmetric or complex Hermitian Wigner matrix and V is a random or deterministic, real, diagonal matrix whose entries are independent of W. We assume ... 
Bulk universality for generalized Wigner matrices
(Springer Science + Business Media, 2011)Consider \(N × N\) Hermitian or symmetric random matrices H where the distribution of the (i, j) matrix element is given by a probability measure \(\nu_{ij}\) with a subexponential decay. Let \(\sigma_{ij}^2\) be the ... 
Bulk universality for Wigner matrices
(WileyBlackwell, 2010)We consider N × N Hermitian Wigner random matrices H where the probability density for each matrix element is given by the density ν(x) = e−U(x). We prove that the eigenvalue statistics in the bulk are given by the Dyson ... 
Bulk universality of general βensembles with nonconvex potential
(AIP Publishing, 201209)We prove the bulk universality of the βensembles with nonconvex regular analytic potentials for any β > 0. This removes the convexity assumption appeared in the earlier work [P. Bourgade, L. Erdös, and H.T. Yau, ...