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We use hook Schur functions to compute trace cocharacters of matrices in hooks. As an example we compute the cocharacters of 3 x 3 matrices in the one by two hook
Limits of spiked random matrices I     Limits of spiked random matrices I  math       font style='font-size:12px;'> 2010/11/15
Given a large, high-dimensional sample from a spiked population, the top sample covariance eigenvalue is known to exhibit a phase transition. We show that the largest eigenvalues have asymptotic dist...
The Schrödinger-Poisson system on the sphere     The Schrö  dinger-Poisson system  the sphere       font style='font-size:12px;'> 2010/11/11
We study the Schr\"odinger-Poisson system on the unit sphere $\SS^2$ of $\RR^3$, modeling the quantum transport of charged particles confined on a sphere by an external potential. Our first results c...
We propose a convex optimization formulation with the nuclear norm and $\ell_1$-norm to find a large approximately rank-one submatrix of a given nonnegative matrix. We develop optimality conditions f...
Given a Riemannian surface, we consider a naturally embedded graph which captures part of the topology and geometry of the surface. By studying this graph, we obtain results in three different directi...
This article concerns the computational problem of counting the lattice points inside convex polytopes, when each point must be counted with a weight associated to it. We describe an efficient algori...
In this series of lectures we introduce the Monge-Kantorovich problem of optimally transporting one distribution of mass onto another, where optimality is measured against a cost function c(x,y). Con...
A universal period doubling cascade analogous to the famous Feigenbaum-Coullet-Tresser period doubling has been observed in area-preserving maps of R2. Existence of the “universal” map with orbits of ...
We prove a refined Agler decomposition for bounded analytic functions on the bidisk and show how it can be used to reprove an interesting result of Guo et al. related to extending holomorphic functio...
Drawing planar graphs of bounded degree with few slopes      planar graphs  bounded degree  few slopes        font style='font-size:12px;'> 2010/12/1
settle a problem of Dujmović, Eppstein, Suderman, and Wood by showing that there exists a function f with the property that every planar graph G with maximum degree d admits a drawing with nonc...
Calibrations in hyperkahler geometry      Calibrations  hyperkahler geometry        font style='font-size:12px;'> 2010/11/30
We describe a family of calibrations arising naturally on a hyperk¨ahler manifoldM. These calibrations calibrate the holomorphic Lagrangian,holomorphic isotropic and holomorphic coisotropic subvarieti...
A gradient bound for free boundary graphs      gradient bound f  free boundary graphs        font style='font-size:12px;'> 2010/12/10
We prove an analogue for a one-phase free boundary problem of the classical gradient bound for solutions to the minimal surface equation. It follows, in particular, that every energy-minimizing free b...
n this note we prove that the spec(C)-points of the representation Artin-stack [repnR/PGLn] of n-dimensional representations of an affine C-algebra R correspond to C-algebra morphisms R - An where An ...
On piecewise linear cell decompositions      piecewise linear cell decompositions        font style='font-size:12px;'> 2010/12/9
In this note, we introduce a class of cell decompositions of PL manifolds and polyhedra which are more general than triangulations yet not as general as CW complexes; we propose calling them PLCW comp...
Resonance equals reducibility for A-hypergeometric systems      toric  hypergeometric  Euler–Koszul  homology  D-module  resonant       font style='font-size:12px;'> 2010/12/8
Classical Theorems of Gel’fand et al., and recent results of Beuk-ers show essentially that non-confluent A-hypergeometric systems have re-ducible monodromy representation if and only if the continuou...

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