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Toric Stacks I: The Theory of Stacky Fans
Toric Stacks I The Theory of Stacky Fans Algebraic Geometry
2011/9/1
Abstract: The purpose of this paper and its sequel (Toric Stacks II) is to introduce and develop a theory of toric stacks which encompasses and extends the notions of toric stacks defined in [Laf02, B...
Approximate Interval Method for Epistemic Uncertainty Propagation using Polynomial Chaos and Evidence Theory
Approximate Interval Method Epistemic Uncertainty Propagation Evidence Theory
2011/9/29
Abstract: The paper builds upon a recent approach to find the approximate bounds of a real function using Polynomial Chaos expansions. Given a function of random variables with compact support probabi...
K-homology and index theory on contact manifolds
K-homology and index theory Operator Algebras Differential Geometry
2011/8/31
Abstract: Let X be a closed connected contact manifold. On X there is a naturally arising class of hypoelliptic (but not elliptic) operators which are Fredholm. In this paper we solve the index proble...
Chip-firing games, potential theory on graphs, and spanning trees
Chip-firing games graphs spanning trees Combinatorics
2011/8/26
Abstract: We study the interplay between chip-firing games and potential theory on graphs, characterizing reduced divisors ($G$-parking functions) on graphs as the solution to an energy (or potential)...
Schrodinger equations, deformation theory and $tt^*$-geometry
Schrodinger equations deformation theory Differential Geometry
2011/8/26
Abstract: This is the first of a series of papers to construct the deformation theory of the form Schr\"odinger equation, which is related to a section-bundle system $(M,g,f)$, where $(M,g)$ is a nonc...
The generic representation theory of the Juyumaya algebra of braids and ties
generic representation theory Juyumaya algebra braids and ties
2011/8/29
Abstract: In this paper we determine the complex generic representation theory of the Juyumaya algebra. We show that a certain specialization of this algebra is isomorphic to the small ramified partit...
Some new results in extremal graph theory
extremal graph theory Combinatorics the underpinning ideas
2011/8/26
Abstract: In recent years several classical results in extremal graph theory have been improved in a uniform way and their proofs have been simplified and streamlined. These results include a new Erd\...
Equivariant inverse spectral theory and toric orbifolds
Laplacian symplectic orbifold toric moment polytope equivariant spectrum constant scalar curvature
2011/8/25
Abstract: Let O be a symplectic toric 2n-dimensional orbifold with a fixed T^n-action and with a toric Kahler metric g. We previously explored whether, when O is a manifold, the equivariant spectrum o...
Index theory for locally compact noncommutative geometries
Index theory compact noncommutative geometries Operator Algebras K-Theory and Homology
2011/8/25
Abstract: Spectral triples for nonunital algebras model locally compact spaces in noncommutative geometry. In the present text, we prove the local index formula for spectral triples over nonunital alg...
Potential theory of one-dimensional geometric stable processes
geometric stable process Green function first exit time tail function Poisson kernel Levy process
2011/8/25
Abstract: The purpose of this paper is to find optimal estimates for the Green function and the Poisson kernel for a half-line and intervals of the geometric stable process with parameter $\alpha\in(0...
Preference aggregation theory without acyclicity: The core without majority dissatisfaction
Core Nakamura number kappa number simple games voting games maximal elements acyclic preferences limit ordinals
2011/9/29
Abstract: Acyclicity of individual preferences is a minimal assumption in social choice theory. We replace that assumption by the direct assumption that preferences have maximal elements on a fixed ag...
A case of combination of evidence in the Dempster-Shafer theory inconsistent with evaluation of probabilities
data fusion Dempster-Shafer theory evidence accumulation probability uncertainty
2011/8/22
Abstract: The Dempster-Shafer theory of evidence accumulation is one of the main tools for combining data obtained from multiple sources. In this paper a special case of combination of two bodies of e...
The Resurgence of Instantons in String Theory
Instantons Resurgent Analysis Topological and Minimal Strings Matrix Models
2011/7/7
Nonperturbative effects in string theory are usually associated to D-branes. In many cases it can be explicitly shown that D-brane instantons control the large-order behavior of string perturbation th...
Major revolts have recently erupted in parts of the Middle East with substantial international repercussions. Predicting, coping with and winning those revolts have become a grave problem for many reg...
Semianalytic theory of self-similar optical propagation and mode locking using a shape-adaptive model pulse
adaptive model pulse Semianalytic theory self-similar optical propagation mode locking
2011/7/7
A semianalytic theory for the pulse dynamics in similariton amplifiers and lasers is presented, based on a model pulse with adaptive shape. By changing a single parameter, this test function can be co...