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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some Applications of Nevanlinna Theory
Nevanlinna理论 指数多项式 算术性质 Green Griffiths-Lang猜想
2023/11/29
In this talk, we will introduce some applications of Nevanlinna theory to “arithmetic properties” of exponential polynomials and some special cases of Green-Griffiths-Lang conjecture with moving targe...
EXPLICIT CLASS FIELD THEORY FOR GLOBAL FUNCTION FIELDS
EXPLICIT CLASS FIELD THEORY GLOBAL FUNCTION FIELDS
2015/8/26
Let F be a global function field and let F ab be its maximal abelian extension. Following an approach of D. Hayes, we shall construct a continuous homomorphism ρ: Gal(F ab/F) → CF , where CF is the id...
Wavelets and the theory of non-parametric function estimation
Pinsker’s theorem sparsity statistical decision problem
2015/8/20
Non-parametric function estimation aims to estimate or recover or denoise a function
of interest, perhaps a signal, spectrum or image, that is observed in noise and possibly
indirectly after some tr...
A Probabilistic and RIPless Theory of Compressed Sensing
Compressed sensing `1 minimization the LASSO the Dantzig selector (weak) restricted isometries random matrices sparse regression operator Bernstein inequalities Gross’ golfing scheme
2015/6/17
This paper introduces a simple and very general theory of compressive sensing. In this theory, the sensing mechanism simply selects sensing vectors independently at random from a probability distribut...
GALOIS THEORY OF ITERATED MORPHISMS ON REDUCIBLE ELLIPTIC CURVES AND ABELIAN SURFACES WITH REAL MULTIPLICATION
Kummer map elliptic curves abelian surfaces with real multiplication
2014/12/8
Let $F$ be a number field and let $A$ be an abelian algebraic group defined over $F$. For a prime $\ell$ and a point $\alpha \in A(F)$, we obtain the tower of extensions $F([\ell^n]^{-1}(\alpha))$ by ...
Potential Theory on Almost Complex Manifolds
Potential Theory Almost Complex Manifolds Complex Variables
2011/9/5
Abstract: Pseudo-holomorphic curves on almost complex manifolds have been much more intensely studied than their "dual" objects, the plurisubharmonic functions. These functions are defined classically...
Positive solutions for singularly perturbed nonlinear elliptic problem on manifolds via Morse theory
singular perturbation nondegenerate critical points Morse theory
2011/2/28
Given (M, g0) we consider the problem −"2g0+hu + u = (u+)p−1 with (", h) ∈ (0, ¯") × B. Here B is a ball centered at 0 with radius in the Banach space of all Ck symmetric covaria...
The aim of this paper is to extend the Morse theory for geodesics to the conical manifolds. In a previous paper [15] we de ned these manifolds as submanifolds of Rn with a nite number of conical sing...
Rubio de Francia's extrapolation theory: estimates for the distribution function
Rubio de Francia's extrapolation theory the distribution function
2010/11/15
Let $T$ be an arbitrary operator bounded from $L^{p_0}(w)$ into $L^{p_0, \infty}(w)$ for every weight $w$ in the Muckenhoupt class $A_{p_0}$. It is proved in this article that the distribution functi...
Sharp Thresholds for Monotone Non Boolean Functions and Social Choice Theory
Non Boolean Functions Social Choice Theory
2010/11/22
A key fact in the theory of Boolean functions $f : \{0,1\}^n \to \{0,1\}$ is that they often undergo sharp thresholds. For example: if the function $f : \{0,1\}^n \to \{0,1\}$ is monotone and symmetr...
The Unknotting Problem and Normal Surface Q-Theory
The Unknotting Problem Normal Surface Q-Theory
2010/12/1
Tollefson described a variant of normal surface theory for 3-manifolds, called Q-theory, where only the quadrilateral coordinates are used.Suppose M is a triangulated, compact, irreducible, boundary-i...
Lagrangian Floer theory and mirror symmetry on compact toric manifolds
Floer cohomology mirror symmetry toric manifolds open-closed Gromov-Witten invariant
2010/12/1
this paper we study Lagrangian Floer theory on toric manifolds from the point of view of mirror symmetry. We construct a natural isomorphism between the Frobenius manifold structures of the (big) quan...
Presents the Approximation Theory Network (AT-NET), a means for the distribution of information related to approximation theory. Offers access to AT-NET bulletins, as well as to related theses and jou...