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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Inverse problem for the harmonic measure
谐波测量 反问题 双曲群
2023/4/17
Sample paths of a random walk on a hyperbolic group are known to converge to the Gromov boundary. The distribution of the exit point is called the harmonic measure. I will discuss the following invers...
On an arbitrary compact Riemann surface, necessary and sufficient conditions are found for the existence of semistable vector bundles with slope between zero and one and a prescribed number of linearl...
Equivalence of Reconstruction from the Absolute Value of the Frame Coefficients to a Sparse Representation Problem
frames nonlinear processing sparse representation
2015/9/29
The purpose of this note is to prove, for real frames, that signal reconstruction from the absolute value ofthe frame coefficients is equivalent to solution of a sparse signal optimization problem, na...
We show that the simple group PSL2(Fp) occurs as the Galois group of an extensionof the rationals for all primes p ≥ 5. We obtain our Galois extensions by studying the Galois action on the second étal...
MODULAR FORMS AND SOME CASES OF THE INVERSE GALOIS PROBLEM
MODULAR FORMS SOME CASES INVERSE GALOIS PROBLEM
2015/8/26
We prove new cases of the inverse Galois problem by considering the residual Galois representations arising from a fixed newform. Specific choices of weight 3 newforms will show thatthere are Galois e...
Some of the Combinatorics Related To Michael’s Problem
Combinatorics Related Michael’s Problem
2015/8/17
We present some new methods for constructing a Michael space, a regular Lindel ofspace which has a non-Lindel of product with the space of irrationals. The central result is a combinatorial statement ...
Let us begin this paper by recalling the following classical metrization theorem of Birkhoff and Kakutani.
Structured Stable Homotopy Theory and the Descent Problem for the Algebraic K-theory of Fields
Structured Stable Homotopy Theory Algebraic K-theory
2015/7/7
his is a relative result which asserts that the K-theory spectra of any two
algebraically closed fields of a given characteristic are equivalent to each other
after completion at a prime not e...
Exact Boundary Conditions for the Initial Value Problem of Convex Conservation Laws
exact boundary conditions artificial boundary conditions convex conservation laws Burgers’ (inviscid) equation
2015/5/4
The initial value problem of convex conservation laws, which includes the famous Burgers’ (inviscid) equation, plays an important rule not only in the-oretical analysis for conservation laws, but also...
We study the complexity of testing if two given matroids are isomorphic. The problem is easily seen to be in p 2 . In the case of linear matroids, which are
represented over polynomially growing fie...
Waring Problem for Finite Quasisimple Groups
Finite Quasisimple Groups Waring Problem Group Theory
2011/9/13
Abstract: The classical Waring problem deals with expressing every natural number as a sum of g(k) kth powers. Similar problems for finite simple groups have been studied recently, and in this paper w...
Abstract: Groups acting freely on Z^n-trees (Z^n-free groups) play a key role in the study of non-archimedean group actions. Following Stallings' ideas, we develop graph-theoretic techniques to invest...
Nonsmooth Formulation of the Support Vector Machine for a Neural Decoding Problem
Nonsmooth Formulation Support Vector Machine Neural Decoding Problem
2011/1/18
This paper formulates a generalized classification algorithm with an applica-tion to classifying (or ‘decoding’) neural activity in the brain. Medical doctors and researchers have long been interested...
A survey of the Poincaré Center Problem in degree 3 using finite field heuristics
survey Poincaré Center Problem degree 3
2011/2/21
We compare a heuristic count of components of the center variety in degree 3 with the equivalent count obtained from known families.From this comparison we conjecture that more than 100 unknown compon...
Half-space theorems and the embedded Calabi-Yau problem in Lie groups
Minimal surface constant mean curvature H-surface
2011/1/20
We study the embedded Calabi-Yau problem for complete embedded constant mean curvature surfaces of finite topology or of positive injectivity radius in a simply-connected three-dimensional Lie group X...