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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：First-Order Aspects of Coxeter Groups
考克斯特群 一阶方面 非阿贝尔自由群
2023/5/5
Since the work of Sela, and Kharlampovich & Myasnikov on Tarski’s problem for non-abelian free groups, the model theoretic analysis of classes of groups arising from combinatorial and geometric group ...
A FIRST LOOK AT DIFFERENTIAL ALGEBRA.
The first $L^2$-Betti number and approximation in arbitrary characteristic
First L2-Betti number approximation in prime characteristic Group Theory
2012/6/19
Let G be a finitely generated group and (G_i) a descending chain of finite index normal subgroups of G. Given a field K, we consider the sequence b_1(G_i;K)/[G:G_i] of normalized first Betti numbers o...
Noncommutative oscillators from a Hopf algebra twist deformation. A first principles derivation
Noncommutative oscillators Hopf algebra twist deformation principles derivation
2011/3/3
Noncommutative oscillators are first-quantized through an abelian Drinfel’d twist deformation of a Hopf algebra and its action on a module. Several impor-tant and subtle issues making possible the qua...
Approximating the first $L^2$-betti number of residually finite groups
residually finite groups math
2010/11/24
We show that the first $L^2$-betti number of a finitely generated residually finite group can be estimated from below by using ordinary first betti numbers of finite index normal subgroups. As an app...
The threshold-two contact process on a random r-regular graph has a first order phase transition
The threshold-two contact process r-regular graph phase transition
2010/11/12
We consider the discrete time threshold-two contact process on a random $r$-regular graph on $n$ vertices. In this process, a vertex with at least two occupied neighbors at time $t$ will be occupied ...
The first boundary value problem for Abreu's equation
Abreu’s equation toric manifolds variational problem
2010/12/3
In this paper we prove the existence and regularity of solutions to the first boundary value problem for Abreu’s equation, which is a fourth order nonlinear partial differential equation closely relat...
A Polynomial Time Algorithm to Find Rational General Solutions of First Order Autonomous ODEs
Rational general solution rst order autonomous ODE rational parameterizations Laurent series Pade approximants polynomial time algorithm
2013/9/9
We give a necessary and su±cient condition for an algebraic ODE to have a rational type general solution. For a ˉrst order autonomous ODE F = 0, we give an exact degree bound for its rational solution...