Using equivariant obstruction theory in combinatorial geometry

Using Equivariant Obstruction Theory in Combinatorial Geometry

A significant group of problems coming from the realm of Combinatorial Geometry can only be approached through the use of Algebraic Topology. From the first such application to Kneser’s problem in 1978 by Lovász [13] through the solution of the Lovász conjecture [1], [8], many methods from Algebraic Topology have been used. Specifically, it appears that the understanding of equivariant theories...

using game theory techniques in self-organizing maps training

شبکه خود سازمانده پرکاربردترین شبکه عصبی برای انجام خوشه بندی و کوانتیزه نمودن برداری است. از زمان معرفی این شبکه تاکنون، از این روش در مسائل مختلف در حوزه های گوناگون استفاده و توسعه ها و بهبودهای متعددی برای آن ارائه شده است. شبکه خودسازمانده از تعدادی سلول برای تخمین تابع توزیع الگوهای ورودی در فضای چندبعدی استفاده می کند. احتمال وجود سلول مرده مشکلی اساسی در الگوریتم شبکه خودسازمانده به حسا...

Combinatorial Problems in Geometry and Number Theory

In a previous paper (given at the International Congress of Mathematicians at Nice 1970) entitled "On the application of combinatorial analysis to number theory geometry and analysis", I discussed many combinatorial results and their applications . I will refer to this paper as I (as much as possible I will try to avoid overlap with this paper) . First I discuss those problems mentioned in I wh...

Equivariant Algebraic Geometry

Canonical equivariant extensions using classical Hodge theory

In [4], Lin and Sjamaar show how to use symplectic Hodge theory to obtain canonical equivariant extensions of closed forms in Hamiltonian actions of compact connected Lie groups on closed symplectic manifolds which have the strong Lefschetz property. In this paper, we show how to do the same using classical Hodge theory. This has the advantage of applying far more generally. Our method makes us...