International Seminar on Low-Dimensional Homotopy Theory and Combinatorial Group Theory

拓扑学家将在俄勒冈州的沃洛瓦湖小屋参加一个密集的国际研讨会。本次会议的重点将是关于低维同伦理论和组合群论中尚未解决的问题的正在进行的工作。这些猜想包括怀特黑德的非球性猜想、安德鲁斯-柯蒂斯猜想、二维沃尔的支配问题、关系缺口问题和艾伦堡-加内亚猜想。它们突出了低维同伦理论中拓扑学和群论的微妙相互作用，也涉及其他数学分支，如几何、组合学和代数K-理论。这次研讨会是在意大利、太平洋西北部和俄罗斯举行的类似会议的后续会议。它的目的是在美国和国际拓扑学家之间保持必要的联系。要解决的问题本质上是几何问题，挑战了人类关于三维空间是什么或可以被认为是什么的基本概念。改进对研讨会所审议的专题和问题的理解，可能会为拓扑学和最终在自然科学中进行思考和建模开辟新的途径。研讨会形式强调对正在进行的想法的详细讨论和参与者的合作，从研究生到职业生涯早期的研究人员再到高级专家。

Topologists will meet for an intensive international workshop at Wallowa Lake Lodge in Oregon. The focus of this meeting will be ongoing work on unsolved problems in low-dimensional homotopy theory and combinatorial group theory. These include Whitehead's Asphericity Conjecture, the Andrews-Curtis Conjecture, Wall's Domination Problem in dimension two, the relation gap problem, and the Eilenberg-Ganea Conjecture. They highlight the very delicate interplay of topology and group theory in low-dimensional homotopy theory and also involve other branches of mathematics like geometry, combinatorics, and algebraic K-theory.This workshop is in succession to similar conferences held in Italy, the Pacific Northwest, and Russia. It aims to maintain needed connections between American and international topologists. The problems to be addressed are geometric in nature, challenging the basic human conception of what three-dimensional space is or can be thought to be. Improvements in the understanding of the topics and problems considered at the seminar may open new avenues of thinking and modelling in topology and eventually in the natural sciences. The workshop format emphasizes detailed discussion of ideas in progress and collaboration of the participants, from graduate students to early-career researchers to senior experts.