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.
