Arkansas Spring Lecture Series 2003: On the Andrews-Curtis and Poincare Conjectures; April 10-12, 2003; Fayetteville, AR

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AbstractAward: DMS-0245047Principal Investigator: Yoav RieckAt the center of the proposed conference will be a series of lectureby Professor Andrew Casson of Yale University. These lecture willfocus on two of the most important open questions in the fields oftopology and group theory. The first question, the PoincareConjecture, was posed by Henri Poincare almost 100 years ago. It isconcerned with the basic structure of very simple 3-dimensionalspaces; while the Andrews-Curtis Conjecture is about algebraicstructures, and is very relevant to the Poincare Conjecture. Inaddition to a survey of existing approaches, partial results and openquestions related to these conjectures, these talks will attempt todescribe some intriguing similarities and differences between the twoconjectures. In addition, 10 leading experts from around the worldwill deliver talks about their own work.This conference will be the 28th annual Arkansas Spring LectureSeries. The format of the lecture series is 5 one hour talks by aworld leading mathematician, accompanied by about 10 lectures ofinvited experts, and several shorter talks by a variety of people,including graduate students. This structure is valuable, particularlyfor younger researchers, that get an excellent learning opportunity.This year's Lecture Series is about 3-dimensional topology. Theimportance of low dimensional topology has been growing in recenttears, with numerous applications starting at robotics and control,and ending with theoretical physics and cosmology. For example, oneintriguing question is what the shape of the Universe is. Thespherical shape of the earth was discovered two millennia ago, and yetwe have no clue as to the shape of the Universe. The work ofProfessor Casson as well as other leading mathematician, may helpanswer this question by leading astronomers is the right direction,and helping design the right experiments to answer these questions.Jeff Weeks, a McArthur Fellow, will discuss such experiments in alecture open to the public and using a language accessible to all.This will give the public an opportunity to understand the work ofworld leading mathematicians. Jeff Weeks talk should have greateducational value in motivating younger students to enjoy basicresearch.