Knots in Washington: Conferences on Knot Theory and its Ramifications 2008-2010

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AbstractAward: DMS-0817858Principal Investigator: Jozef H. Przytycki, Yongwu Rong,Alexander N. Shumakovitch, Hao WuA series of conferences devoted to knot theory and itsramifications will be held in 2008-2010, continuing the "Knots inWashington" conferences held every semester in the greaterWashington, D.C. area since fall 1995. Plenary talks willsurvey the state of knowledge in areas such as Khovanov homology,Heegard Floer homology, and categorification of existinginvariants such as skein modules. Contributed talks and periodsdevoted to interaction among participants provide opportunitiesfor graduate students and recent PhDs to be a part of "Knots inWashington," and the organizers encourage students and juniorresearchers to attend these meetings.Low dimensional topology studies shapes of three and fourdimensional spaces. These dimensions are of particular interestto us because they are the dimensions of our space and ourspace-time. Knot theory is a subfield of low dimensionaltopology, which studies the knottedness in our space. One of themain goals of knot theory is to distinguish knotted objects. Thisis often done by means of the so called "knot invariants,"functions that replace geometric objects, such as knots, withthose that are easier to compare. Over the past two decades,there have been a flourish of new invariants in low dimensionaltopology, boosted by ideas from gauge theory, quantum algebras,and mathematical physics. The purpose of the "Knots inWashington Conferences" is to bring together the researchers ofthe field, including established mathematicians as well asgraduate students and recent PhDs, to discuss the state of theart of the subject. The conference web page ishttp://home.gwu.edu/~przytyck/knots/index.html.