Mathematical Sciences: Polynomial Invariants in Knot Theory
{'Code': '03040200', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Ralph M. Krause', 'PO_EMAI': None, 'PO_PHON': None}
This research centers on polynomial invariants in knot                     theory, their structure and implications for topology, and                      their interrelationships with mathematical physics.  In                         particular, the project concentrates on the investigation of                    state models for knot polynomials.  State models were first                     introduced by the principal investigator for the                                Alexander-Conway polynomial, and for the Jones polynomial.  The                 project investigates these models and related models                            (Yang-Baxter models) involving statistical mechanics and                        quantum groups, and their relations with more general state                     models for the skein polynomial (Homfly and Kauffman) that are                  combinatorial in nature.  The principal investigator intends to                 use state models to explore topological problems and to explore                 their connection with possible intrinsic (diagram-free)                         definitions of these invariants.                                                     Some fairly simple algebra concerning polynomials in one                   and two variables has found application to the problem of                       distinguishing between essentially different knots (as opposed                  to merely different presentations of the same knot).  Simple                    though the idea is, important applications exist to the coiling                 and possible knotting of the genetic material DNA, as well as                   to problems in statistical mechanics.
{'FirstName': 'Louis', 'LastName': 'Kauffman', 'PI_MID_INIT': 'H', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Louis H Kauffman', 'EmailAddress': 'kauffman@uic.edu', 'NSF_ID': '000475644', 'StartDate': '06/01/1989', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Illinois at Chicago', 'CityName': 'CHICAGO', 'ZipCode': '606124305', 'PhoneNumber': '3129962862', 'StreetAddress': '809 S MARSHFIELD AVE M/C 551', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Illinois', 'StateCode': 'IL', 'CONGRESSDISTRICT': '07', 'CONGRESS_DISTRICT_ORG': 'IL07', 'ORG_UEI_NUM': 'W8XEAJDKMXH3', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF ILLINOIS', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '126700', 'Text': 'TOPOLOGY'}
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