Mathematical Sciences: Presentations of Inverse Monoids
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{'SignBlockName': 'Ann K. Boyle', 'PO_EMAI': None, 'PO_PHON': None}
This research is concerned with the development of a theory                of presentations of inverse monoids.  There are two general areas               of problems which will be studied.  The first is concerned with                 basic decision problems which arise when an inverse monoid is                   presented by generators and relations.  In particular, the word                 problem and the E-unitary problem will be studied, with initial                 emphasis focussed on the one relator case.  Many of the geometric               techinques from combinatorial group theory as well as basic                     results from language theory and automata theory will be used.                  The second problem is concerned with a study of the closed                      inverse submonoids of the free inverse monoid and related                       problems.  In particular, the relationship between the closed                   inverse submonoids of a free inverse monoid, the topology of                    finite graphs, the rational and recognizable subsets of a free                  inverse monoid and the dot depth of a finite aperiodic inverse                  monoid will be studied in detail.  In addition, an attempt will                 be made to begin a computational theory of finite inverse                       semigroups of partial one-one transformations.                                       This research concerns the theory of monoids, the simplest                 of the abstract algebraic objects introduced in the last century.               The particular ones that the investigators are interested in are                precisely those structures arising in automata theory and the                   theory of formal languages in computer science.  Their techniques               range from group theory to geometry to computations.  Their                     approaches to the problems are imaginative.  This proposal should               make important contributions to both mathematics and computer                   science.
[{'FirstName': 'John', 'LastName': 'Meakin', 'PI_MID_INIT': 'C', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'John C Meakin', 'EmailAddress': 'jmeakin@math.unl.edu', 'NSF_ID': '000262582', 'StartDate': '06/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}, {'FirstName': 'Stuart', 'LastName': 'Margolis', 'PI_MID_INIT': 'W', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Stuart W Margolis', 'EmailAddress': 'margolis@math.hunter.cuny.edu', 'NSF_ID': '000190525', 'StartDate': '06/01/1987', 'EndDate': None, 'RoleCode': 'Co-Principal Investigator'}]
{'Name': 'University of Nebraska-Lincoln', 'CityName': 'LINCOLN', 'ZipCode': '685032427', 'PhoneNumber': '4024723171', 'StreetAddress': '2200 VINE ST # 830861', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Nebraska', 'StateCode': 'NE', 'CONGRESSDISTRICT': '01', 'CONGRESS_DISTRICT_ORG': 'NE01', 'ORG_UEI_NUM': 'HTQ6K6NJFHA6', 'ORG_LGL_BUS_NAME': 'BOARD OF REGENTS OF THE UNIVERSITY OF NEBRASKA', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '126400', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
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