Mathematical Sciences: Lattice Theory and Algebraic         Combinatorics
{'Code': '03040300', 'Directorate': {'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Gary Cornell'}
The research involves problems in lattice theory and                       algebraic combinatorics, including the conjectures that finite-                 rank Arguesian lattices with distributive skeleton are                          representable, that homomorphic images of representable lattices                are representable, and that the dual of a representable lattice                 need not be representable.  Other work in lattice theory will                   involve the investigation of new continuous analogues of finite                 partition lattices.  The problems in algebraic combinatorics are                to prove a conjectured bijection between shifted standard Young                 tableau of a certain shape and maximal-length words in the                      Coxeter group of type B(n), and to study the applications of a                  new combinatorial formulation of multivariate Lagrange inversion.                    Lattices appear throughout mathematics, making lattice                     theory an important topic of study, not only for its own                        intrinsic interest, but for its applications in mathematics and                 related disciplines.
{'FirstName': 'Mark', 'LastName': 'Haiman', 'EmailAddress': 'mhaiman@math.berkeley.edu', 'StartDate': '03/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Massachusetts Institute of Technology', 'CityName': 'Cambridge', 'ZipCode': '021394301', 'PhoneNumber': '6172531000', 'StreetAddress': '77 MASSACHUSETTS AVE', 'CountryName': 'United States', 'StateName': 'Massachusetts', 'StateCode': 'MA'}
{'Code': '1264', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8717795.xml'}