Fomin This award funds Professor Sergey Fomin's exploration of new relations between combinatorics and algebra. A new approach to the theory of Schubert and Grothendieck polynomials based on exponential solutions to the Yang-Baxter equations has suggested new developments in the combinatorics of Coxeter groups. This work will build on this via symmetric functions, local associative algebras and universal algebra. This research falls in the broad category of combinatorics, which is one of the most active fields in today's mathematics. At its roots, combinatorics is the study of systematic counting. Counting can be incredibly difficult when the objects are difficult to list, and combinatorists look for general methods for overcoming these difficulties. Today's combinatorics makes use of a wide variety of the most advanced and modern mathematical techniques. Although its roots go back several centuries, the field has had an explosive development in the past few decades. This growth comes from its importance in communications and information technology and from the success of modern techniques to problems of counting. ***

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Application #
9400914
Program Officer
Sidney W. Graham
Project Start
Project End
Budget Start
1994-07-01
Budget End
1997-12-31
Support Year
Fiscal Year
1994
Total Cost
$103,359
Indirect Cost
Name
Massachusetts Institute of Technology
Department
Type
DUNS #
City
Cambridge
State
MA
Country
United States
Zip Code
02139