MATHEMATICAL SCIENCES: Homology Representations Arising FormPosets of Partitions and Subspace Arrangements

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9400875 Sundaram This award funds the research of Professor Sheila Sundaram in algebraic combinatorics. In particular Prof. Sundaram will the homology of subposets of the partition lattice. She will try to establish that Whitney homology modules associated to certain posets are in fact permutation modules. This conjecture has implications regarding refinements of the tangent and Genocchi numbers. 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 and arrangement. 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. ***