From symmetric to quasisymmetric functions - combinatorics and topology

25.11.2015, 14:00  –  2.09.2.22
Institutskolloquium

Christine Bessenrodt (Hannover), Birgit Richter (Hamburg)

• 14:00 Christine Bessenrodt (Hannover): From symmetric to quasisymmetric functions - combinatorial refinements
• 15:00 Coffee break
• 15:30 Birgit Richter (Hamburg): From symmetric to quasisymmetric functions - the topological point of view

Abstracts:
Christine Bessenrodt: From symmetric to quasisymmetric functions - combinatorial refinements
Symmetric functions are important objects in mathematics, coming with intricate combinatorial tools. Requesting not full but only shift invariance, Gessel introduced quasisymmetric functions in 1983; these have since been applied in diverse areas. As refinements of the classical Schur functions, a special basis for the Hopf algebra of symmetric functions, quasisymmetric Schur functions were defined by Haglund, Luoto, Mason and van Willigenburg in 2011. Jointly with Luoto and van Willigenburg, we have defined and investigated quasisymmetric pendants of skew Schur functions. The associated new combinatorics involving compositions and tableaux will be discussed, substantiating that the quasisymmetric Schur functions truly deserve their name.

Birgit Richter: From symmetric to quasisymmetric functions - the topological point of view
In topology, the identification of the cohomological interpretation of the Hopf algebra of symmetric functions is a classical result that is heavily used. In joint work with Andy Baker we developed a topological model of the Hopf algebra of quasisymmetric functions. I shall explain these models and describe some applications of the topological approach.