25 mar 2015 -- 14:30
Aula di Consiglio, Dip. Matematica, Università "La Sapienza", Roma
Models (simplicial, cellular...) of topological spaces are usually equipped with various operations: products, dualities, cohomological operations, and so on. One can also consider topological spaces from another point of view: instead of looking at the internal structure of each space, one can consider their collective structure. In the particular case of finite spaces, they are in bijection with quasi-orders, and it is natural to investigate their linear span using techniques of algebraic combinatorics. New operations and structure theorems arise from this point of view, as well as connexions with Hopf algebras such as the one of quasi-symmetric functions. Joint work with L. Foissy and C. Malvenuto.