Monday, 09 May 2011 10:37
10.05.2011
"Homology of distributive structures"
Józef Przytycki (The George Washington University)
Abstrakt: While homology theory of associative structures, such as groups and rings, has been extensively studied in the past beginning with the work of Hopf, Eilenberg, and Hochschild, the non-associative structures, such as quandles, were neglected until recently. The distributive structures have been studied for a long time and even C.S. Peirce in 1880 emphasized the importance of (right) self-distributivity in algebraic structures. However, homology for such universal algebras was introduced only fifteen years ago by Fenn, Rourke and Sanderson. I will develop this theory in the historical context and describe relations to topology and similarity with some structures in logic. I will also speculate how to define homology for Yang-Baxter operators and how to relate our work to Khovanov homology and categorification. We use here the fact that Yang Baxter equation can be thought of as a generalization of self-distributivity.
Monday, 11 April 2011 06:27
12.04.2011
Kohomologie Ekwiwariantne i rachunek funkcji wymiernych
Andrzej Weber
Abstrakt: Badamy rozmaitości zespolone z działaniem torusa. Twierdzenie o lokalizacji Atiyah-Botta i formula Berline-Vergne pozwala obliczyć globalne niezmienniki osobliwych podrozmaitości badając jedynie otoczenia punktów stałych działania. Formuła ta zastosowana do obliczeń klas Cherna-MacPhersona rozmaitości Schuberta prowadzi do interesujących tożsamości wiążących funkcje wymierne wielu zmiennych.
