12.04.2011
Kohomologie Ekwiwariantne i rachunek funkcji wymiernych
Andrzej Weber
Abstrakt: Badamy rozmaito?ci zespolone z dzia?aniem torusa. Twierdzenie o lokalizacji Atiyah-Botta i formula Berline-Vergne pozwala obliczy? globalne niezmienniki osobliwych podrozmaito?ci badaj?c jedynie otoczenia punktów sta?ych dzia?ania. Formu?a ta zastosowana do oblicze? klas Cherna-MacPhersona rozmaito?ci Schuberta prowadzi do interesuj?cych to?samo?ci wi???cych funkcje wymierne wielu zmiennych.
19.04.2011
"Grupy holonomii p?askich rozmaito?ci z w?asno?ci? R_{infty}"
(wspólna praca z R.Lutowskim)
Andrzej Szczepa?ski (Uniwersytet Gda?ski)
Abstrakt: Je?eli f:G ----> G jest automorfizmem grupy sko?czenie generowanej, sick to dwa alementy $alpa i eta in G$ s? f-sprze?one, gdy $eta = galpha (f(g))^{-1}$. Ilo?? takich klas sprz??ono?ci nazywa si? liczb? Reidemeistera R(f) odwzorowania f. Grupa ma w?asno?? R_{infty} gdy wszystkie jej automorfizmy maj? liczb? R(f) = infty. Wspomnimy te? o zwi?zkach z liczbami Lefschetza i Nilsena.
10.05.2011
"Homology of distributive structures"
Józef Przytycki (order Helvetica, malady sans-serif">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.
