Samodzielna Pracownia Geometrii Nieprzemiennej
Kierownik:
- dr hab. Piotr M. Hajac (docent)
email
pok. 603, tel.: 022 5228 221
Pracownicy:
- dr Emily Burgunder (adiunkt)
(X.2008 - IX.2009)
email - dr Tomasz Maszczyk (adiunkt)
(I.2006 - IX.2009)
email
pok. 423, tel.: 022 5228 236 - dr Bartosz Zieliński (adiunkt)
(X.2006 - IX.2009)
email
pok. 608, tel.: 022 5228 218
O Pracowni
Noncommutative geometry entered the research programme of IMPAN in 1999. Five years later, with the help of the Warsaw University transfer-of-knowledge grant Quantum Geometry, this branch of IMPAN's mathematics gained an international dimension. Since 2004, there are about 20 visitors per year who contribute their research experience and give talks at the weekly Noncommutative Geometry Seminar held in the Institute. Among our invitees were Alain Connes and Maxim Kontsevitch, and the seminar talks are announced to about 100 mathematicians worldwide.
The aforementioned scientific activity helped to cristalize a local research team consisting of Piotr M. Hajac, Ulrich Krähmer, Tomasz Maszczyk and Bartosz Zieliński. Ulrich Krähmer was a Marie Curie fellow in the years 2005--2007. In January 2008, the Noncommutative Geometry Research Unit was formally created by the Institute Scientific Council. Since October 2008, the team will be enlarged by Emily Burgunder, who chose IMPAN for her European Postdoctoral Institute fellowship.
As an example of the collaboration between the local team and its guests, let us point out the work on Quantum-group equivariant pullbacks of C*-algebras and finite free distributive lattices. This is a largely completed though still running project carried out by: Paul F. Baum, Piotr M. Hajac, Ulrich Krähmer, Rainer Matthes, Chiara Pagani, Wojciech Szymański, Elmar Wagner and Bartosz Zieliński. Results obtained within this and other noncommutative geometry projects were reported in 20 articles.
To summarize, the key words characterizing IMPAN's research in noncommutative geometry are: K-theory of operator algebras and noncommutative Galois-type extensions, index theory and quantum groups, Hopf-cyclic homology and Chern-Galois character, corings and monoidal categories. The assumed research strategy is to explore the feedback between solving concrete difficult problems and developing new mathematical structures. The proposed approach is to unite rather than separate different fields of mathematics by taking advantage of complemetary tools that they offer. To this end, a large scale and intensive international collaboration is currently sustained and planned for the future.
