This award will partially support the program "Noncommutative Geometry Emphasis year" https://sites.math.northwestern.edu/~tamarkin/Emphasis/ at Northwestern University in the academic year 2018-2019. This program will include the mini-workshop "Recent developments in Topological Cyclic Homology" (https://sites.math.northwestern.edu/~tamarkin/Emphasis/Topcyc) and the conference "Modern Trends in Non-commutative Geometry" (https://sites.math.northwestern.edu/~tamarkin/Emphasis/Tsyganfest). The mini-workshop will be held on the weekend Nov 3-4, 2018 and the conference will be held during the week May 20-24 (Monday-Friday) in 2019. Both events will take place at Northwestern University in Evanston IL. The goal of this program is to promote interaction between researchers working in areas related to non-commutative geometry. The mini-workshop and the conference will provide opportunities for researchers to disseminate their ideas and to broaden their perspectives. They will also provide opportunities for graduate students and postdocs to interact with senior experts in the areas related to noncommutative geometry.
Noncommutative geometry is connected to many branches of mathematics and mathematical physics and the main idea of noncommutative geometry is to study geometry via algebras of functions on "noncommutative manifolds". On such a "noncommutative manifold", the relevant object is no longer the space of points, but rather an associative algebra, which may be noncommutative. The topics of the program will include: noncommutative Hodge theory, (topological) cyclic/Hochschild homology, K-theory, index theory, deformation quantization, Riemann-Hilbert correspondence and microlocal categories.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
