Noncommutative geometry applies ideas from geometry to mathematical structures
determined by noncommuting variables. Within mathematics, it is a highly
interdisciplinary subject drawing ideas and methods from many areas of
mathematics and also from physics. Natural questions involving noncommuting
variables arise in abundance in many parts of mathematics. On the basis of
ideas and methods from algebraic and differential topology and Riemannian
geometry, as well as from the theory of operator algebras and from homological
algebra, an extensive machinery has been developed which permits the
formulation and investigation of the geometric properties of noncommutative
structures. This includes in particular K-theory and cyclic homology. Areas of
intense research in recent years are related to topics such as index theory,
quantum groups and Hopf algebras, the Novikov and Baum-Connes conjectures as
well as to the study of specific questions in other fields such as number
theory, modular forms, topological dynamical system, renormalization
theory.
Program
Activities commence Monday, June 29 in the morning. Most of the activity is
scheduled for the afternoon. Currently, we plan to have on-site talks
Friday morning, the scientific activity ending Friday at lunchtime CET.
| Time |
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
| 9:10-10:00 |
9:30: Get-together at MFO and introdution to the hybrid workshop concept. |
|
Departure for hike to Oberwolfach Kirche |
|
Dustin Clausen |
| 10:00-10:30 |
Coffee break |
|
|
|
Coffee break |
| 10:30-11:20 |
|
|
|
|
Birgit Richter |
| 11:30-12:20 |
|
|
|
|
Christopher Wulff |
| 12:30-13:30 |
lunch |
lunc |
lunch |
lunch |
lunch |
| 14:30-15:00 |
cake, cofffe, discussion |
cake, coffee, discussion |
cake, coffee,discussion |
cake, coffee, discussion |
cake, coffee, discussion |
| 15:00-15:30 |
|
zoom coffee gathering |
zoom coffee gathering |
zoom coffee gathering |
| 15:30-16:20 |
Alain Connes |
Hang Wang |
Makoto Yamashita |
Raphael Ponge |
|
| 16:30-17:20 |
Ralf Meyer |
Vito Zenobi |
Guillermo Cortinas |
Cherry Gong/ Jianchao Wu |
|
| 17:30-18:20 |
Henri Moscovici |
Zhizhang Xie |
Yanli Song |
Boris Tsygan |
|
| 20:00- |
|
Problem session |
|
Gong Show: Philipp Schmitt
Dev Mukherjee
Achim Krause
Julian Kranz
Zhizheng Han
|
|
- Alain Connes (Paris): Quantized calculus and Weil positivity, the
archimedean place
- Ralf Meyer (Göttingen): Analytic cyclic homology for dagger algebras
- Henri Moscovici: On Hopf cyclic cohomology and characteristic
classes
-
- Hang Wang (Shanghai): Index theory for elliptic operators invertible
at infinity
- Vito Zenobi (Göttingen/Rome): Delocalized Cocycles, Higher
rho-invariants and Positive Scalar Curvature
- Zhizhang Xie (College Station): Connes-Chern characters for higher rho
invariants of elliptic operators and higher eta invariants
- Makoto Yamashita (Oslo): Homology and K-theory of torsion free ample
groupoids and Smale spaces
- Guillermo Cortinas (Buenos Aires): Bivariant Hermitian K-theory
- Yanli Song (St. Louis): Higher Index theorem for proper action of Lie
groups
- Raphael Ponge (Chengdu): Cyclic homology and group actions on manifolds
- Cherry Gong (Los Angeles)/Jianchao Wu (College Station): The Novikov conjecture for geometrically discrete groups of diffeomorphisms
- Boris Tsygan (Evanston): Rigidity and characteristic classes for cyclic homology over p-adic numbers
- Dustin Clausen (Bonn): liquid modules
- Birgit Richter (Hamburg): Stability of Loday constructions
- Christopher Wulff (Göttingen); Slant products on the Higson-Roe exact sequence
Gong show
-
Philipp Schmitt: Universal algebraic index theorem
- Devarshi Mukherjee: Dagger completions and their application in
Non-archimedean cyclic homology
- Achim Krause: Bökstedt periodicity and quotients of DVRs
- Julian Kranz: An identification of the Baum-Connes and Davis-Lück assembly
maps
- Zhizheng Han: L2 invariants on symmetric spaces and
Plancherel Formula
Non-Commutative Geometry and Cyclic Homology 2020