Mike Hermele (University of Colorado, Physics Department) Lattice models Part 2
Feb. 20, 2019 4pm (MATH 220)
Functional Analysis
Ulrik Enstad (University of Oslo)
X
In the 80's, Rieffel gave a general procedure to construct projective modules over twisted group C*-algebras. As an application, he constructed and classified projective modules over noncommutative tori. The modules obtained from this general set-up have been termed Heisenberg modules, and have since seen several other applications, e.g. in the construction of projective modules over noncommutative solenoids due to Latremoliere and Packer.
More recently, Luef and Jakobsen have shown that Heisenberg modules provide a natural framework for the theory of Gabor frames over locally compact abelian groups. In fact, the atoms of multi-window Gabor frames serve as generators of Heisenberg modules.
I this talk I will give a survey of frames in Hilbert modules and of the connection between Heisenberg modules and Gabor frames. If time permits, I will show how Heisenberg modules can be used to shed light on the Balian-Low theorem, a classical theorem in Gabor analysis.
Heisenberg modules and their connection to Gabor frames
Feb. 20, 2019 5pm (Math 350)
Math Club
Peter Elliott (CU Boulder)
X
An overview of mathematics in which subjects are studied that do not, at first, seem relevant to the problem at hand.
Heisenberg modules and their connection to Gabor frames