Math 6395: C*-algebras associated with Dynamical Systems,
Spring 2016
Basic Info
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Instructor: |
Dr. Mark
Tomforde
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Office: |
601 PGH
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Office Hours: |
By appointment.
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Lecture: |
TuTh 4:00PM--4:50PM in Room 2 AH
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Course Description:
We will discuss various classes of C*-algebras constructed from
dynamical systems, and examine the interplay that exists between the analysis,
algebra, and dynamics. The course will start with an introduction to symbolic
dynamics and discrete dynamical systems, and afterward we will construct classes
of C*-algebras (e.g., Cuntz-Krieger algebras, graph C*-algebras, crossed
products by the integers) that are intimately related to the dynamical systems.
Textbook:
An electronic copy of the textbook will be given to you. If you want to by a
physical copy, there are fairly inexpensive used copies available on Amazon.com.
As with any textbook, there are a few errors throughout the book. The following
are errata and clarifications found since the second printing.
List of Errata for "An Introduction to Symbolic Dynamics and Coding"
There is also a website
for the book that you may find useful.
Material for Symbolic Dynamics Portion of Course:
From Jan. 19 to Feb. 18 Dr. Ott will lead discussion sections where you
can talk about the reading and work problems.
Sections from the textbook to be covered.
Chapter 1, Sec. 1.1--1.5
Chapter 2, Sec. 2.1--2.5
Chapter 6, Sec. 6.1--6.3
Chapter 7, Sec. 7.1--7.5
If you're ambitious, you can also look ahead to Sec. 13.6, 13.8, 13.9
Here are problems from Chapters 1 and 2 that look interesting. I may add problems
from Ch. 6 and Ch. 7 later, depending on how fast the course progresses.
Problems:
1.1.1
1.2.2
1.2.3
1.2.4
1.2.5
1.3.2
1.4.1
1.4.2
1.4.4
1.4.5
1.5.1
1.5.2
1.5.3
1.5.4
1.5.5
1.5.6
1.5.7
2.1.1
2.1.2
2.1.3
2.1.5
2.1.6
2.2.1
2.2.2
2.2.3
2.2.4
2.2.6
2.2.7
2.2.8
2.2.9
2.2.10
2.2.14
2.3.1
2.3.2
2.3.3
2.3.4
2.3.5
2.3.6
2.4.1
2.4.2
2.4.3
2.4.4
2.4.5
2.4.6
2.4.7
2.4.9
Material for C*-algebras Portion of Course:
To be added after Feb. 22 when Dr. Tomforde returns and begins to lecture.