**Math 509, Topics in Analysis, Spring 2018**

**Positive Maps on Operator Algebras and Quantum Markov Semigroups**

**Lectures by Eric Carlen**

The class meets Mondays and Thursdays form 12:00 to 1:20 p.m. in His 525. My office hours are 1:30-2:30 Monday and 2:30-3:30 Wednesday. My office is 632 Hill Center. My email is carlen at math dot rutgers dot edu.

**Course Descrption**

A description of the course explains the topics it will cover. Math 502 will have provided sufficient preparation, and while ideally students would have completed it already, it should also be fine to take the two courses in parallel. A syllabus will be posted at the end of the second week when we will have settled on a suitable pace.

**Course Materials**

The text for the course is my own notes, which are being assembled into what is essentially a text — except the exercises will appear in the homework assignments. The notes will be posted in chapters, and the first two chapters are already on line. The remaining chapters will be written in the same form, and in fact, Chapters 3-5 are essentially ready, and will be posted before the course begins. Much of the material in the notes is taken from research papers, already even in chapter 2, and there is no existing texts that would serve the needs of this course, especially in the later parts when the topics will be taken from current research.

(1): Positive Maps on Operator algebras and Quantum Markov Semigroups, Chapters 1-4..

**Homework assignments**

The homework assignments are listed on the Homework assigments web page.

**Grading**

There will be homework assignments approximately every third class meeting and and a take-home final Exam.

**Assignment Solutions**

Here you will find detailed solutions to the assignments and tests, posted after the dues dates, of course!