Noncommutative Analysis

Month: October, 2014

Topological K-theory of C*-algebras for the Working Mathematician – Lecture 1

Claude (Haim) Schochet is spending this semester at the Technion, and he kindly agreed to give a series of lectures on K-theory. This mini-course is called “Topological K-theory of C*-algebras for the Working Mathematician”.

There will be seven lectures (they take place in Amado 814, Mondays 11:00-12:30):

  1. A crash course in C*-algebras.
  2. K-theory by axioms and core examples.
  3. K-theory strengths and limitations.
  4. Payoffs in functional analysis: elliptic operators on compact spaces, essentially normal and Toeplitz operators.
  5. Payoffs in algebraic topology: bivariant K-theory by axioms, core examples, and the UCT.
  6. Modelling of groups, groupoids, and foliations.
  7. Payoffs in geometry: Atiyah-Singer and Connes index theorems.

Since the pace will be really fast and the scope very broad, I plan to write up some of the notes I take, to help myself keep track of these lectures. When I write I will probably introduce some mistakes, and this is completely my fault. I will also probably not be able to hold myself from making some silly remarks, for which only I am responsible.

I also hope that these notes I post may help someone who has missed one or several of the talks make up and come to the next one.

The first talk took place last Monday. To be honest I wasn’t 100% on my guard since I heard such crash courses so many times, I was sure that I’ve heard it all before but very soon I was in territory which is not so familiar to me (The title “crash course” was justified!). Maybe I will make up some of the things I write, or imagine that I heard them.

(The next lectures will be on stuff that is more advances and I will take better notes, and hopefully provide a more faithful representation of the actual lecture).

I will refer in short to the following references:

1. Pedersen – C*-algebras and their automorphism groups.

2. Brown and Ozawa – C*-algebras and finite dimensional approximation.

3. Davidson – C*-algebras by example.

4. Dixmier – C*algebras

5. Blackadar – K-theory for operator algebras

Read the rest of this entry »

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New year, change of coordinates, change of mass, good bye BGU

I had a busy summer.

In August my family and I moved from Lehavim to Rosh Pina. In September my family grew: my daughter Sarah was born two days before the (Hebrew) new year. There is a lot of excitement and happiness around this, but this blog is not the place to expand.

What I do want to expand about is that today (October 1) my new appointment at the Department of Math at the Technion officially begins (of course this is only official because my baby is still very fresh and I am at home right now). This is a great place to work in, and I am very grateful for my good fortune, but it means, sadly, that as of today I no longer work in the Department of Math at Ben-Gurion University.

From September 2011 to September 2014 BGU was my academic home (and a little more), and I was very proud to be a member of the Math Department there. Unfortunately, for family reasons we decided to move to the north of the country, and it did not make sense to stay there (and so I applied for a job at the Technion, which I was very fortunate to get). I will miss my friends at BGU, the excellent students, the great colleagues, the vibrant seminars and the wonderful staff very much. I will also miss the Negev, Beer-Sheva and Lehavim.