# Robert Bruner

Professor

313-577-2479 (dept)

313-577-7596 (fax)

1201 FAB

## Website(s)

# Robert Bruner

I started first grade in a one room schoolhouse outside of Downs, Kansas, where I was the only first grader. My family then moved to Kansas City, Missouri, where I attended *excellent* public elementary and high schools for second through tenth grade. I have always been proud of fellow Missourians Mark Twain and Harry S Truman.

I finished high school at Phillips Exeter Academy in Exeter, New Hampshire, which opened up an entire world to me. I had superb instruction and access to resources in math and science, and also in literature and language. It was psychologically beneficial to be surrounded by people of many different points of view.

When I went to college at Amherst, my interests were mathematics, physics, philosophy and poetry, but I also took courses in anthropology, psychology and religion (specifically, religions of China and India).

At the University of Chicago, I found algebraic topology, and related fields, which have an especially appealing mix of algebra and topology. Aside from the lively mathematical culture, Chicago was an great place to attend graduate school, because I could see many of the blues musicians I appreciated play live in small clubs.

I learned late in life (age 40+) that collaboration is an especially effective way to make a greater contribution to mathematics, much more effective than working in isolation. I have learned an enormous amount from my collaborators.

If you are not a preofessional mathematician, and wonder what we topologists do, you might like my little essay "What is Topology?"

## Research interest(s)/area of expertise

- Algebraic Topology
- Computations in Stable Homotopy Theory
- Topological modular forms
- Connective K-theory, and relations to number theory
- Red shift
- Root invariants

## Research

Please see my papers, talks, software, and various notes.

## Education

- PhD - University of Chicago, 1977
- SM - University of Chicago, 1974
- BA - Amherst College, 1972 (summa cum laude).

## Awards and grants

College of Science Teaching Award, 1997

Board of Governors Faculty Recognition Award, 2005

Knut and Alice Wallenberg Foundation Visiting Professorship, 2020

## Selected publications

See my publications, talks and software list for a complete listing.

**Books**

(with John Rognes) * The Adams spectral sequence for topological modular forms*, 2021, xix+690 pp.

(with John Greenlees) * Connective real K-theory of finite groups *, 2010. vi+318 pp.

(with John Greenlees) * The connective K-theory of finite groups *, 2003, viii+127 pp.

(with Peter May, Jim McClure, and Mark Steinberger) * H∞-ring spectra and their applications*, 1986, viii+388 pp.