Professor Davis has published more than 140 papers, mostly in algebraic topology, beginning in 1973. Four foci of the topological work have been immersions of projective spaces in Euclidean space, periodicity in the homotopy groups of spheres, v1-periodic homotopy groups of compact Lie groups, and topological robotics. An offshoot of this was some papers in combinatorial number theory, mostly related to Stirling numbers of the second kind. His website maintains a collection of all known results about immersions and embeddings of real projective spaces. He feels that his nonimmersion theorem published in 1984 in the Annals of Mathematics was his best and most important paper.

# Don Davis

### Professor Emeritus

B.S., MIT, 1967

Ph.D., Stanford, 1972

###
Explore this Profile×

### Research Areas

### Additional Interests

- Algebraic topology
- Homotopy theory
- Immersions of projective spaces
- Topological robotics
- Combinatorial number theory
- Baseball statistics
- Coaching for high school math contests

### Research Statement

### Biography

After one post-doctoral year at University of California, San Diego, and two at Northwestern University, Professor Davis joined the faculty at Lehigh in 1974 as Assistant Professor. He became full Professor in 1984 and will retire in 2024. He served as department Chairman from 1994-1998. He directed 13 PhD theses. He received Lehigh’s Joseph Libsch Research award in 1989.

He had sabbatical leaves of one or two semesters at Northwestern University, University of Warwick, Princeton’s Institute for Advanced Study, Berkeley’s Mathematical Sciences Research Institute, Oxford University, and Johns Hopkins University. He has given more than 150 invited lectures in North America, Europe, and Japan. He was named an inaugural Fellow of the American Mathematical Society in 2012.

Since 1981, he has been giving a high school math contest at Lehigh, and in 1993 he formed the Lehigh Valley Math Team. This team, which now attracts students from an 80-mile radius, won the American Regions Math League national championship in 2005, 2009, 2010, and 2011, and has finished second or third six other times. He received several major awards for this coaching.

Ten representative publications.

*v_1- and v_2-periodicity in stable homotopy theory*, with Mark Mahowald, Amer Jour Math, 103 (1981) 615-659.

*A strong nonimmersion theorem for real projective spaces*, Annals of Math 120 (1984) 517-528.

*The image of the stable J-homomorphism*, with Mark Mahowald, Topology 28 (1989) 39-58.

The Nature and Power of Mathematics , Princeton University Press, 1993. Reprinted by Dover in 2003.

From representation theory to homotopy groups, Memoirs of American Math Society 759 (2002) 50 pages.

v_1-periodic homotopy groups of SO(n), with Martin Bendersky, Memoirs of American Math Society 815 (2004) 90 pages.

Projective product spaces, Jour of Topology 3 (2010) 265-279.

2-adic partial Stirling functions and their zeros, Jour of Combinatorics 5 (2014) 355-378.

An n-dimensional Klein bottle, Proc Royal Society Edinburgh 149 (2019) 1207-1221.

Two robots moving geodesically on a tree, with Mike Harrison and David Recio-Mitter, Algebraic and Geometric Topology 22 (2022) 785-814.

### Teaching

In recent years, Professor Davis has mostly taught topology classes and Survey of Calculus courses.