Cary Malkiewich
(CARE-ee mall-KEV-itch) (he, him)
Assistant Professor

Department of Mathematical Sciences

Binghamton University

PO Box 6000

Binghamton, New York 13902-6000

malkiewich at

Curriculum Vitae

Research Statement

(Last updated Oct 1, 2023.)

My primary research area is algebraic topology. I like to apply stable homotopy theory (spectra) to questions about manifolds and cell complexes. My work has taken a recent turn towards scissors congruence: last year I proved that it is described by a Thom spectrum, and I am developing the consequences of this surprising result for the higher scissors congruence groups. I am partially supported by the grants NSF DMS-2005524 and NSF DMS-2052923.

Key words: algebraic topology, homotopy theory, spectra, G-spectra, parametrized spectra, free loop spaces, topological Hochschild homology (THH), algebraic K-theory, duality, traces, transfers, scissors congruence, Nielsen theory (fixed-point theory), h-cobordisms, high-dimensional manifolds.

Textbook in progress
Publications and Preprints

Other publications and preprints:


I am currently teaching MATH 330: Number Systems and MATH 601A: Stable homotopy and algebraic K-theory.

Talk Slides
Expository Writings

In preparation:

For a curated list of expository writings by other authors, see this website.

Detailed Expository Writings
Conferences and Seminars

I am one of the organizers of Binghamton's Geometry and Topology Seminar. I am co-organizing a workshop on scissors congruence K-theory in the summer of 2023 and a collaborative workshop on the same subject in the summer of 2024. In the past I organized the Topology Seminar at UIUC and the Stanford student topology seminar, and was involved with the "xkcd" discussion group, and the String topology seminar.

Extracurricular Activities

I've learned a lot from my experience as a teacher, a parent, and a relationship partner. If you're interested in some of the insights that I picked up along the way, you can find them here.