Areas of Interest
Algebraic topology, especially stable homotopy theory, algebraic K-theory, applications to manifolds and cell complexes.
Research
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: in 2022 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.
Courses
Fall 2026
| Course |
Section |
Title |
Schedule |
Room |
| Math 330 |
03 |
Number Systems |
MWF 11:45–1:15
|
WH-100B
|
| Math 601B |
01 |
Topics in Topology |
MWF 2:45–3:45
|
WH-309
|
Ph.D. Students
-
Lucas Williams,
Spring, 2026
— Invariants for Families of Periodic Points
-
Ezekiel Lemann,
Fall, 2025
— Some results on scissors congruence and K-theory
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