Noah Riggenbach

Noah Riggenbach is a Postdoctoral Scholar at Northwestern University conducting advanced research in algebraic topology and arithmetic geometry. His work centers on algebraic K-theory and trace methods, with publications spanning topological cyclic homology applications to diverse algebraic structures.

Education:

• PhD in Mathematics, Indiana University Bloomington (2021). Thesis: "The S1 Assembly Map on K-Theory and Topological Cyclic Homology" supervised by Michael Mandell.

Riggenbach's research bridges abstract homotopy theory with arithmetic geometry, specializing in computational approaches to algebraic K-theory through trace methods. His investigations frequently employ cyclotomic spectra and synthetic techniques to analyze rings and schemes, with particular emphasis on p-adic geometries and singular varieties. This work establishes critical connections between chromatic homotopy theory and arithmetic properties of algebraic objects.

Analysis of his publication trends (2021-2024) reveals consistent focus on applying topological cyclic homology to compute K-theory for specialized structures: truncated polynomials, cuspidal curves over perfectoid bases, double points, and p-adic unit disks. His methodology increasingly integrates cyclotomic synthetic spectra and perfectoid space theory, reflecting the field's evolution toward derived techniques and chromatic approaches.

Scientific Awards:

• No awards documented in source materials.

Riggenbach's current postdoctoral role emphasizes independent research without documented student advising or grant leadership. His collaborative work with established researchers like Benjamin Antieau and Elden Elmanto indicates integration into leading K-theory research networks.

No specific laboratories or structured research teams are referenced, though his office location (Lunt 304) situates him within Northwestern's mathematical research environment.