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Author ORCID Identifier

https://orcid.org/0009-0000-8838-1423

Date Available

5-1-2026

Year of Publication

2026

Document Type

Doctoral Dissertation

Degree Name

Doctor of Philosophy (PhD)

College

Arts and Sciences

Department/School/Program

Mathematics

Faculty

Kate Ponto

Faculty

Bert Guillou

Abstract

Character theory arises in many distinct fields of mathematics, but its many instantiations often share a few key features: they arise in contexts where one object is acted on or parametrized by another, and they are often computed via "trace-like" formulas. Focusing on these properties, we present a categorical formalism for constructing such characters. We first define a notion of "loop representation" for symmetric monoidal bicategories, then build a character for such representations via the canonical symmetric monoidal trace. We then show that this character defines a symmetric monoidal functor which satisfies commutativity properties with respect to both restriction- and induction-like functors, precisely mirroring the representation theoretic relationship between characters and restriction and induction of representations. We also show that a 1-categorical analog of this formalism recovers the classical character of a finite group representation, and explore connections to algebraic geometry and the Grothendieck-Riemann-Roch theorem via the Chern character.

Digital Object Identifier (DOI)

https://doi.org/10.13023/etd.2026.249

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