Automorphic Forms,
Representation Theory
& Number Theory
Assistant Professor working at the intersection of automorphic forms, representation theory, and number theory.
Background
I am an Assistant Professor at Oklahoma State University. Previously, I was an NSF Postdoctoral Fellow at the University of Toronto under the mentorship of James Arthur. I earned my PhD from the University of Missouri in 2018, advised by Shuichiro Takeda, now at Osaka University.
I am also a faculty advisor for the Oklahoma State University Chapter of the Association for Women in Mathematics.
Research Interests
My research lies at the intersection of automorphic forms, representation theory, and number theory. At the heart of this intersection sits the Langlands Program — a vast and ambitious framework conjecturing that deep arithmetic information encoded in Galois representations is reflected in analytic objects called automorphic representations. Automorphic forms serve as far-reaching generalizations of periodic functions, while representation theory provides the tools to decompose spaces of these functions systematically, ultimately illuminating fundamental questions in number theory concerning L-functions, Diophantine equations, and the distribution of prime numbers.
Key Components
The core of the intersection. Classical holomorphic modular forms are recast as representations of adelic groups, enabling their systematic study via the tools of harmonic analysis and opening the door to the full power of modern representation theory.
Galois representations encode the symmetries of roots of polynomials over number fields. The Langlands conjectures predict that these arithmetic objects correspond precisely to specific automorphic representations — a profound bridge linking the discrete world of algebra to the analytic world of automorphic forms.
Representation theory provides the structural framework for understanding the spaces in which automorphic forms live. By decomposing these spaces into irreducible components, one obtains automorphic L-functions — powerful invariants carrying deep arithmetic information.
Automorphic forms give rise to complex L-functions whose analytic properties — analytic continuation, functional equations, and the location of zeros — are central to resolving deep questions in number theory. Understanding these functions is one of the principal goals of the Langlands Program.
The Selberg Trace Formula — and its far-reaching generalization, the Arthur-Selberg Trace Formula — is one of the most powerful tools in the subject. It forges a remarkable connection between the analytic spectral world of automorphic forms and the geometric world of closed geodesics, and serves as a primary mechanism for establishing instances of Langlands functoriality.
Publications & Preprints
Organized Conferences
Upcoming
Past
Research Groups
Teaching
My courses and interactions with students are guided by the following axioms written by Professor Federico Ardila at San Francisco State University:
Current Courses: MATH 3013 — Linear Algebra & MATH 4453 — Mathematical Interest Theory
Office Hours: Tuesdays and Thursdays 9:00–11:00 AM, or by appointment.
Course History
Becoming an Actuary
Actuaries are analytical professionals who use mathematics, statistics, and financial theory to assess and manage risk. The profession consistently ranks among the top careers for job satisfaction, salary, and employment outlook. Actuaries work in insurance, finance, consulting, government, and healthcare.
Actuarial credentials are granted by two main organizations: the Society of Actuaries (SOA), which focuses on life, health, pension, and finance, and the Casualty Actuarial Society (CAS), which focuses on property and casualty insurance. Most students begin with the SOA pathway. The first two preliminary exams — P and FM — are jointly administered by both societies.
SOA Pathway to Associate (ASA)
To earn the Associate of the Society of Actuaries (ASA) designation, candidates must complete a combination of exams, e-Learning modules, and validation requirements. There is flexibility in the order of completion. Visit the SOA ASA requirements page for full details.
Tips for Getting Started
SOA Practice Exams
Career & Job Resources
Recommended reading: The 2-Hour Job Search by Steve Dalton — a practical guide to finding actuarial internships and entry-level positions efficiently.