Trajan Hammonds
Office: Fine Hall
Email: trajanh [at] math [dot] princeton [dot] edu
I am a fifth year math PhD student at Princeton advised by Prof Akshay Venkatesh. I am currently on the academic job market.
Research
I am interested in analytic aspects of automorphic forms and representations. This includes relative character asymptotics, spectral reciprocity of L-functions, and L^p bounds for eigenfunctions.
- Uniform asymptotics for relative characters I: The non-archimedean case in preparation
- Optimal L4 estimates and microlocal analysisin preparation
With Anshul Adve. - The completed standard L-function of modular forms on G2. [arXiv]
With Fatma Cicek, Giuliana Davidoff, Sarah Dijols, Aaron Pollack, and Manami Roy.
Research (from Undergrad)
- Rank and bias in families of hyperelliptic curves via Nagao's conjecture. [arXiv]
With Ben Logsdon, Seoyoung Kim, Alvaro Lozano-Robledo, and Steven J. Miller.
Journal of Number Theory. - The explicit Sato-Tate conjecture for primes in arithmetic progressions. [arXiv]
With Casimir Kothari, Noah Luntzlara, Steven J. Miller, Jesse Thorner, and Hunter Wieman.
International Journal of Number Theory. - Counting roots of polynomials over (Z/p^2Z). [arXiv]
With Jeremy Johnson, Angela Patini, and Robert Walker. Houston Journal of Mathematics.
Teaching
- Fall 2024: Grader for Algebra I (MAT 345).
- Spring 2024 : Grader for Local Fields (MAT 346).
- Fall 2023: Grader for Representation Theory (MAT 449).
- Spring 2023: AI for Linear Algebra with Applications (MAT 202).
- Fall 2022: Grader for Algebraic Number Theory (MAT 419).
- Spring 2022 : Grader for Local Fields (MAT 346).
- Spring 2020 (CMU): Grader for Principles of Real Analysis I (21-355).
- Fall 2019 (CMU): Teaching Assistant for Matrices and Linear Transformations (21-241).
- Fall 2018 (CMU): Teaching Assistant for Concepts of Mathematics (21-127).
Other Activites
- Fall 2021 : Gave four lectures on Langlands' Euler Products in Sarnak Student Seminar
- Spring 2022 : Gave two lectures on Sparse Equidistribution Theorems in preparatory learning seminar for IAS special year
- Fall 2022 : Organized Research Seminar on Uses of the Relative Trace Formula in Analytic Number Theory (co-organized with N.Z.)
- Fall 2022 : Organized Learning Seminar on Automorphic Representations
- Spring 2023 : Organized Learning Seminar on Michel-Venkatesh Method (co-organized with L.Y.)