Research Interests
My research interests are primarily in number theory, formalized mathematics, logic, and computer-assisted mathematical writing.
- Analytic number theory: primes, sieve methods, zero-free regions, and $begin:math:text$L$end:math:text$-functions.
- Arithmetic geometry and Galois theory: Galois representations, Iwasawa theory, motives, and $begin:math:text$p$end:math:text$-adic methods.
- Automorphic forms: trace formulas, Langlands-type structures, and arithmetic applications.
- Logic and formalization: proof assistants, Homotopy Type Theory, and computer-assisted reasoning.
I am a disabled independent researcher. Reliable written communication and suitable computing equipment are essential for my study, writing, coding, document organization, and research work.
Selected Public Research and Writing
Selected public examples of my independent research and writing activity are listed below. A larger private archive is maintained offline.
- Yang Number Systems: An Introduction — exploratory work on generalized number-system structures.
- Complex Numbers Cohomology — notes on cohomological perspectives related to complex-number structures.
- Motivic Sieves and Number Theory — exploratory notes connecting sieve ideas with motivic language.
- Exponential Number Theory — initial notes on exponential analogues in number-theoretic structures.
- Non-Associative Galois Theory — exploratory work on Galois-type ideas beyond associative settings.
- The Necessity of AI in Future Mathematical Discoveries — a reflection on computing and mathematical research.
Some older files and drafts may be made available upon request.
Selected Seminar Talks
As an undergraduate, I gave several seminar presentations in graduate-level mathematics courses at the University of British Columbia. Selected topics included:
- Selberg Trace Formula for Compact Quotients, MATH 592, 2015.
- Group and Galois Cohomology, MATH 613E, 2015.
- The Arthur-Selberg Trace Formula, MATH 592, 2015.
- Hodge-de Rham Theory and Drinfeld Associators, MATH 620D, 2015.
- What is the Riemann Hypothesis and Why Do We Care?, PIMS Young Researchers Conference, 2014.
- A Feast of \(L\)-functions, MATH 529, 2011.
- Hardy's theorem and Selberg's theorem on zeros of \(\zeta(s)\), MATH 613E, 2011.
Slides for selected talks may be provided upon request.
Publications and Notes
- An Annotated Bibliography for Comparative Prime Number Theory , with Greg Martin.
- Lecture notes for the CRM workshop on counting arithmetic objects, prepared with Stanley Yao Xiao.
Public Record
I also maintain a separate public record concerning institutional accountability and disability-related matters. This material is separate from the research summary above. Relevant documents may be provided or cited by version date when appropriate.
Contact
For research, writing, accessibility, or equipment-related correspondence, please contact me by email. Due to a speech/language disability, written communication is preferred.