- Introduction
- Papers and presentations
- Notes, problems, and organized learning
- Archive from undergrad (MIT) and earlier
- Miscellaneous

Hi! I'm Victor Wang, a fourth-year math graduate student at Princeton. You can contact me at vywang (at) math.princeton (dot) edu. I am broadly interested in number theory, geometry (esp. algebraic), and discrete math (esp. with arithmetic, topological, or other structure). My advisor is Peter Sarnak.

See also arXiv and Google Scholar Citations.

1-color-avoiding paths, special tournaments, and incidence geometry (with Jonathan Tidor and Ben Yang); written during MIT SPUR 2016. We thought about a recent question of Loh (2015): must a 3-colored transitive tournament on N vertices have a 1-color-avoiding path of vertex-length at least N^(2/3)? This question generalizes the classical Erdos–Szekeres theorem on monotone subsequences (1935). To me this problem seems natural and surprisingly rich. Note: Gowers and Long just uploaded a very nice preprint (September 2016) on this problem and its natural generalizations.

On Hilbert 2-class fields and 2-towers of imaginary quadratic number fields, J. Number Theory 160 (2016), 492–515; written at Duluth REU 2015. I thought about a question of Martinet (1978): must every imaginary quadratic number field K/Q have an infinite Hilbert 2-class field tower when the discriminant of K has 5 prime factors? Naturally one tries to use class-field-theoretic constructions and inequalities, but difficulties arise from the combinatorics of certain 5 x 5 (or smaller) binary matrices of quadratic symbols. I proved some new cases and found some precise reasons and examples explaining some of the difficulties.

Simultaneous core partitions: parameterizations and sums, Electronic J. Combin. 23(1) (2016), #P1.4, 34 pages; written at Duluth REU 2015. This showed me a beautiful side of partitions and hook lengths that I had not seen before, and gave me a nice opportunity to interact with the vibrant core partitions community. Specifically, I re-interpreted some number-theoretic stabilizer sizes of Fayers in a friendlier way, which led to proofs of some enumerative-combinatorial conjectures of Fayers, as well as a simpler proof of a foundational structural result of Fayers.

Local-global principles in number theory (Hasse–Minkowski for quadratics), MIT Student Colloquium for Undergraduates in Math (11/2016).

Riemann–Roch with Hodge theory, MIT Curves Learning Seminar (9/2016).

1-color-avoiding paths, special tournaments, and incidence geometry (presented with Jonathan Tidor), MIT SPUR Conference (8/2016); slides available here.

Martinet's question on Hilbert 2-class field towers, AMS Contributed Papers Session in Number Theory, Joint Mathematics Meetings, Seattle, WA (1/2016); slides available here.

Roots of unity filter (finite Fourier analysis), MIT Student Colloquium for Undergraduates in Math (10/2015).

18.100p (p-adic analysis), MIT Student Colloquium for Undergraduates in Math (11/2014).

Informal notes on the Cohen–Lenstra heuristics: PDF.

Preliminary lecture notes from USA MOP 2018 (Math Olympiad Summer Program):

- Theoretical, BK: Polynomials, Mod, Algebraic conjugates and number theory.
- Theoretical, K: Linear algebra, Fields and Frobenius, Power series and p-adic integers, Equations mod p and Weil.
- Thematic, BK: Manipulation and bounding, Diophantine equations, Analytic number theory.
- Thematic, K: Complex numbers and geometry, Hard ideas (as opposed to soft ideas).

Some good books I've read:

- Cassels,
*Rational Quadratic Forms*(a good place to see several fundamental subjects applied and unified in interesting ways: linear and bilinear algebra, integral lattice theory, as well as basic abstract algebra and number theory). - Serre,
*Lectures on the Mordell-Weil Theorem*(Diophantine analysis).

See here.

Since January 2014 or so, I've enjoyed collaborating (as a math consultant) with many great teammates on Expii, an online education project seeking to break down topics while providing fun, relatable content (such as the theme-based Expii Solve) and a curated problem stream (organized and scaffolded through concept maps in the background). I hope that Expii's resources and outreach will complement the existing infrastructure in education, helping to give teachers the freedom to spend less time on tasks that can be automated, and more on the deepest human aspects that cannot be. Our current focus is on high school math and science, but we do have other topics like elementary number theory or advanced plane geometry.

If people played Codenames with only math terms, would we get better at finding connections in math? How about other topics (academic or not)?

A guide I've found helpful on whether to trash, recycle, or compost (in Princeton): webpage; PDF.

Food for thought: if socialism is 0-dimensional (in terms of purely economic incentives), and modern capitalism is 1-dimensional, what lies beyond? Related: time banking; Digital Social Credits idea of Andrew Yang (too bad it will automatically be superficially compared with China's system).