Papers
- Vivian Kuperberg and Matilde Lalín. “Arithmetic constants for symplectic variances of the divisor function,” 2024. [arXiv]
- Noam Kimmel and Vivian Kuperberg. “Positive density for consecutive runs of sums of two squares,” 2024. [arXiv]
- Thomas Bloom and Vivian Kuperberg. “Odd moments and adding fractions,” 2023. [arXiv]
- Muhammad Afifurrahman, Vivian Kuperberg, Alina Ostafe, and Igor Shparlinski. “Statistics of ranks, determinants and characteristic polynomials of rational matrices,” 2024. Accepted to Forum Mathematicum. [arXiv]
- Régis de la Bretèche and Vivian Kuperberg. “Lower bounds on weighted moments of primes in short intervals in number fields,” 2023. Accepted to the Israel Journal of Mathematics. [arXiv]
- Vivian Kuperberg. “Sums of singular series along arithmetic progressions and with smooth weights,” 2023. Accepted to the International Journal of Number Theory. [arXiv]
- Vivian Kuperberg and Matilde Lalín. “Symplectic conjectures for sums of divisor functions and explorations of an orthogonal regime,” 2022. Accepted to the Transactions of the American Mathematical Society. [arXiv]
- Vivian Kuperberg. “Odd moments in the distribution of primes,” 2021. Accepted to Algebra and Number Theory. [arXiv]
- Noam Kimmel and Vivian Kuperberg. “Consecutive runs of sums of two squares,” 2024. [arXiv][journal]
- Vivian Kuperberg. “Sums of singular series with large sets and the tail of the distribution of primes,” 2023. [arXiv][journal]
- Vivian Kuperberg. “On pseudo-polynomials divisible only by a sparse set of primes and α-primary pseudo-polynomials,” 2022. [arXiv][journal]
- Vivian Kuperberg, Brad Rodgers, and Edva Roditty-Gershon. “Sums of singular series and primes in short intervals in algebraic number fields,” 2022. [arXiv][journal]
- Vivian Kuperberg and Matilde Lalín. “Sums of divisor functions and von Mangoldt convolutions in 𝔽q[T] leading to symplectic distributions,” 2022. [arXiv][journal]
- Martin Kassabov, Vivian Kuperberg, and Timothy Riley. “Soficity and variations on Higman’s group,” 2019. [arXiv][journal]
- Sameer Kailasa, Vivian Kuperberg, and Nicholas Wawrykow. “Chip-firing on trees of loops,” 2018. [arXiv][journal]
- Robert Connelly, Matthew Funkhouser, Vivian Kuperberg, Evan Solomonides. “Packings of equal disks in a square torus,” 2017. [arXiv][journal]
- Vivian Kuperberg. “Hadamard matrices modulo p and small modular Hadamard matrices,” 2016. [arXiv][journal]
Teaching and Notes
Here are notes from classes I’ve taken, seminar talks I’ve given, and classes I’ve taught while a counselor at Canada/USA Mathcamp.
In spring 2025, I am teaching a course called The distribution of prime numbers at ETH.
Seminar talks
Disclaimer! These lecture notes may be incomplete, riddled with typos or mathematical inaccuracies, or lacking in citations and references. Please e-mail me with any corrections!
- Odd moments in the distribution of primes, Fall 2021. [beamer]
- Primes with restricted digits, at an analytic number theory reading seminar at Stanford, Summer 2020. [pdf]
- Reduced residues and primes in short intervals, at an analytic number theory reading seminar at Stanford, Summer 2020. [pdf]
- Roth’s Theorem via almost-periodicity, at an analytic number theory reading seminar at Stanford, Summer 2020. [pdf]
- The distribution of prime numbers and sums of singular series, area exam, Spring 2020. [beamer]
- Dirichlet’s Class Number Formula, Dirichlet Style, at Stanford’s Kiddie Colloquium, Winter 2020. [pdf]
- Maass Waveforms, at an L-functions reading seminar at Stanford, Fall 2019. [pdf]
- Siegel’s Theorem, at an elliptic curves reading seminar at Stanford, Winter 2019. [pdf]
- Hochschild Homology, at an Arizona Winter School prep seminar at Stanford, Winter 2019. [pdf]
Mathcamp classes
Disclaimer! These lecture notes may be incomplete, riddled with typos or mathematical inaccuracies, lacking in citations and references, or just plain silly. Please e-mail me with any corrections!
- How To Count Primes, Mathcamp 2021. [pdf]
- Dysfunctional Analysis, Mathcamp 2019. [pdf]
- Wreath Products, Mathcamp 2018. [pdf]
- Topological Tverberg’s Theorem, Mathcamp 2018. [pdf]
- Triangulations and Flip-Graphs, Mathcamp 2018. [pdf]
- Vertex-Transitive Polytopes, Mathcamp 2017. [pdf]
Courses
Disclaimer! The lectures behind these notes are due to the professors listed; any typos or mathematical inaccuracies are due to me. Please e-mail me with any corrections!
Nonacademics
The following is an incomplete list of nonacademic things I’ve been involved with.
- This is the front and back of a shirt I designed with two of my friends for the Mathcamp community after Mathcamp 2013.
- I designed this shirt in 2015 for the Cornell math department.
- Here is a drawing I made of four mutually orthogonal latin squares, as generalized “SET” cards.
- As an undergraduate, I helped organize Math Bake-Offs at Cornell. My submission to the 2017 bake-off (which was voted Prettiest Baked Item) was a Hopf fibration cake.
- For the 2019 prospective student visit at Stanford, Hannah Larson and I made baked goods. These included cookies with an alternating group action, brownies, and a double torus cake with a figure-eight knot embedded with no crossings on its surface (progress photos here and here).
- In the summer of 2021, I made a toroidal cake with seven colored regions which are all pairwise adjacent.
- In November 2023, I made a (functional!) gingerbread abacus.
- I like puzzles and co-wrote the Mathcamp 2018, Mathcamp 2019, and Mathcamp 2022 puzzle hunts.
