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.
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.
