Katharine (Katy) Woo

Email: k.woo (at) eth-its (dot) ethz (dot) ch

Office: Institute for Theoretical Studies, Scheuchzerstrasse 70, 8006 Zurich

About

I am a ETH ITS Junior Fellow and a NSF postdoctoral fellow at ETH Zürich mentored by Emmanuel Kowalski. Previously, I was a NSF postdoctoral fellow at Stanford University mentored by Kannan Soundararajan. I completed my doctorate at Princeton University, advised by Peter Sarnak, and my bachelor's degree at Stanford University, advised by Kannan Soundararajan. My research is in analytic number theory, especially in prime values of polynomials and point-counting on varieties. I am also interested in arithmetic statistics and cryptography. I am currently funded by the NSF MSPRF 2502864.

Research

• (with Dante Bonolis and Lillian B. Pierce) Genuine and strongly genuine polynomials: With an application to the persistence of Galois groups under specialization. arXiv:2607.01969
• (with Dante Bonolis and Lillian B. Pierce) Counting points in thin sets: A survey. arXiv:2603.23334
• (with Noah Kravitz and Max Xu) The distribution of prime values of random polynomials. arXiv:2512.03292
• Sums of Hecke eigenvalues along polynomial sequences and base change for GL(2). arXiv:2604.18923
• Counting points on a family of degree one del Pezzo surfaces. arXiv:2508.09391
• (with Dante Bonolis and Emmanuel Kowalski) Stratification theorems for exponential sums in families. arXiv:2506.18299
• (with Dante Bonolis and Lillian B. Pierce) Counting integral points in thin sets of type II: singularities, sieves, and stratification. arXiv:2505.11226
• On Manin's conjecture for Châtelet surfaces. arXiv:2409.17381
• (with Neer Bhardwaj, Raymond McCulloch, Nandagopal Ramachandran) Integer-valued o-minimal functions. Quarterly Journal of Mathematics (2025). Link
• (with Giorgos Kotsovolis) Prime number theorems for polynomials from homogeneous dynamics. GAFA (2025). Link
• (with Mayank Pandey) Small scale distribution of linear patterns in primes. Journal of the London Mathematical Society (2024). Link

Upcoming Talks

• (November 2026) ISTA Number Theory Seminar. "Additive combinatorics and arithmetic applications".
• (November 2026) Rényi Institute Number Theory Seminar. TBD.

Recent Talks

• (September 2026) Princeton/IAS Number Theory Seminar. "Additive combinatorics and arithmetic applications."
• (September 2026) DMV 2026 Number Theory Section. "Sums of Hecke eigenvalues along polynomials and base change."
• (September 2026) Fouvry 73 Workshop. "Counting integral points in thin sets of type II, Part I".
• (May 2026) MFO Group Actions and Harmonic Analysis in Number Theory. "Sums of Hecke eigenvalues along polynomials and base change."
• (April 2026) Berkeley RTG Seminar. "Applying stratification theorems to counting integral points in thin sets of type II."
• (April 2026) Harvard Number Theory Seminar. "Applying stratification theorems to counting integral points in thin sets of type II."
• (April 2026) UIUC Number Theory Seminar. "The distribution of prime values of random polynomials".
• (March 2026) CRM Arithmetic Statistics Workshop. "Applying stratification theorems to counting integral points in thin sets of type II."
• (February 2026) OSU Algebra and Number Theory Seminar. "The distribution of prime values of random polynomials".
• (February 2026) UCI Number Theory Seminar. "The distribution of prime values of random polynomials."
• (January 2026) University of Washington Number Theory Seminar. "Counting points on a family of del Pezzo surfaces of degree one." Slides
• (January 2026) International Seminar on Automorphic Forms. "Summing Hecke eigenvalues along polynomials and arithmetic applications."
• (December 2025) UC Davis Algebraic Geometry and Number Theory Seminar. "Rational points on degree one del Pezzo surfaces (and base change for GL(2))."
• (November 2025) MFO Arithmetic Statistics for Algebraic Objects. "Applying stratification theorems to counting integral points in thin sets of type II."
• (November 2025) MFO Analytic Number Theory. "Manin's conjecture for Châtelet surfaces."

Talk Notes/Slides

• "Counting points on a family of del Pezzo surfaces of degree one." Slides
• "Counting integral points in thin sets of type II: singularities, sieves, and stratification." Slides
• "On Manin's conjecture for Châtelet surfaces." Slides
• "Prime number theorems for polynomials from homogeneous dynamics." Slides
• "Small scale distribution of primes in four-term arithmetic progressions." Notes

Teaching and Miscellaneous

• (Teaching at Princeton) In Summer 2022, Summer 2023, and Spring 2024, I was the teaching assistant for Mat 202 (Linear Algebra). In Fall 2023, I was a teaching assistant for Mat 103 (Calculus I). In Fall 2024, I received the Department Graduate Teaching Award.
• (Miscellaneous at Princeton) In 2021-2022, I organized a preparatory learning seminar for the 2022-2023 IAS Special Year with Noah Kravitz and Giorgos Kotsovolis. I was a member of the math department's graduate student committee and an organizer of the Noetherian Ring, Princeton's group for women and gender minorities in math.
• (Teaching at Stanford) In Summer 2025, I advised a group research project on the circle method through SURIM . In Spring 2019 and Spring 2020, I was the teaching assistant for CS 355 (Advanced Topics in Cryptography).
• (Miscellaneous at Stanford) In 2018-2019, I was the President of the SUMO (Stanford's student math organization). In 2019-2020, I helped inaugurate the Stanford math department's peer advising program.
• (General Miscellaneous) I have an extremely fluffy cat: Nine
• (Undergraduate Research)
  • (with Dan Boneh and Dima Kogan) Oblivious pseudorandom functions from isogenies. Advances in Cryptography -- ASIACRYPT 2020, 2020. Link
  • (with Katherine Gallagher, Lucia Li, Naomi Sweeting, and Katja Vassilev) Generating functions for power moments of elliptic curves over F_p. Journal of Number Theory, 2020. Link
  • (with Naomi Sweeting) Formulas for the Chebotarev densities of Galois extensions of number fields. Research in Number Theory, 2020. Link
  • (with Naomi Sweeting) On the zeros of a class of modular functions. Annals of Combinatorics, 2019. Link