Katharine (Katy) Woo

Email: katywoo (at) stanford (dot) edu

Office: Building 380, 384 B

About

I am 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.

Starting in 2026, I will be a ETH ITS Junior Fellow at ETH Zürich mentored by Emmanuel Kowalski.

Research

• (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. arXiv:2404.10737
• (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

• (July 2025) Rational Points 2025. "On Manin's conjecture for Châtelet surfaces."
• (August 2025) AMS Fall Western Sectional Meeting Special Session on Analytic Number Theory and Related Topics. "Prime values of polynomials: dot-product structure."
• (September 2025) Geometric and Analytic Number Theory Conference. "Counting integral points in thin sets of type II: singularities, sieves, and stratification."
• (September 2025) IMJ-PRG Theory of Numbers Seminar. TBD.

Recent Talks

• (April 2025) University of Arizona Algebra and Number Theory Seminar. "On Manin's conjecture for Châtelet surfaces."
• (April 2025) AMS Spring Eastern Sectional Meeting Special Session on Counting and Asymptotics in Number Theory. "Prime values of polynomials: dot-product structure."
• (April 2025) Joint Athens-Atlanta Number Theory Seminar. "On Manin's conjecture for Châtelet surfaces."
• (March 2025) RTG2491 Spring School on Decoupling and More. "On Manin's conjecture for Châtelet surfaces."
• (March 2025) ISTA Algebraic Geometry and Number Theory Seminar. "On Manin's conjecture for Châtelet surfaces."
• (March 2025) ISTA Browning Group Seminar. "Towards Serre's conjecture: singularities, sieves, and stratification."
• (March 2025) Université Paris-Saclay Séminaire Arithmétique et Géométrie Algébrique. "On Manin's conjecture for Châtelet surfaces."
• (March 2025) Oxford Number Theory Seminar. "On Manin's conjecture for Châtelet surfaces."
• (February 2025) Philadelphia Area Number Theory Seminar. "On Manin's conjecture for Châtelet surfaces."
• (February 2025) JHUnior Number Theory Days. "On Manin's conjecture for Châtelet surfaces."
• (February 2025) Princeton/IAS Number Theory Seminar. "On Manin's conjecture for Châtelet surfaces."
• (December 2024) Number Theory Web Seminar. "On Manin's conjecture for Châtelet surfaces." Slides
• (December 2024) Stanford Number Theory Seminar. "On Manin's conjecture for Châtelet surfaces."
• (November 2024) Joint Columbia-CUNY-NYU Number Theory Seminar. "On Manin's conjecture for Châtelet surfaces."
• (October 2024) AGAG Seminar. "On Manin's conjecture for Châtelet surfaces."
• (September 2024) Recent Trends in Homogeneous and Teichmüller Dynamics. "Prime number theorems for polynomials from homogeneous dynamics."
• (September 2024) PANTS XXXVIII. "On Manin's conjecture for Châtelet surfaces."

Talk Notes/Slides

• (December 2024) Number Theory Web Seminar. "On Manin's conjecture for Châtelet surfaces." Slides
• (January 2024) JMM 2024 AIM Special Session. "Prime number theorems for polynomials from homogeneous dynamics." Slides
• (February 2023) AIM FRG Grad Seminar. "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 am a current 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 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)
  • (my undergrad thesis) An exponential sum involving the divisor function for F_q[T]. pdf
  • (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