Katharine (Katy) Woo

Email: khwoo (at) princeton (dot) edu

Office: Fine Hall 504

About

I am a fifth year graduate student in mathematics at Princeton University, advised by Peter Sarnak. Previously, I completed 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 GRFP under Grant No. DGE-2039656.

Research

• 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. arXiv:2312.11445
• (with Mayank Pandey) Small scale distribution of linear patterns in primes. Journal of the London Mathematical Society (2024). Link

Upcoming Talks

• (February 2025) JHUnior Number Theory Days. TBD.
• (March 2025) ISTA Algebraic Geometry and Number Theory Seminar. TBD.
• (March 2025) RTG2491 Spring School on Decoupling and More. "On Manin's conjecture for Châtelet surfaces."
• (April 2025) AMS Spring Eastern Sectional Meeting Special Session on Counting and Asymptotics in Number Theory. TBD.
• (April 2025) University of Arizona Algebra and Number Theory Seminar. TBD.
• (September 2025) Geometric and Analytic Number Theory Conference. TBD.

Recent Talks

• (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."
• (April 2024) UVA Number Theory Seminar. "Some results towards Manin's conjecture".
• (February 2024) Yale Group actions, Dynamics and Geometry Seminar. "Prime number theorems for polynomials from homogeneous dynamics."
• (February 2024) KSU Number Theory Seminar. "Prime number theorems for polynomials from homogeneous dynamics."
• (January 2024) Stanford Analytic Number Theory Seminar. "Prime number theorems for polynomials from homogeneous dynamics."
• (January 2024) JMM 2024 AIM Special Session. "Prime number theorems for polynomials from homogeneous dynamics." Slides
• (September 2023) Duke Number Theory Seminar. "Towards Manin's conjecture for certain del Pezzo surfaces of degree one."
• (September 2023) IAS/Princeton Number Theory Seminar. "Prime number theorems for polynomials from homogeneous dynamics."
• (May 2023) IAS Women and Math Program Princeton Day. "Prime number theorems beyond the circle method."
• (May 2023) IAS Women and Math Program Evening Research Talks. "Small scale distribution of primes in four-term arithmetic progressions."
• (April 2023) Stanford Analytic Number Theory Seminar. "Small scale distribution of primes in four-term arithmetic progressions."
• (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).
• (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 two extremely fluffy cats: Nine and Ten
• (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