Mentorship

Ph.D. students
3. Debmalya Basak
2. Nawapan (Ploy) Wattanawanichkul
1. Tanmay Khale

Undergraduate research

I have helped run NSF-funded Research Experiences for Undergraduates (REUs) every summer since Summer 2014. I mentor teams of students (usually 2-4) and guide them in a research project that I develop on my own. Occasionally, I have mentored some high school students through these programs; they are denoted with an asterisk *.

2023 (University of Virginia NSF REU)

A. Anas Chentouf, Catherine Cossaboom, Samuel Goldberg, Jack B. Miller. Patterns of primes in joint Sato-Tate distributions.
- Catherine Cossaboom: Goldwater Scholar

2022 (University of Virginia NSF REU)

- Daniel Hu, Hari Iyer and Sasha Shashkov, Modular forms and an explicit Chebotarev variant of the Brun-Titchmarsh theorem, Res. Number Theory 9 (2023), no. 3, Paper No. 46.
- Quanlin Chen and Eric Shen, On Effective Sato-Tate Distributions for Surfaces Arising from Products of Elliptic Curves
- Henry Glunz, Significant digits of primes in subsets. Integers, 23 (2023), Article 46.
  - Daniel Hu: Goldwater Scholar
  - Hari Iyer: Goldwater Scholar
  - Sasha Shashkov: Goldwater Scholar

2021 (University of Virginia NSF REU)

- Alexandra Hoey, Jonas Iskander, Steven Jin, and Fernando Trejos Suarez, An unconditional explicit bound on the error term in the Sato-Tate conjecture, Quarterly Journal of Mathematics (Oxford), 73 (2022), no. 4, 1189–1225.
- Ikuya Kaneko* and Jesse Thorner, Highly uniform prime number theorems, submitted for publication.
  - Alexandra Hoey: 2022 Alice T. Schafer Prize Honorable Mention
  - Steven Jin: NSF Graduate Fellowship, Churchill Scholar

2020 (University of Virginia NSF REU)

- Tanmay Khale, Cooper O'Kuhn, Apoorva Panidapu*, Alex Sun, and Shengtong Zhang, A Bombieri-Vinogradov Theorem for primes in short intervals and small sectors, Journal of Number Theory (229), 2021, 142-167.
- Apoorva Panidapu* and Jesse Thorner, Short-interval sector problems for CM elliptic curves, Involve 16 (2023), no. 1, 1–12.
  - Alex Sun: NSF Graduate Fellowship
  - Apoorva Panidapu*: First Prize, Davidson Fellowship ($50,000); Winner, 2021 Steven Strogatz Prize for Mathematics Communication; Winner, 2021 Diana Award

2019 (Emory University NSF REU)

- Nate Gillman, Michael Kural, Alexandru Pascadi, Junyao Peng, and Ashwin Sah, Patterns of primes in the Sato-Tate conjecture, Research in Number Theory, 6 (2020), Art. 9.
- Caleb Ji, Joshua Kazdan, and Vaughan McDonald, Primes with Beatty and Chebotarev conditions, Journal of Number Theory, 216 (2020), 307-334.
- Michael Kural, Vaughan McDonald, and Ashwin Sah, Mobius formulas for densities of sets of prime ideals, Archiv der Mathematik, 115 (2020), 53-66.
  - Ashwin Sah: Goldwater Scholar; 2021 Morgan Prize Winner
  - Nate Gillman: Goldwater Scholar

2018 (Williams College, SMALL Program)

- Trajan Hammonds, Casimir Kothari, Noah Luntzlara, Steven J. Miller, Jesse Thorner, and Hunter Wieman, The explicit Sato-Tate conjecture for primes in arithmetic progressions, International Journal of Number Theory 17 (2021) No. 8, 1905-1923
  - Casimir Kothari: NSF Graduate Fellowship

2017 (Emory University NSF REU)

- Ryan Alweiss and Sammy Luo, Bounded gaps between primes in short intervals, Research in Number Theory, 4 (2018), Art. 15.
  - Ryan Alweiss: NSF Graduate Fellowship
  - Sammy Luo: NSF Graduate Fellowship

2016 (Emory University NSF REU)

- Yang Liu, Peter S. Park, and Zhuo Qun Song, Bounded Gaps Between Products of Distinct Primes, Research in Number Theory, 3, (2017) 26.
- Yang Liu, Peter S. Park, and Zhuo Qun Song, The "Riemann Hypothesis" is True for Period Polynomials of Almost All Newforms, Research in the Mathematical Sciences, 3 (2016), 31.
  - Yang Liu: NDSEG Fellowship
  - Peter Park: Goldwater Scholar, NSF Graduate Fellowship

2015 (Emory University NSF REU)

- Evan Chen, Peter S. Park, and Ashvin Swaminathan, Linnik's Theorem for Sato-Tate laws on elliptic curves with complex multiplication, Research in Number Theory 1 (2015), 28.
- Evan Chen, Peter S. Park, and Ashvin Swaminathan, On logarithmically Benford sequences, Proceedings of the American Mathematical Society 144 (2016), 4599-4608.
- Evan Chen, Peter S. Park, and Ashvin Swaminathan, Elliptic curve variants of the least quadratic nonresidue problem and Linnik's Theorem, Int. J. Number Th. 14 (2018), 255-288.
  - Evan Chen: 2019 Morgan Prize Honorable Mention, NSF Graduate Fellowship
  - Peter Park: Goldwater Scholar, NSF Graduate Fellowship
  - Ashvin Swaminathan: 2018 Morgan Prize Winner, Goldwater Scholar, NSF Graduate Fellowship

2014 (Emory University NSF REU)

- Lynn Chua, Soohyun Park, and Geoffrey Smith, Bounded gaps between primes in special sequences, Proceedings of the American Mathematical Society 143 (2015), 4597-4611.
  - Geoffrey Smith: Goldwater Scholar