Education

Background

I am a fifth-year PhD student in mathematics at Princeton University, working with Manjul Bhargava. My general research interests lie in number theory and algebraic geometry; more specifically, I am interested in arithmetic statistics, invariant theory, rational points on varieties, and enumerative geometry. I am also quite fond of learning languages and can read/speak French and Latin with moderate proficiency. In my free time, I play the violin and enjoy listening to classical music.

Education

• Princeton University, Princeton, NJ
• PhD in Mathematics, 2022 (expected)
• Thesis: "On the statistics of 2-Selmer groups of hyperelliptic curves and 2-torsion in class groups of number fields," in preparation.
• Harvard University, Cambridge, MA
• AM in Physics, 2017
• AB in Mathematics, 2017
• summa cum laude & with highest departmental honors
• Senior thesis: "Inflection points of linear systems on families of curves" (thesis) (talk)
• Advisors: Joe Harris  & Anand Patel
• The Harker School, San Jose, CA
• High school diploma, 2013

Research Publications

1. The second moment of the size of the 2-Selmer group of elliptic curves (with Manjul Bhargava and Arul Shankar), in preparation, 2021.

2. On the failure of Hecke's Theorem for non-maximal cubic orders (with Artane Siad), in preparation, 2021.

3. Geometry-of-numbers methods in the cusp (with Arul Shankar, Artane Siad, and Ila Varma), preprint available upon request, 2021.

4. Failure of monogenicity in sextic number fields, preprint available upon request, 2021.

5. Average $$2$$-torsion in class groups of rings associated to binary $$n$$-ic forms, submitted for publication, 45 pages, 2020.

6. Most integral odd-degree binary forms fail to properly represent a square, submitted for publication, 42 pages, 2020.

7. On the EKL-degree of a Weyl Cover (with Joseph Knight and Dennis Tseng), Journal of Algebra, 565(1) (2021), 64-81. (arXiv)

8. Inflectionary invariants for isolated complete intersection curve singularities (with Anand Patel), to appear in Memoirs of the American Mathematical Society, 100 pages, 2020.

9. Appendix to: An arithmetic count of the lines meeting four lines in $$\mathbb{P}^3$$ (with Borys Kadets, Padmavathi Srinivasan, Libby Taylor and Dennis Tseng), to appear in Transactions of the American Mathematical Society, 2 pages, 2020.

10. (with Aaron Landesman, James Tao, and Yujie Xu), Indiana University Mathematics Journal, 69(7) (2020), 2461-2492. (arXiv)

11. (with Aaron Landesman, James Tao, and Yujie Xu), Algebra and Number Theory, 13(5) (2019), 995-1038. (arXiv)

12. Elliptic curve variants of the least quadratic nonresidue problem and Linnik's Theorem (with Evan Chen and Peter Park), International Journal of Number Theory, 14(1) (2018), 255-288. (arXiv)

13. Lifting subgroups of symplectic groups over $$\mathbb{Z}/\ell\mathbb{Z}$$ (with Aaron Landesman, James Tao, and Yujie Xu), Research in Number Theory, 3(14) (2017), 1-12. (arXiv)

14. Permutations that destroy arithmetic progressions in elementary $$p$$-groups (with Noam D. Elkies),  Electronic Journal of Combinatorics, 24(1) (2017), 1-10. (arXiv)

15. On logarithmically Benford sequences (with Evan Chen and Peter Park), Proceedings of the American Mathematical Society, 144(11) (2016), 4599-4608. (arXiv)

16. On arboreal Galois representations of rational functions, Journal of Algebra, 448 (2016), 104-126. (arXiv)

17. Linnik’s theorem for Sato-Tate laws on elliptic curves with complex multiplication (with Evan Chen and Peter Park), Research in Number Theory, 1(1) (2015), 1-11. (arXiv)

18. Analysis on surreal numbers (with Simon Rubinstein-Salzedo), Journal of Logic and Analysis, 6(5) (2014), 1-39. (arXiv)

Expository Articles

1. Inflection points of linear systems on families of curves (Harvard senior thesis), 2017.

2. An introduction to the theory of valued fields (Harvard junior paper), 2015.

Presentations

Invited Talks

• The second moment of the size of the 2-Selmer group of elliptic curves, Workshop on Explicit Methods in Number Theory, Mathematisches Forschungsinstitut Oberwolfach, 2021.

• "Average $$2$$-torsion in the class groups of rings associated to binary $$n$$-ic forms," Bhargava Seminar, Princeton University, 2020.

• "Average $$2$$-torsion in the class groups of rings associated to binary $$n$$-ic forms," Number/Representation Theory Seminar, University of Toronto, 2020.

• "Most hyperelliptic curves are pointless," Bhargava Seminar, Princeton University, 2019.

• "Inflectionary invariants for plane curve singularities," Special Session on Research in Mathematics by Undergraduates, JMM, 2018.

• "Surjectivity of Galois representations in rational families of abelian varieties," Algebra, Geometry, and Number Theory Seminar, Tufts University, 2017.

• "Inflection points of linear systems on families of curves," Algebraic Geometry Seminar, Stanford University, 2017.

• "Analysis on surreal numbers: functions and integration," ASL Special Session, JMM, 2016.

• "Surreal analysis: an analogue of real analysis for surreal numbers," Siemens Competition Regional Finals, California Institute of Technology, 2012.

Contributed Talks

• "Counting lattice points in cusps of fundamental domains," Number Theory Tea, Princeton University, 2020.
• "Three lectures on the average size of $$2$$-Selmer groups of elliptic curves," Bhargava Seminar, Stanford University, 2020.
• "On the paucity of soluble superelliptic equations," Bhargava Seminar, Stanford University, 2020.
• "On the paucity of soluble superelliptic equations," Bhargava Seminar, Princeton University, 2019.

• "Inflectionary invariants for local complete intersection curve singularities," Graduate Student Seminar, Princeton University, 2018.

• "Inflectionary invariants for plane curve singularities," LinkedIn Bangalore, 2018.

• "Surjectivity of Galois representations in rational families of abelian varieties," JMM, 2017.

• "Permutations that destroy arithmetic progressions in elementary p-groups," JMM, 2017.

• "Elliptic curve variants of the least quadratic nonresidue problem and Linnik's Theorem," JMM, 2016.

• "Permutations that destroy arithmetic progressions," Harvard Math Table, 2016.

• "On arboreal Galois representations of rational functions," JMM 2015.

• "How small is that prime?," Harvard Math Table, 2015.

• "Arboreal Galois representations of rational functions," Harvard Math Table, 2014.

• "Surreal analysis: an analogue of real analysis for surreal numbers," Harvard Math Table, 2013.

• "Surreal analysis: an analogue of real analysis for surreal numbers," CMS Summer Meeting, 2013.

Research Experience

• PhD Thesis, Department of Mathematics, Princeton University

• 2017 - present: Working in arithmetic invariant theory (advisor: Manjul Bhargava)​​​​​

• Arizona Winter School, University of Arizona

• 2020: Worked in classical Chabauty (advisor: David Zureick-Brown)

• 2019: Worked in $$\mathbb{A}^1$$-enumerative geometry (advisor: Kirsten Wickelgren)

• Senior thesis, Department of Mathematics, Harvard University

• 2016 - 2017: Worked in algebraic geometry (advisors: Joe Harris & Anand Patel)

• Emory REU, Department of Mathematics, Emory University

• Summer 2016: Worked in arithmetic geometry (advisors: David Zureick-Brown & Ken Ono)

• Summer 2015: Worked in analytic number theory (advisors: Jesse Thorner & Ken Ono)

• Duluth REU, Department of Mathematics, University of Minnesota Duluth

• Summer 2015: Worked in combinatorial number theory (advisors: Noam D. Elkies & Joseph Gallian)

• Summer 2014: Worked in Galois representations (advisor: Joseph Gallian)

• Independent study, Department of Mathematics, Stanford University

• 2011 – 2014: Worked in logic & analysis (advisor: Simon Rubinstein–Salzedo)

• 2011 – 2013: Worked in analytic number theory (advisor: Daniel M. Kane)

Teaching Experience

• Course Instructor, Department of Mathematics, Princeton University

• [Math 202] Linear algebra with applications, 2020.

• Course Assistant, Department of Mathematics, Harvard University

• [Math 137] Introduction to algebraic geometry (Peter Kronheimer), 2017. Q-score: 5.0/5.0

• [Math 131] Topology I: Topological spaces & the fundamental group (Joe Harris), 2016. Q-score: 4.5/5.0

• [Math 123] Algebra II: Theory of rings & fields (Arul Shankar), 2016. Q-score: 4.9/5.0

• [Math 114] Analysis II: Measure, integration, & Banach spaces (Daniel Cristofaro-Gardiner), 2015. Q-score: 4.9/5.0

• [Math 55b] Honors real & complex analysis (Dennis Gaitsgory), 2015. Q-score: 4.3/5.0

• [Math 55a] Honors abstract algebra (Dennis Gaitsgory), 2014. Q:-score 4.6/5.0

Honors and Awards

• Princeton Engineering Council Teaching Award (Math 202), 2021

• Frank and Brennie Morgan Prize, 2017

• David B. Mumford Prize, 2017

• Paul and Daisy Soros Fellowship for New Americans, 2017 - 2019

• NSF Graduate Research Fellowship, 2017 - 2012

• Hertz Fellowship -- Finalist, 2017

• Centennial Fellowship, Princeton University, 2017 - 2022

• Declined PhD Fellowship Offers:

• Dean's Fellowship, Columbia University

• President's Fellowship, Massachusetts Institute of Technology

• Berkeley Fellowship, University of California, Berkeley

• Harvard University Certificate of Distinction in Teaching (Math 131, 114, 123)

• John Harvard Scholar for Academic Achievement (2016, 2015, 2014)

• Robert Fletcher Rogers Prize, 2016

• Phi Beta Kappa -- Junior 24, 2016

• Barry M. Goldwater Scholarship (Fellow - 2016, Honorable Mention - 2015)

• Detur Book Prize for Academic Excellence, 2014

• Siemens Competition in Math, Science, and Technology -- Regional Finalist, 2013

• Siemens AP Science Award -- National Winner, 2013

• National Merit Scholar, 2013

• Class Valedictorian -- The Harker School, 2013

Journal Refereeing

• Research in Number Theory

• Research in the Mathematical Sciences

• Proceedings of the American Mathematical Society

• Mathematical Proceedings of the Cambridge Philosophical Society

• Involve, a Journal of Mathematics

Classical Music

Last updated: July 22, 2021